Whole-process collaborative toughness improvement method for urban medical system

Abstract

The invention discloses a whole-process collaborative toughness improvement method for an urban medical system, and relates to the field of urban toughness construction decision. The method aims to solve the problem that the toughness improvement effect is limited due to the fact that a single-stage optimization strategy cannot comprehensively reflect the complexity of the whole earthquake process. The method comprises the following steps: associating target city traffic with basic information of a medical system, and constructing a test city medical system model; utilizing a Monte Carlo simulation method to simulate post-earthquake uncertainty scenes under different reinforcement strategies in the urban medical system model; clustering the post-earthquake uncertainty scenes by using a Kmeans + + algorithm, and extracting a clustering center as a representative damage scene; and taking the reinforcement and recovery strategies in different representative damage scenes as individuals in the population, searching an optimal individual by using a genetic algorithm, and improving the toughness of the medical system of the target city by using the reinforcement and recovery strategy corresponding to the optimal individual.

Description

Technical Field

[0001] The present invention belongs to the field of urban resilience construction decision-making. Background Art

[0002] Interdependent infrastructure systems play an indispensable role in modern cities, especially the linkage between transportation and medical systems, which is even more critical during extreme events such as earthquakes. As the global urbanization process accelerates, the complexity of infrastructure continues to increase, and the dependencies between these systems make them extremely vulnerable to disasters such as earthquakes. In previous earthquakes, hospital function interruptions, limited medical services, and paralyzed transportation networks have frequently occurred, directly hindering the effective implementation of post-disaster rescue and recovery work. Especially for urban medical systems, the problem of functions failing to meet social needs in terms of emergency rescue and continuous medical services after disasters has become increasingly prominent. These phenomena indicate that it is urgent to improve the seismic resilience of the current urban medical system, and a comprehensive improvement strategy must be adopted to ensure the rapid recovery and continued operation of the medical system after the earthquake.

[0003] Existing research mainly focuses on improving the seismic resilience of transportation systems. The core methods include strengthening and renovating key infrastructure (such as bridges, roads, etc.) to enhance the system's seismic resistance and ability to recover quickly after an earthquake. However, most of these studies are limited to the post-earthquake recovery stage, and usually improve the seismic performance of infrastructure by optimizing and reinforcing key components of the system under a limited budget. Some scholars use system-level importance analysis methods to consider the reinforcement priority of components in the transportation system from multiple aspects such as technology, society, and economy. In addition, scholars have also developed stochastic optimization models to maximize the connectivity of post-earthquake transportation networks, thereby effectively selecting reinforcement strategies under a limited budget; other studies analyze the relationship between the budget and benefits of reinforcement through optimization methods such as multi-objective genetic algorithms. Although these methods improve the seismic resistance of the system, there are still problems of huge computational complexity and long time consumption in solving high-dimensional complex optimization problems. In order to meet these challenges, some scholars have proposed a finite sample analysis method to determine the reinforcement priority of key components of the system through the correlation between component damage in sample data and the post-earthquake function of the system. This method between traditional importance ranking and stochastic optimization has improved computational efficiency to a certain extent. In addition, some studies have proposed transportation system optimization methods based on intelligent technology, such as using multimodal transportation networks to share post-disaster pressure and developing intelligent transportation systems to achieve real-time monitoring and emergency management of transportation networks, thereby enhancing system resilience. By combining intelligent information technology with transportation management, it will help to further improve the earthquake resilience of the transportation system to ensure the efficient implementation of post-earthquake rescue work.

[0004] In terms of the medical system, whether a hospital can quickly restore its functions and provide emergency medical services after a disaster is directly related to the success or failure of post-disaster rescue. Therefore, it is particularly important to improve the disaster resistance of hospitals. Scholars have significantly enhanced the disaster resistance of hospital buildings by adopting technical means such as seismic isolation and shock absorption, ensuring that hospitals can continue to operate during disasters. In addition, the development of seismic isolation systems based on optimization design methods is also constantly improving, including the use of meta-heuristic algorithms such as genetic algorithms and whale optimization algorithms to quickly find the optimal solution. The development of intelligent solution algorithms has brought new possibilities for disaster resilience optimization design in this field.

[0005] Although existing research has made some progress in improving the disaster resistance of transportation and medical systems, there is a general problem of phased separation. Most methods focus on either pre-earthquake prevention and reinforcement or post-earthquake recovery and management, lacking systematic and coordinated consideration of the entire earthquake process. However, urban transportation and medical systems are essentially interdependent and highly coupled, and this complex dependency closely affects the functional performance of the system at all stages before and after an earthquake. Therefore, a single-stage optimization strategy cannot fully reflect the complexity of the entire earthquake process, resulting in limited resilience improvement effects. Summary of the invention

[0006] The present invention aims to solve the problem that a single-stage optimization strategy cannot fully reflect the complexity of the entire earthquake process, resulting in limited resilience improvement effects. A method for improving the collaborative resilience of an urban medical system throughout the entire process is now provided.

[0007] A method for improving the collaborative resilience of the entire urban medical system, including:

[0008] The basic information of the target city's transportation and medical systems is linked to build an urban medical system model that takes into account the relationship between transportation and medical care, as well as the relationship between hospital structures, non-structures and medical equipment;

[0009] Using the Monte Carlo simulation method, post-earthquake uncertainty scenarios under different reinforcement strategies are simulated in the urban medical system model, wherein the post-earthquake uncertainty scenarios include: the damage state of the bridge after the earthquake, the available number of medical departments in the hospital, and the restoration time of the bridge and the hospital;

[0010] The Kmeans++ algorithm is used to cluster the post-earthquake uncertainty scenarios, and the cluster centers are extracted as representative damage scenarios;

[0011] The reinforcement and restoration strategies under different representative destruction scenarios are regarded as individuals in the population, and the optimal individual is found by using a genetic algorithm. The reinforcement and restoration strategies corresponding to the optimal individual are then used to improve the resilience of the target city's medical system.

[0012] Furthermore, the above-mentioned basic information of the target city's transportation and medical systems is associated to construct an urban medical system model that takes into account transportation and medical care as well as hospital structures, non-structures and medical equipment, including:

[0013] Obtain road information based on GIS data and remote sensing image information within the target city, abstract the traffic facilities and their connection relationships in the road information into a topological structure, and establish a post-earthquake traffic network topology model;

[0014] Based on the population distribution information of residents, the demand for medical services in post-disaster situations is assessed and a medical demand model is constructed;

[0015] Based on the structural type, construction year, location of each department and medical equipment configuration of individual hospitals within the target city, the vulnerability data of non-structural and medical equipment-related disasters in the hospital were integrated to establish a quantitative model of the post-earthquake function of individual hospitals;

[0016] The post-earthquake traffic network topology model, medical demand model and single hospital post-earthquake function quantification model together constitute the urban medical system model.

[0017] Furthermore, the objective function expression of the above genetic algorithm is:

[0018]

[0019] Among them, z represents the reinforcement status, including whether the bridge b was reinforced before the earthquake, whether the hospital h was reinforced at the structural level before the earthquake, and whether the hospital h was reinforced at the non-structural level before the earthquake;

[0020] x represents the repairing status, including whether the bridge b is being repaired in time period t in scenario ξ and whether the hospital h is being repaired in time period t in scenario ξ;

[0021] A represents the completion status, including whether the bridge b is repaired within time period t in scenario ξ and whether the hospital h is repaired within time period t in scenario ξ;

[0022] Θ is the set of post-earthquake uncertainty scenarios under different reinforcement strategies simulated by Monte Carlo, and Ω is the set of representative damage scenarios;

[0023] E represents the desired optimization goal under multiple uncertain scenarios, and F ξ is the weighted optimization objective under scenario ξ.

[0024] Furthermore, the above weighted optimization objective F under scenario ξ ξ The expression is:

[0025]

[0026] Among them, f1 ξ is the optimization objective based on recovery time in scenario ξ, f2 ξ is the optimization objective based on functional improvement in scenario ξ, ω1 and ω2 are f1 ξ and f2 ξ The weight coefficient of

[0027]

[0028] WRT pre To strengthen the weighted recovery time of the urban medical system after the earthquake, WRT ξ is the weighted recovery time of the urban medical system after the earthquake after reinforcement under scenario ξ, Q 0,pre In order to strengthen the functional surplus of the urban medical system at time t0 after the fore-earthquake, Q0 ξ is the functional surplus of the urban medical system after reinforcement at time t0 after the earthquake under scenario ξ.

[0029] Furthermore, the desired optimization target E in the above scenario ξ is obtained through the medical accessibility calculated by the proxy model,

[0030] The input of the agent model is the post-earthquake damage status of bridges in the target area and the available number of medical departments in the hospital under the post-earthquake damage scenario, and the output is the post-earthquake medical accessibility.

[0031] Furthermore, the post-earthquake damage status of bridges in the target area and the available number of medical departments in the hospital in the above post-earthquake damage scenario are obtained as follows:

[0032] The post-earthquake damage scenarios were simulated in the urban medical system model using the Monte Carlo simulation method, and the functional reduction of bridges, the available number of hospital departments, and the repair time of bridges and hospitals were evaluated under each post-earthquake damage scenario.

[0033] Furthermore, the constraints of the above objective function include: pre-earthquake reinforcement strategy constraints, cost constraints and repair resource constraints.

[0034] Furthermore, the above-mentioned pre-earthquake reinforcement strategy constraints include:

[0035]

[0036] in, represents the reinforcement strategy selection variable of hospital h before the earthquake, h∈H, H is the set of individual hospitals in the urban medical system, is a binary variable indicating whether the hospital h structure was reinforced before the earthquake and has is a binary variable indicating whether the non-structural structure of hospital h was reinforced before the earthquake and has

[0037] Furthermore, the above cost constraints include:

[0038]

[0039] Among them, c b Cost of reinforcing bridge b, z b is a binary variable indicating whether bridge b was reinforced before the earthquake and has z b ∈{0,1},Cost B Investment in strengthening the transportation system, The cost of reinforcing the hospital structure. Cost of non-structural reinforcement of the hospital H is the cost investment for strengthening the medical system, b∈B, and B is the set of bridges in the urban medical system.

[0040] Furthermore, the above resource constraints include:

[0041]

[0042] Among them, x b,t indicates whether bridge b is under repair in time period t, x h,t Indicates whether hospital h is under repair in time period t, n ET,b and n ET,h are the number of repair engineering teams for bridges and hospitals after the earthquake, t∈T, and T is the set of long-term repair periods after the earthquake.

[0043] The beneficial effects of the present invention are:

[0044] 1. Considering the correlation between the functions and recovery of the transportation and medical systems, the key impact of pre-earthquake reinforcement decisions on post-earthquake recovery was quantified, and a stochastic optimization model for improving resilience throughout the entire process was established. Under resource constraints, the model achieved comprehensive reinforcement and repair decisions for related systems, minimizing post-earthquake functional losses and shortening recovery time.

[0045] 2. The present invention combines the functional fast calculation agent model with the random destruction scenario reduction method to design an efficient and intelligent solution algorithm, which significantly reduces the decision-making calculation cost and improves the efficiency of solving random optimization problems.

[0046] 3. The present invention optimizes the reinforcement and recovery decisions of the associated system, which not only improves the practical application value of the model, but also facilitates the promotion of resilience improvement strategies. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flowchart of a method for improving the overall collaborative resilience of the urban medical system;

[0048] Figure 2It is the topological relationship diagram of the urban medical system;

[0049] Figure 3 To map the medical needs of the urban medical system;

[0050] Figure 4 This is the PGA distribution map in the region when the earthquake scenario M = 7.8;

[0051] Figure 5 is the bridge vulnerability curve;

[0052] Figure 6 Bayesian network diagram for key medical departments;

[0053] Figure 7 This is a diagram of the training process of the proxy model;

[0054] Figure 8 is the loss curve of the proxy model;

[0055] Fig. 9 Schematic diagram of the difference and correlation test results between the predicted values ​​and actual values ​​based on the surrogate model. DETAILED DESCRIPTION

[0056] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0057] Based on the problems of existing technologies, it is necessary to integrate complex disaster scenarios, coordinate defense and recovery strategies at different stages, maximize the disaster resilience of urban medical systems, and propose efficient and intelligent decision-making algorithms to improve the efficiency of optimization solutions. This provides new ideas for the construction of future resilient cities and strong technical support for relevant decision makers in formulating urban disaster resilience plans.

[0058] Reference Figures 1 to 9 Specifically describing this implementation mode, a method for improving the collaborative resilience of an urban medical system throughout the entire process described in this implementation mode includes:

[0059] Step 1: Summarize the relevant basic information data of the target city's medical system, and conduct correlation modeling on the transportation and medical systems to obtain an urban medical system model that takes into account transportation and medical care as well as the structure, non-structure and medical equipment within the hospital.

[0060] Specifically include:

[0061] Step 1.1, establish a transportation network topology model: collect available GIS (geographic information) data and remote sensing image information in the target area to obtain road information, and clean, organize and process it to ensure availability. Abstract transportation facilities and connection relationships into a topological structure, assign node and edge attributes such as coordinates, length, capacity and speed limit, and establish a post-earthquake transportation network topology model.

[0062] Step 1.2: Build a medical demand model: Collect information on the distribution of resident population to determine regional differences in medical demand. Evaluate the demand for medical services in post-disaster situations and ensure the rational allocation of medical resources.

[0063] Step 1.3, single hospital information collection: collect key information such as the structural type, construction year, location of each department, and medical equipment configuration of each department of the single hospital in the target area. Integrate the vulnerability data of non-structural and medical equipment-related disasters in the hospital to establish a quantitative model of the post-earthquake function of the single hospital.

[0064] The topological network of the urban medical system model and the urban medical needs are as follows: Figure 2 and Figure 3 Based on historical earthquakes and considering the attenuation of earthquake motion, the size of the PGA (memory area containing data and control information of a service process) of the field points within the target area is determined, as shown in Figure 4 shown.

[0065] Step 2: Considering the uncertainty of the damage state, functional reduction and recovery time of components in the urban medical system after the earthquake, the Monte Carlo simulation method is used to generate potential post-earthquake damage scenarios in the urban medical system model constructed in step 1. Figure 5 The bridge seismic vulnerability model shown in Figure 1 simulates the damage state of the bridge after the earthquake. Figure 6 The Bayesian network shown determines the availability probability of each key medical department in the hospital. Then, in each damage scenario, the functional reduction of the bridge, the available number of hospital departments, and the repair time of the bridge and hospital are evaluated, and then the travel time of the traffic system and the treatment capacity of a single hospital under each post-earthquake damage scenario are estimated. Specifically, it includes:

[0066] Step 2.1. First, based on the acquired road information, the road connection relationship is topologically constructed and the relevant attributes are assigned to model the traffic system. Subsequently, the travel OD matrix in the recovery period is predicted based on daily traffic data and the characteristics of post-earthquake travel demand. Then, the damage to key components (such as roads, bridges, and tunnels) after the earthquake and the impact of building debris along the street on traffic capacity are analyzed to evaluate the system's capacity reduction. Combined with the traffic allocation method, the traffic flow distribution of each section is calculated by considering demand changes and capacity losses. The shortest path search algorithm is used to predict the travel time from different demand points to medical supply points, and finally a comprehensive analysis of the functional level of the transportation system is conducted.

[0067] Step 2.2, establish a single hospital function analysis method. First, based on the basic data collected about the hospital, a single hospital model is built. Secondly, the seismic response analysis of the hospital structure is carried out to evaluate the damage state of the building structure and estimate the repair time. At the same time, the vulnerability data of non-structures and medical equipment in the hospital are integrated to analyze their impact on the hospital function. Then, combining the association between structure, non-structure and medical equipment, the availability of the department is evaluated, and the recovery time of non-structural components is estimated. Based on the number of medical resources and the needs of different types of casualties, the hospital's rescue capacity is analyzed, and finally the comprehensive rescue capacity of the hospital after the earthquake is evaluated by quantifying the urgency of different types of casualties.

[0068] Step 3: Construct an agent model based on artificial neural network to quickly calculate the functions of urban medical system.

[0069] Combined with the traffic system travel time under the post-earthquake damage scenario generated in step 2 and the treatment capacity of each single hospital, an artificial neural network proxy model of the city's medical system function is constructed. The input data of the artificial neural network proxy model is the post-earthquake damage status of bridges in the target area under the post-earthquake damage scenario generated in step 2 and the available number of medical departments in the hospital, and the output data is the normalized post-earthquake medical accessibility. By training the above input and output data, a high-precision urban medical system function prediction model is obtained. The training process of the artificial neural network proxy model is referenced Figure 7 As shown, the difference between the model prediction value and the actual value and the correlation test results refer to Figure 8 The step three is specifically as follows:

[0070] Step 3.1, Generate training data for the neural network. Based on the uncertain destruction scenario generated in step 2, calculate the travel time of the post-earthquake transportation system and the rescue capacity of each single hospital, so as to determine the functional level of the post-earthquake urban medical system and generate a training data set.

[0071] Step 3.2: Data normalization. The input data of the neural network model are the damage status of bridges after the earthquake and the number of available departments in the hospital, and the output data is the normalized accessibility of medical treatment after the earthquake. Through training, a high-precision proxy model for calculating the function of the urban medical system is obtained.

[0072] Step 3.3, the internal parameters of the neural network are set as shown in Table 1. In order to avoid underfitting and overfitting problems during training, 10,000 sets of random samples are used to train the proxy model. The data set is divided into training set, validation set and test set in a ratio of 0.7:0.15:0.15 to ensure the generalization ability of the model.

[0073] Table 1 Neural network internal parameter settings

[0074]

[0075] Step 3.4, neural network training process. First, build a neural network model, determine the number of network layers, the number of neurons in each layer, and the activation function, and randomly initialize the weight parameters. Then, perform forward propagation, pass the input data to the output layer layer by layer and generate predicted output. Next, calculate the loss function value and measure the model error by comparing the predicted result with the true value. Then, through back propagation, the loss value is propagated layer by layer to calculate the gradient of the parameters of each layer. According to the optimization algorithm (such as the gradient descent method), the parameters of the model are gradually updated until the predetermined convergence conditions are reached or other stopping criteria are met. Finally, use the validation set to evaluate the model performance and adjust the hyperparameters if necessary to further optimize the predictive ability of the model.

[0076] Step 3.5: Establish a high-precision functional proxy model based on a neural network. The training process of the proxy model is as follows: Figure 8 shown. Fig. 9 The difference and correlation test results between the predicted values ​​and actual values ​​based on the proxy model are shown. Through this step, the neural network proxy model finally generated can predict the functional performance of the urban medical system with high accuracy.

[0077] Step 4: Considering various uncertainties and complexities after the earthquake, we analyzed the correlation between transportation and medical care in the urban medical system and established a comprehensive and coordinated decision-making model for pre-disaster reinforcement and post-disaster restoration. Specifically, it includes:

[0078] Step 4.1, Phase I Optimize the pre-earthquake reinforcement plan. Under limited economic conditions, the pre-earthquake reinforcement decision is usually modeled as a 0 / 1 knapsack problem. The pre-earthquake reinforcement model aims to select whether to reinforce components within the system under limited resources to minimize the functional loss of the system and quantify the impact of the reinforcement decision on potential post-earthquake damage scenarios.

[0079] Step 4.2: Make decisions based on the impact of reinforcement options on post-earthquake damage scenarios. Phase II determines the optimal parallel repair order of the urban medical system under potential damage scenarios based on the reinforcement plan. The restoration order decision is usually modeled as a TSP problem (traveling salesman problem), which considers the limitation of repair resources and plans the repair order of components in the system to shorten the post-earthquake weighted recovery time and improve system resilience. The sets, parameters and decision variables in the mathematical model of specific resilience improvement are shown in Tables 2 to 4:

[0080] Table 2 Definition of sets in the stochastic optimization model for resilience improvement

[0081]

[0082] Table 3 Parameter definitions in the stochastic optimization model for toughness improvement

[0083]

[0084]

[0085]

[0086] Table 4 Decision variables in the stochastic optimization model for improving resilience

[0087]

[0088]

[0089] The specific objectives and constraints of the mathematical model are shown in formulas (1) to (35):

[0090] Formula (1) defines the optimization objective of the model, which is the expected optimization objective under representative destruction scenarios:

[0091]

[0092] Among them, z represents the reinforcement state, including z b , and x indicates the repair status, including and A indicates the repair status is complete, including and

[0093]

[0094] Formulas (5) to (16) define the selection of pre-earthquake reinforcement strategies, taking into account the limitation of reinforcement costs, and reflect the impact of different reinforcement strategies on the remaining functions and repair time of bridges and hospitals. Formula (5) determines the reinforcement strategy of hospital h based on whether the hospital is reinforced at the structural and non-structural levels. Different reinforcement strategies will affect the hospital's post-earthquake rescue capacity and repair time, and thus affect the recovery decision. Formulas (6) to (9) define the undetermined coefficients corresponding to the four strategies of no reinforcement of structure and non-structure, structural reinforcement only, non-structural reinforcement only, and structural and non-structural reinforcement. After selecting a reinforcement strategy, only the undetermined coefficients of the rescue capacity and repair time corresponding to the strategy are not 0, and the rest are 0, thereby realizing the corresponding relationship between different reinforcement strategies and rescue capacity and repair time.

[0095]

[0096] Equations (10) and (11) define different reinforcement strategies for hospital h and calculate the rescue capacity and repair time of hospital h under the uncertain damage scenario ξ after the earthquake.

[0097]

[0098] Equations (12) and (13) define the impact of whether bridge b is reinforced on its traffic capacity and repair time under the uncertain post-earthquake damage scenario ξ.

[0099]

[0100] Formula (14) constrains the type of reinforcement decision variables:

[0101]

[0102] Equations (15) and (16) constrain the reinforcement costs of the transportation system and the medical system respectively.

[0103]

[0104] Equations (17) to (32) define the mathematical model of post-earthquake recovery decision-making, which describes in detail the repair status of bridges and hospitals, resource constraints, and the process of functional recovery of bridges and single hospitals. Equations (17) and (18) establish the relationship between the start and end time of the repair of bridge b and hospital h. Equations (19) to (22) define whether bridge b or hospital h is repaired within time period t under uncertain damage scenario ξ.

[0105]

[0106] Equations (23) and (24) constrain the number of bridges b and hospitals h that can be repaired simultaneously, reflecting the limitation of repair resources.

[0107]

[0108] Equations (25) to (28) define whether the repair of bridge b or hospital h is completed within time period t under the uncertain damage scenario ξ after the earthquake. Equations (29) and (30) constrain the types of decision variables in the recovery phase.

[0109]

[0110] Equations (31) and (32) indicate that in the post-earthquake damage scenario ξ, after the bridge b or hospital h is repaired, its function is restored to the pre-earthquake level, realizing the real-time update of the functional status of the bridge and hospital during the post-earthquake recovery process.

[0111]

[0112] Formulas (33) to (35) define the functional level calculation and the weighted recovery time method of different functional demand points in the recovery process of the urban medical system under the uncertain damage scenario after the earthquake. Formula (33) calculates the post-earthquake functional level using the proxy model constructed in step 3. Formulas (34) and (35) calculate the weighted recovery time considering the weights of different functional demand points.

[0113]

[0114] Step 5: Through the Kmeans++-based clustering algorithm, representative scenes are extracted from a large number of potential damage scenes as the input of the stochastic optimization model. A stochastic optimization intelligent solution algorithm integrating the uncertainty damage scene reduction technology is established. The specific steps of step 5 are:

[0115] Step 5.1: Generate post-earthquake uncertainty scenarios through MCS simulation.

[0116] Through multiple Monte Carlo simulations, the post-earthquake structural damage state, medical function reduction and recovery time under different reinforcement strategies are simulated in the urban medical system model constructed in step 1 as post-earthquake uncertainty scenarios. For a bridge, its post-earthquake uncertainty scenarios include: damage state, remaining traffic capacity and recovery time. After reinforcement, the damage state threshold changes, resulting in different damage states, function reduction and recovery time before and after reinforcement under the same random conditions. For hospitals, post-earthquake uncertainty scenarios include: structural damage state (post-earthquake damage state of bridges and hospitals), number of available departments (function reduction) and recovery time. After reinforcement, the corresponding parameters also change. Each uncertainty scenario is numbered to clarify information such as damage state, function reduction or number of available departments and recovery time.

[0117] Step 5.2: Reduction of uncertainty scenarios after the earthquake.

[0118] The post-earthquake uncertainty scenarios generated by MCS are normalized (bridge capacity, number of available hospital departments, and recovery time are scaled to 0-1). The post-earthquake uncertainty scenarios generated by Monte Carlo simulation are clustered using the Kmeans++ algorithm, and the cluster centers are extracted as representative damage scenarios to achieve effective reduction of post-earthquake uncertainty scenarios. The specific process is as follows:

[0119] Step 5.2.1. Input post-earthquake uncertainty scenario.

[0120] Step 5.2.2: Normalization processing.

[0121] The post-earthquake structural damage status, medical function reduction and recovery time in the post-earthquake uncertainty scenario are organized into a matrix, with rows representing damage scenarios. Each column of data is normalized to ensure that the data range is between 0 and 1, forming a standard sample set for clustering.

[0122] Step 5.2.3: Initialize the cluster centers. Randomly select the initial cluster centers from the sample set, calculate the probability of selecting the next cluster center based on the distance between each data point and the selected cluster center, and select k cluster centers in turn.

[0123] Step 5.2.4: Clustering by K-means algorithm. Assign data points to the closest cluster center and complete clustering by updating the position of each cluster center. Repeat the above operation until the position of the cluster center does not change.

[0124] Step 5.2.5: Output the reduced representative damage scenarios. The cluster centers obtained by the Kmeans++ algorithm are denormalized to form a set of representative damage scenarios, including the damage status, remaining capacity, and recovery time of bridges, as well as the damage status, available number of departments, and recovery time of hospitals.

[0125] Step 5.3, an efficient and intelligent solution algorithm integrating representative damage scenarios and proxy models. Combine the functions constructed in step 3 to quickly calculate the proxy model and the representative damage scenario obtained in step 5.2, substitute the representative damage scenario into the objective function of the stochastic optimization model, that is, formula (1), and calculate the average value of the objective function under the representative damage scenario as the target value of stochastic optimization. Adopt an adaptive genetic algorithm to solve the two-stage stochastic optimization model problem, and dynamically adjust the algorithm parameters to avoid local optimal solutions. Then obtain a feasible solution within a certain time range as a decision-making plan for pre-earthquake reinforcement and post-earthquake recovery.

[0126] The specific process is as follows:

[0127] Step 5.3.1. In the initialization phase, a population of strategies (reinforcement and recovery strategies) is randomly generated. Each individual represents a potential solution of a strategy, and the potential solution of the strategy is {x, A, z}. Each strategy can be connected to different representative damage scenarios.

[0128] Step 5.3.2: Calculate fitness. Based on the representative destruction scenarios and strategy populations, the accessibility to medical care obtained by the proxy model is used to calculate the mean of the functional loss of the urban medical system and the weighted recovery time after the earthquake, and then the maximum expectation is calculated as the fitness value using formula (1).

[0129] Step 5.3.3, Genetic evolution cycle. Select the initial potential solution as the parent individual for crossover, generate new offspring individuals, and perform mutation operations. Evaluate the fitness value of the offspring and update the population.

[0130] Step 5.3.4: Dynamically adjust algorithm parameters. According to the population fitness value, dynamically adjust the genetic algorithm parameters such as crossover rate and mutation rate to avoid local optimal solutions.

[0131] Step 5.3.5: Check the termination condition. If the maximum number of iterations is reached or a satisfactory solution is found, the algorithm is terminated and the optimal solution or its approximate solution is output.

[0132] The purpose of this implementation is to analyze the impact of pre-earthquake reinforcement on potential post-earthquake damage scenarios, consider the complex coupling relationship between transportation and medical care, establish a two-stage stochastic optimization model based on pre-earthquake component reinforcement selection and post-earthquake repair order optimization, and construct a resilience improvement method that combines pre-earthquake reinforcement and post-earthquake recovery. At the same time, this implementation also solves the problem of long time consumption in traditional evaluation methods, and improves sampling efficiency through a post-earthquake uncertain damage scenario reduction method. By reducing sampling bias and further combining a high-precision proxy model based on a neural network, an efficient and intelligent solution algorithm for the whole process resilience improvement optimization problem is developed. The algorithm can quickly solve the reinforcement and recovery strategies while ensuring accuracy, and quantify the improved system resilience level, significantly improving the computational efficiency. Taking the M7.8 earthquake as an example, after the optimization decision, the post-earthquake functional surplus is increased by about 32%, the recovery time is shortened by 12%, the weighted recovery time is shortened by 30%, and the solution time is reduced to 0.3% of the traditional method, effectively solving the problem of excessive computational cost in the random optimization solution process.

[0133] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.

Claims

1. A method for improving the collaborative resilience of the entire urban medical system, characterized in that: include: The basic information of the target city's transportation and medical systems is linked to build an urban medical system model that takes into account the relationship between transportation and medical care, as well as the relationship between hospital structures, non-structures and medical equipment; Using the Monte Carlo simulation method, post-earthquake uncertainty scenarios under different reinforcement strategies are simulated in the urban medical system model, wherein the post-earthquake uncertainty scenarios include: the damage state of the bridge after the earthquake, the available number of medical departments in the hospital, and the restoration time of the bridge and the hospital; The Kmeans++ algorithm is used to cluster the post-earthquake uncertainty scenarios, and the cluster centers are extracted as representative damage scenarios; The reinforcement and restoration strategies under different representative destruction scenarios are regarded as individuals in the population, and the optimal individual is found by using a genetic algorithm. The reinforcement and restoration strategies corresponding to the optimal individual are then used to improve the resilience of the target city's medical system.

2. A method for improving the overall collaborative resilience of an urban medical system according to claim 1, characterized in that: The basic information of the target city's transportation and medical systems is associated to construct an urban medical system model that takes into account transportation and medical care as well as hospital structures, non-structures, and medical equipment, including: Obtain road information based on GIS data and remote sensing image information within the target city, abstract the traffic facilities and their connection relationships in the road information into a topological structure, and establish a post-earthquake traffic network topology model; Based on the population distribution information of residents, the demand for medical services in post-disaster situations is assessed and a medical demand model is constructed; Based on the structural type, construction year, location of each department and medical equipment configuration of individual hospitals within the target city, the vulnerability data of non-structural and medical equipment-related disasters in the hospital were integrated to establish a quantitative model of the post-earthquake function of individual hospitals; The post-earthquake traffic network topology model, medical demand model and single hospital post-earthquake function quantification model together constitute the urban medical system model.

3. A method for improving the overall collaborative resilience of an urban medical system according to claim 1, characterized in that: The objective function expression of the genetic algorithm is: Among them, z represents the reinforcement status, including whether the bridge b was reinforced before the earthquake, whether the hospital h was reinforced at the structural level before the earthquake, and whether the hospital h was reinforced at the non-structural level before the earthquake; x represents the repairing status, including whether the bridge b is being repaired in time period t in scenario ξ and whether the hospital h is being repaired in time period t in scenario ξ; A represents the completion status, including whether the bridge b is repaired within time period t in scenario ξ and whether the hospital h is repaired within time period t in scenario ξ; Θ is the set of post-earthquake uncertainty scenarios under different reinforcement strategies simulated by Monte Carlo, and Ω is the set of representative damage scenarios; E represents the desired optimization goal under multiple uncertain scenarios, and F ξ is the weighted optimization objective under scenario ξ.

4. A method for improving the overall collaborative resilience of an urban medical system according to claim 3, characterized in that: The weighted optimization objective F under the scenario ξ ξ The expression is: Among them, f1 ξ is the optimization objective based on recovery time in scenario ξ, f2 ξ is the optimization objective based on functional improvement in scenario ξ, ω1 and ω2 are f1 ξ and f2 ξ The weight coefficient of WRT pre To strengthen the weighted recovery time of the urban medical system after the earthquake, WRT ξ is the weighted recovery time of the urban medical system after the earthquake after reinforcement under scenario ξ, Q 0,pre In order to strengthen the functional surplus of the urban medical system at time t0 after the fore-earthquake, Q0 ξ is the functional surplus of the urban medical system after reinforcement at time t0 after the earthquake under scenario ξ.

5. A method for improving the overall collaborative resilience of an urban medical system according to claim 4, characterized in that: The desired optimization target E in the scenario ξ is obtained through the accessibility of medical treatment calculated by the proxy model. The input of the agent model is the post-earthquake damage status of bridges in the target area and the available number of medical departments in the hospital under the post-earthquake damage scenario, and the output is the post-earthquake medical accessibility.

6. A method for improving the overall collaborative resilience of an urban medical system according to claim 5, characterized in that: The method for obtaining the post-earthquake damage status of bridges in the target area and the available number of each medical department in the hospital in the post-earthquake damage scenario is as follows: The post-earthquake damage scenarios were simulated in the urban medical system model using the Monte Carlo simulation method, and the functional reduction of bridges, the available number of hospital departments, and the repair time of bridges and hospitals were evaluated under each post-earthquake damage scenario.

7. A method for improving the overall collaborative resilience of an urban medical system according to claim 4, characterized in that: The constraints of the objective function include: pre-earthquake reinforcement strategy constraints, cost constraints and repair resource constraints.

8. A method for improving the overall collaborative resilience of an urban medical system according to claim 7, characterized in that: The pre-earthquake reinforcement strategy constraints include: in, represents the reinforcement strategy selection variable of hospital h before the earthquake, h∈H, H is the set of individual hospitals in the urban medical system, is a binary variable indicating whether the hospital h structure was reinforced before the earthquake and has is a binary variable indicating whether the non-structural structure of hospital h was reinforced before the earthquake and has 9. A method for improving the overall collaborative resilience of an urban medical system according to claim 8, characterized in that: The cost constraints include: Among them, c b Cost of reinforcing bridge b, z b is a binary variable indicating whether bridge b was reinforced before the earthquake and has z b ∈{0,1},Cost B Investment in transportation system reinforcement, The cost of reinforcing the hospital structure. Cost of non-structural reinforcement of the hospital H is the cost investment for strengthening the medical system, b∈B, and B is the set of bridges in the urban medical system.

10. A method for improving the overall collaborative resilience of an urban medical system according to claim 9, characterized in that: The resource constraints include: Among them, x b,t Indicates whether bridge b is under repair in time period t, x h,t Indicates whether hospital h is under repair in time period t, n ET,b and n ET,h are the number of repair engineering teams for bridges and hospitals after the earthquake, t∈T, and T is the set of long-term repair periods after the earthquake.

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