Flood disaster propagation simulation method based on bus-subway double-layer traffic network

Abstract

The invention relates to a flood disaster propagation simulation method based on a bus-subway double-layer traffic network. The method comprises the following steps: constructing the bus-subway double-layer traffic network according to bus nodes, a bus node connection relationship, subway nodes, a subway node connection relationship and bus-subway transfer nodes; disaster disturbance is introduced into the bus-subway double-layer traffic network, the influence of flood disasters on the double-layer traffic network is simulated, and a node state updating formula and a flood disturbance formula are obtained; iteratively calculating each node state at each moment through the node state updating formula and the flood disturbance formula; and obtaining a disaster chain propagation path based on dynamic evolution of each node state in time. Compared with the prior art, the method has the advantages that the blank of complex network disaster propagation research is filled, and the dynamic behavior of the bus-subway system in extreme weather can be comprehensively revealed by the provided dynamic model.

Description

Technical Field

[0001] The present invention relates to an urban traffic network, and more particularly to a method for simulating the propagation of flood disasters based on a bus-subway double-layer traffic network. Background Art

[0002] With the continuous advancement of urbanization, buses and subways have gradually become two core components of urban public transportation, playing an important role in alleviating traffic congestion, improving commuting efficiency, and reducing emissions. However, these systems also face various challenges. In particular, in recent years, flood disaster events have occurred frequently, and the vulnerability of the bus and subway systems has been fully exposed. How to improve the stability and recovery ability of the traffic network in the event of disasters has become an urgent problem to be solved.

[0003] At present, the research on disaster response of urban traffic systems is mostly limited to the emergency response and resilience analysis of single systems, and the interaction between different traffic systems has not been fully considered, especially the coupled impact of bus and subway systems in the face of sudden disasters. Most traditional traffic network studies focus on the structural characteristics of single-layer networks, mainly analyzing factors such as the topological structure, traffic flow distribution, and stability of traffic systems, and lack systematic research on the interaction between multi-layer traffic networks.

[0004] Especially under flood disaster conditions, the transfer nodes between buses and subways usually become the key paths for disaster propagation. Flood disasters affect the operation of traffic system nodes through factors such as water depth, diffusion rate, and drainage capacity, and further spread to other nodes through the inter-layer coupling relationship, affecting the stability and operation efficiency of the entire traffic network. However, most existing studies focus on the degree distribution, clustering coefficient, and connectivity analysis of single-layer networks, and there is less research on the dynamic evolution process of the network under disaster disturbances, especially in the analysis of disaster propagation characteristics across levels and nodes, and the research progress is limited.

[0005] The literature "Research on the Resilience of Urban Bus-Subway Double-Layer Network under Extreme Meteorological Disasters" analyzed the resilience issues of the urban public transportation system under extreme meteorological disasters, established a cascading failure model of the urban bus-subway double-layer network under extreme typhoon and rainstorm meteorological disasters, and used the cascading failure model to describe the indirect impact of extreme meteorological disasters on the urban public transportation system, so as to analyze the resilience characteristics of the urban bus-subway double-layer network under extreme typhoon and rainstorm meteorological disasters. However, this literature regarded flood disasters as static impacts, that is, only considered the initial damage caused by flood disasters to the transportation network, and failed to depict the continuous impact of flood disasters on the transportation network during the entire disaster process. At the same time, this literature only constructed a bus-subway double-layer network model and mainly focused on the network topology structure and cascading failure process within a single layer, and failed to fully depict the interactive impact between the two layers of the network, that is, when a layer of the network (such as the bus system) fails, how it further affects another layer of the network (such as the subway system) through transfer channels and inter-layer coupling effects. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned existing technologies and provide a method for simulating the propagation of flood disasters based on a bus-subway double-layer transportation network.

[0007] The purpose of the present invention can be achieved through the following technical solutions:

[0008] A method for simulating the propagation of flood disasters based on a bus-subway double-layer transportation network, the method includes:

[0009] Construct a bus-subway double-layer transportation network according to bus nodes, bus node connection relationships, subway nodes, subway node connection relationships, and bus-subway transfer nodes; introduce disaster disturbances into the bus-subway double-layer transportation network, simulate the impact of flood disasters on the double-layer transportation network, and obtain a node state update formula and a flood disturbance formula; through the node state update formula and the flood disturbance formula, iteratively calculate the states of each node at each moment; based on the dynamic evolution of the states of each node over time, obtain the disaster chain propagation path.

[0010] Further, the bus-subway double-layer transportation network includes: a bus layer, a subway layer, and inter-layer coupling, where

[0011] The nodes in the bus layer are bus nodes, the edges are bus node connection relationships, and the direct connection relationships between bus nodes are represented by a bus adjacency matrix;

[0012] The nodes in the subway layer are subway nodes, the edges are subway node connection relationships, and the direct connection relationships between subway nodes are represented by a subway adjacency matrix;

[0013] The bus layer and the subway layer are connected through a bus-subway transfer node to obtain the inter-layer coupling, and the connection relationship of the bus-subway transfer node is represented by an inter-layer adjacency matrix.

[0014] Furthermore, the node state update formula is:

[0015]

[0016] Where, represents the state value of node i on the l-th layer at time t, is the local non-linear mapping function of node i on the l-th layer at time t. ∈1 represents the coupling strength between nodes on the same layer, and ∈2 represents the coupling strength between the bus layer and the subway layer. represents the direct impact of the flood disaster on the state of node i on the l-th layer at time t, represents the direct connection relationship between node i and node j in the l-th layer, represents the number of neighbors of node i on the l-th layer, N i represents the neighbor set of node i.

[0017] Even further, the adopts the Logistic mapping form to simulate the non-linear evolution of node i on the l-th layer at time t. The specific expression is:

[0018]

[0019] Even further, the is a variable, and its value is associated with the flood perturbation formula. The expression is:

[0020]

[0021] Where, is the disaster impact intensity, h i (t) is the flood perturbation, representing the water depth of node i at time t.

[0022] Even further, the flood perturbation formula is:

[0023]

[0024] Where, h i (t) is the flood perturbation of node i, representing the water depth of node i at time t, and h j (t) is the flood perturbation of adjacent node j, representing the water depth of node j at time t. α is the water accumulation persistence coefficient, β is the diffusion intensity, b ij is the water accumulation propagation coefficient between node i and node j, and γ i is the drainage capacity coefficient of node i, N iDenotes the set of neighbors of node i.

[0025] Furthermore, the method further includes: obtaining the stability of the bus - subway double - layer transportation network, the inter - layer interaction effect of the bus - subway double - layer transportation network, and the disaster situation of the bus - subway double - layer transportation network according to the dynamic evolution of each node state over time;

[0026] The process of obtaining the dynamic evolution of each node state over time includes:

[0027] By adjusting the parameters in the node state update formula and the flood disturbance formula, iteratively calculating the state of each node at each moment, and obtaining the stability of the bus - subway double - layer transportation network;

[0028] According to the calculation results of the state of each node at each moment, obtaining the failed nodes and their failure moments, simulating how flood disturbances spread in the double - layer network through transfer nodes, analyzing the role of key nodes, and obtaining the disaster chain propagation path;

[0029] Differentially setting the parameters of the bus layer and the subway layer in the node state update formula and the flood disturbance formula, iteratively calculating the state of each node at each moment, and obtaining the inter - layer interaction effect of the bus - subway double - layer transportation network;

[0030] Calculating the dynamic change of the size of the largest connected sub - graph and the dynamic change of the network transportation efficiency, and comprehensively evaluating the disaster situation of the bus - subway double - layer transportation network.

[0031] Furthermore, the largest connected sub - graph is the connected sub - graph with the most nodes in the bus - subway double - layer transportation network. By iteratively calculating the state of each node at each moment, it can be obtained whether the nodes in the bus - subway double - layer transportation network fail. If there are too many failed nodes in the bus - subway double - layer transportation network, the bus - subway double - layer transportation network will split into several connected sub - graphs.

[0032] Furthermore, the calculation formula for the size of the largest connected sub - graph is:

[0033]

[0034] Where C max (t) represents the number of nodes in the largest connected sub - graph of the bus - subway double - layer transportation network at time t, and N represents the total number of nodes in the bus - subway double - layer transportation network.

[0035] Furthermore, the calculation formula for the network transportation efficiency is:

[0036]

[0037] Where W ijDenote the passenger flow between node i and node j as d ij (t) represents the shortest path length from node i to node j at time t.

[0038] Compared with the prior art, the beneficial effects of the present invention include:

[0039] 1. The present invention innovatively introduces an interlayer coupling influence mechanism, constructs a dynamic interaction model for a two-layer network, accurately describes the propagation path of disasters in the two-layer traffic network, and makes up for the deficiency of existing research in failing to distinguish and characterize the interlayer influence; the present invention proposes a mechanism for the chain propagation of flood disasters in the two-layer traffic network, enabling the present invention to accurately predict the diffusion range and propagation path of disasters after the occurrence of disasters, accurately simulate the chain propagation effect of flood disasters on the traffic network, and provide a basis for the disaster-time decision-making, post-disaster recovery, and node optimization of the traffic system during the occurrence of flood disasters, enabling the traffic network to better avoid the situation of being paralyzed during disasters;

[0040] 2. In addition to paying attention to the bus layer and the subway layer, the present invention also pays attention to the interlayer coupling between the two layers. In application, it can dynamically adjust the coupling strength, reveal the interactive influence between the bus and subway systems, and deeply study the dynamic process of disaster response in complex systems; during the occurrence of disasters, the role of transfer nodes is particularly prominent. The present invention takes transfer nodes as one of the bases for interlayer coupling, clarifies the key role of these transfer nodes in the process of disaster propagation, and makes the simulation of flood disaster propagation more accurate and closer to reality;

[0041] 3. The present invention proposes a dynamic update mechanism for the impact of flood disasters. By introducing key parameters such as waterlogging depth, diffusion intensity, and drainage capacity, it constructs a spatio-temporal evolution process of disaster perturbation, which can not only simulate the direct impact of flood disasters, but also depict how floods spread through the topological structure of the urban traffic network, so as to more accurately evaluate the impact of disasters on the resilience of the traffic system and improve the response speed of the traffic system to disaster emergencies;

[0042] 4. The present invention fills a gap in the research on disaster propagation in complex networks in theory. The proposed combined node state update formula and flood perturbation formula for the bus-subway two-layer traffic network can comprehensively reveal the dynamic behavior of the bus-subway system under extreme weather. Through practical applications, this model can provide technical support for urban traffic planning, disaster emergency management, and infrastructure optimization, thereby enhancing the resilience and safety of the urban comprehensive traffic system. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is the flowchart of the method of the present invention;

[0044] Figure 2 is the simulation result diagram of the relative size of the largest connected component of LCC in an embodiment of the present invention;

[0045] Figure 3 This is a graph showing the simulation results of the NTE network transportation efficiency in an embodiment of the present invention. Detailed implementation manners

[0046] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0047] Embodiment 1

[0048] This embodiment aims to disclose a simulation method for flood disaster propagation based on a bus - subway double - layer transportation network. The method is as Figure 1 shown, and the specific steps are as follows, including:

[0049] Step S1, construct a bus - subway double - layer transportation network according to bus nodes, bus node connection relationships, subway nodes, subway node connection relationships, and bus - subway transfer nodes.

[0050] All nodes in the text refer to various stations in reality.

[0051] The bus - subway double - layer transportation network includes: a bus layer, a subway layer, and inter - layer coupling. Among them,

[0052] The nodes in the bus layer (l = 1) are bus nodes, and the edges are bus node connection relationships. The direct connection relationships between bus nodes are represented by the bus adjacency matrix ;

[0053] The nodes in the subway layer (l = 2) are subway nodes, and the edges are subway node connection relationships. The direct connection relationships between subway nodes are represented by the subway adjacency matrix ;

[0054] The bus layer and the subway layer are connected through bus - subway transfer nodes to obtain inter - layer coupling. The connection relationships of bus - subway transfer nodes are represented by the inter - layer adjacency matrix ;

[0055] Step S2, construct a disaster perturbation model, introduce disaster perturbation in the bus - subway double - layer transportation network, simulate the impact of flood disasters on the double - layer transportation network, and obtain the node state update formula and the flood perturbation formula.

[0056] The node state update formula is:

[0057]

[0058] Among them, represents the state value of node i at the l-th layer at time t, is the local non-linear mapping function of node i at the l-th layer at time t. ∈1 represents the coupling strength between nodes in the same layer, and ∈2 represents the coupling strength between the bus layer and the subway layer. represents the direct impact of the flood disaster on the state of node i at the l-th layer at time t, represents the direct connection relationship between node i and node j in the l-th layer, represents the number of neighbors of node i at the l-th layer, N i represents the neighbor set of node i.

[0059] l = 1: represents the bus layer.

[0060] l = 2: represents the subway layer.

[0061] When nodes i and j are connected. nodes i and j are not connected.

[0062] is used to normalize the influence and prevent the over-influence of high-connected nodes on the results.

[0063] describes the traffic state of the current node, such as passenger density, operation efficiency, etc.

[0064] Adopts the Logistic mapping form to simulate the non-linear evolution of node i at the l-th layer at time t, and describes the dynamic evolution of the node state (such as the change of passenger flow over time). The specific expression is:

[0065]

[0066] Specifically, ∈1 represents the mutual connection between bus stops or subway stops, such as the connectivity of lines and the influence of passenger distribution at adjacent stops. In this embodiment, ∈1 is limited to be set as 0.1 - 0.5, and the specific value is adjusted according to the connection density of the network structure.

[0067] Specifically, ∈2 represents the transfer influence between bus stops and subway stops, the passenger flow distribution relationship between the two traffic modes, etc. In this embodiment, ∈2 is limited to be set as 0.05 - 0.2, and is adjusted according to the transfer efficiency between the bus and the subway.

[0068] is the perturbation term, which is a variable, and its value is associated with the flood perturbation formula. The expression is:

[0069]

[0070] Among them, is the intensity of disaster impact, h i (t) is the flood disturbance, representing the waterlogging depth of node i at time t.

[0071] The flood disturbance formula is:

[0072]

[0073] where h i (t) is the flood disturbance of node i, representing the waterlogging depth of node i at time t, h j (t) is the flood disturbance of adjacent node j, representing the waterlogging depth of node j at time t, α is the waterlogging persistence coefficient, β is the diffusion intensity, b ij is the waterlogging propagation coefficient between node i and node j, γ i is the drainage capacity coefficient of node i, N i represents the neighbor set of node i.

[0074] h i (t) specifically represents the impact intensity of the flood disaster in a certain area, h i (t + 1) specifically represents the waterlogging depth at the next moment, αh i (t) specifically represents the persistence of the waterlogging at the current node.

[0075] The value range of α is 0 ≤ α ≤ 1, describing the residual effect of waterlogging without the influence of other factors. For example, it is set to 0.9 in low-lying areas and 0.3 in areas with high drainage efficiency.

[0076] When α → 1, the dissipation speed of waterlogging at node i is slower.

[0077] When α → 0, the waterlogging quickly subsides.

[0078] Specifically, it represents the diffusion effect of waterlogging. β specifically describes the efficiency of waterlogging propagation from adjacent areas to node i, used to describe the ability of waterlogging to spread from adjacent nodes, and can be set according to the terrain and drainage facility conditions, such as 0.05 - 0.2.

[0079] If b ij = 1, the waterlogging propagation between i and j is smooth.

[0080] If b ij = 0, there is no propagation between i and j (such as in areas with isolated terrain or drainage zones).

[0081] γ i h i (t) is the drainage capacity of node i at time t, set 0 ≤ γ i ≤ 1, such as 0.8 for an efficient drainage system and 0.1 for a failed area.

[0082] γ i →1: It indicates that the drainage facility is efficient and the accumulated water can be quickly drained.

[0083] γ i →0: It indicates that the drainage facility fails and the accumulated water can hardly be drained.

[0084] Step S3, set the initial conditions of each node at present.

[0085] In this embodiment, the state variables of each node are initialized, and the initial values can be assigned according to the passenger flow density of the station and normalized, distributed in the interval (0, 1). Set the flood disturbance parameters α, β, and γ i , and assign the water depth h i (0) to a specific node at the initial moment.

[0086] Step S4, through the node state update formula and the flood disturbance formula, iteratively calculate the states of each node at each moment.

[0087] Step S5, based on the dynamic evolution of the states of each node in time, obtain the disaster chain propagation path.

[0088] Based on the dynamic evolution of the states of each node in time, the stability of the bus - subway double - layer traffic network, the inter - layer interaction effect of the bus - subway double - layer traffic network, and the disaster situation of the bus - subway double - layer traffic network can also be obtained;

[0089] The dynamic evolution process based on the states of each node in time includes:

[0090] By adjusting the intra - layer coupling strength ∈1 and the inter - layer coupling strength ∈2, iteratively calculate the states of each node at each moment to obtain the stability of the bus - subway double - layer traffic network;

[0091] According to the calculation results of the states of each node at each moment, obtain the failed nodes and their failure moments, simulate how the flood disturbance spreads in the double - layer network through the transfer nodes, analyze the role of key nodes, and obtain the disaster chain propagation path;

[0092] Differentially set the parameters of the bus layer and the subway layer in the node state update formula and the flood disturbance formula, iteratively calculate the states of each node at each moment to obtain the inter - layer interaction effect of the bus - subway double - layer traffic network;

[0093] Calculate the dynamic changes in the size of the largest connected sub - graph and the dynamic changes in the network transportation efficiency, and comprehensively evaluate the disaster situation of the bus - subway double - layer traffic network.

[0094] In another embodiment, in the analysis, the inter - layer coupling mechanism is also optimized through the model analysis results, emergency optimization suggestions are proposed, and the network disaster resistance ability is improved.

[0095] The largest connected component is the connected component with the most nodes in the bus - subway double - layer transportation network. By iteratively calculating the states of each node at each moment, it can be obtained whether the nodes in the bus - subway double - layer transportation network fail. If there are too many failed nodes in the bus - subway double - layer transportation network, the bus - subway double - layer transportation network will split into several connected components.

[0096] The calculation formula for the size of the largest connected component (LCC) is:

[0097]

[0098] where C max (t) represents the number of nodes in the largest connected component of the bus - subway double - layer transportation network at time t, and N represents the total number of nodes in the bus - subway double - layer transportation network.

[0099] The size of the largest connected component is used to describe the change in the connectivity of the network under flood disaster conditions. The larger the LCC, the more robust the structure of the network, and the smaller the impact of the disaster on the overall connectivity of the network.

[0100] The calculation formula for the network transportation efficiency (NTE) is:

[0101]

[0102] where W ij represents the passenger flow between node i and node j, and d ij (t) represents the shortest path length from node i to node j at time t.

[0103] The network transportation efficiency is used to quantify the impact of disaster disturbances on the functional performance of the transportation system. The larger the NTE, the stronger the transportation capacity of the network, and the smaller the damage to its functional performance caused by the disaster.

[0104] When a flood disaster occurs, the present invention can be applied to the bus - subway transportation network of a specific city through a real - time traffic monitoring system and drainage facility data:

[0105] 1. Apply the present invention in the planning of the urban bus - subway network, optimize the design of transfer nodes by adjusting the network structure and coupling strength;

[0106] 2. When a flood disaster occurs, use the model to predict the disaster situation of key nodes and provide a decision - making basis for emergency dispatching;

[0107] 3. Provide technical support for enhancing the resilience of the urban transportation system by simulating the network response characteristics under different disaster disturbance intensities.

[0108] The following is an example for illustration in reality:

[0109] This embodiment is based on the crawler data of the bus and subway traffic network map of a certain city. A total of 14 subway lines, 147 subway stations, 465 bus lines, and 2,090 bus stations are crawled. The Space L method is used to construct the bus-subway composite network of a certain city. A bus-subway transfer channel is formed between the bus stations within 500 m around the subway stations. This transfer channel serves as the coupling connection between the networks, thereby constructing an urban bus-subway composite traffic network model.

[0110] In terms of setting the perturbation parameters, the areas with relatively high floodwater accumulation risks are selected as the initial perturbation nodes, and the initial water accumulation depth h i (0) is set to 0.8, reflecting the areas with relatively serious water accumulation. At the same time, flood propagation parameters are set in the model to simulate the dynamic changes of water accumulation, including the water accumulation persistence parameter α = 0.9, which describes the residual effect of water accumulation without external forces; the diffusion intensity parameter β = 0.2, indicating the ability of water accumulation to spread to surrounding nodes; and the drainage capacity parameter γ = 0.3, reflecting the low efficiency of the drainage system in the old city. In addition, in order to describe the interaction characteristics of the network, different values of the intra-layer coupling strengths ∈1 and ∈2 of the subway and bus networks are set respectively, so as to control the dynamic changes of the connectivity and traffic distribution among the nodes in the network.

[0111] During the dynamic simulation process, at the initial moment (time step t = 0), external perturbations are applied to the selected key area nodes to simulate the impact of water accumulation in the initial stage of the flood disaster. As time evolves, the flood perturbations spread through the bus and subway networks, resulting in the gradual emergence of the loss of connectivity and function of the double-layer network. By observing and recording the changes in the network state at different time steps, the dynamic impacts of flood perturbations on the network connectivity (which can be represented by LCC) and the network transportation efficiency (NTE) are analyzed. As Figure 2 and Figure 3 The simulation results show that under the high-coupling strength combination (such as ∈1 = 0.4, ∈2 = 0.2), although the network connectivity decreases rapidly in the initial stage of the perturbation, the overall function recovery is relatively stable; while under the low-coupling strength combination (such as ∈1 = 0.2, ∈2 = 0.1), the network function is damaged the most, and the recovery speed is significantly slowed down.

[0112] The results show that reasonably adjusting the intra-layer and inter-layer coupling strength parameters can effectively reduce the damage of disasters to the network function, which provides an important theoretical basis for the disaster resistance optimization of the actual traffic network.

[0113] Embodiment 2

[0114] Based on Embodiment 1, this embodiment provides an electronic device, including: one or more processors and a memory. The memory stores one or more programs, and the one or more programs include instructions for executing the aforementioned flood disaster propagation simulation method based on the bus-subway double-layer transportation network.

[0115] At the hardware level, the electronic device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory. Of course, it may also include other hardware required for other services. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to implement the aforementioned flood disaster propagation simulation method based on the bus-subway double-layer transportation network. Of course, in addition to the software implementation, the present invention does not exclude other implementation methods, such as logic devices or a combination of software and hardware. That is to say, the execution subject of the following processing flow is not limited to each logic unit, and can also be hardware or a logic device.

[0116] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM), and / or non-volatile memory in the form of, for example, read-only memory (ROM) or flash memory (flash RAM). The memory is an example of a computer-readable medium.

[0117] Computer-readable media includes permanent and non-permanent, removable and non-removable media, and information storage can be achieved by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory, or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD), or other optical storage, magnetic cassette tapes, disk storage, or other magnetic storage devices, or any other non-transmission media that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transitory media such as modulated data signals and carrier waves.

[0118] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A flood disaster propagation simulation method based on a bus-subway double-layer transportation network, characterized in that: The method comprises: A bus-subway double-layer transportation network is constructed according to bus nodes, bus node connection relationships, subway nodes, subway node connection relationships, and bus-subway transfer nodes; disaster disturbances are introduced into the bus-subway double-layer transportation network to simulate the impact of flood disasters on the double-layer transportation network, and a node state update formula and a flood disturbance formula are obtained; the node state update formula and the flood disturbance formula are used to iteratively calculate the state of each node at each moment; based on the dynamic evolution of the state of each node over time, a disaster chain propagation path is obtained.

2. The flood disaster propagation simulation method based on a bus-subway double-layer transportation network according to claim 1 is characterized in that: The bus-subway double-layer transportation network includes: a bus layer, a subway layer and inter-layer coupling, wherein: The nodes in the bus layer are bus nodes, the edges are bus node connections, and the direct connection relationship between bus nodes is represented by a bus adjacency matrix; The nodes in the subway layer are subway nodes, the edges are subway node connection relationships, and the direct connection relationship between subway nodes is represented by the subway adjacency matrix; The bus layer and the subway layer are connected via bus-subway transfer nodes to obtain the inter-layer coupling, and the connection relationship of the bus-subway transfer nodes is represented by an inter-layer adjacency matrix.

3. The flood disaster propagation simulation method based on a bus-subway double-layer transportation network according to claim 1 is characterized in that: The node status update formula is: in, represents the state value of node i in layer l at time t, is the local nonlinear mapping function of the node i in the lth layer at time t, ∈1 represents the coupling strength between nodes in the same layer, ∈2 represents the coupling strength between the bus layer and the subway layer, represents the direct impact of flood disaster on the state of node i in the lth layer at time t, represents the direct connection relationship between node i and node j in layer l, N represents the number of neighbors of node i in layer l, i Represents the neighbor set of node i.

4. The flood disaster propagation simulation method based on a bus-subway double-layer transportation network according to claim 3 is characterized in that: Said The Logistic mapping form is used to simulate the nonlinear evolution of the l-th layer node i at time t. The specific expression is:

5. The flood disaster propagation simulation method based on a bus-subway double-layer transportation network according to claim 3 is characterized in that: Said is a variable whose value is associated with the flood disturbance formula, and the expression is: in, is the disaster impact intensity, h i (t) is the flood disturbance, which indicates the water depth of node i at time t.

6. The flood disaster propagation simulation method based on a bus-subway double-layer transportation network according to claim 5 is characterized in that: The flood disturbance formula is: Among them, h i (t) is the flood disturbance of node i, which means the water depth of node i at time t, h j (t) is the flood disturbance of the adjacent node j, which means the water depth of node j at time t, α is the water persistence coefficient, β is the diffusion intensity, and b ij is the water propagation coefficient between node i and node j, γ i is the drainage capacity coefficient of node i, N i Represents the neighbor set of node i.

7. The flood disaster propagation simulation method based on a bus-subway double-layer transportation network according to claim 1 is characterized in that: The method further includes: obtaining the stability of the bus-subway double-layer transportation network, the inter-layer interaction effect of the bus-subway double-layer transportation network, and the disaster situation of the bus-subway double-layer transportation network according to the dynamic evolution of each node state in time; The acquisition process of the dynamic evolution of each node state over time includes: By adjusting the parameters in the node status update formula and the flood disturbance formula, the node status at each time is repeatedly iterated to obtain the stability of the bus-subway double-decker transportation network. According to the calculation results of the status of each node at each time, the failed nodes and their failure times are obtained, and the flood disturbance is simulated to spread in the double-layer network through the transfer nodes, and the role of key nodes is analyzed to obtain the chain propagation path of the disaster; Differentiate the parameters of the bus layer and the subway layer in the node state update formula and the flood disturbance formula, repeatedly iterate and calculate the state of each node at each time, and obtain the inter-layer interaction effect of the bus-subway double-layer transportation network; The dynamic changes of the maximum connected subgraph size and the network transportation efficiency are calculated to comprehensively evaluate the disaster situation of the bus-subway double-decker transportation network.

8. The flood disaster propagation simulation method based on a bus-subway double-layer transportation network according to claim 7 is characterized in that: The maximum connected subgraph is the connected subgraph containing the most nodes in the bus-subway double-layer transportation network. By iteratively calculating the state of each node at each moment, it can be obtained whether the nodes in the bus-subway double-layer transportation network are invalid. If there are too many invalid nodes in the bus-subway double-layer transportation network, the bus-subway double-layer transportation network will be split into several connected subgraphs.

9. The flood disaster propagation simulation method based on a bus-subway double-layer transportation network according to claim 7 is characterized in that: The calculation formula of the maximum connected subgraph size is: Among them, C max (t) represents the number of nodes in the largest connected subgraph in the bus-subway double-layer transportation network at time t, and N represents the total number of nodes in the bus-subway double-layer transportation network.

10. The flood disaster propagation simulation method based on a bus-subway double-layer transportation network according to claim 7, characterized in that: The calculation formula of the network transportation efficiency is: Among them, W ij represents the passenger flow between node i and node j, d ij (t) represents the shortest path length from node i to node j at time t.

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