Flood disaster population exposure calculation method and system based on spatial constraint

Abstract

The invention provides a flood disaster population exposure calculation method and system based on spatial constraint, and relates to the technical field of flood disasters, and the method comprises the steps: determining the current ponding mask spatial distribution of a target city for model prediction according to an obtained rainfall observation sequence; inputting the current multivariate state information of each resident into a pre-trained reinforcement learning model, estimating state transition probability distribution based on the reinforcement learning model, and predicting and outputting a risk avoiding action currently executed by each resident; determining the spatial position of each resident at the next moment according to the predicted and output risk avoiding action; determining population distribution of each space unit of the target city at the next moment according to the spatial position of each resident at the next moment; and determining a flood disaster population exposure value of the target city at the target moment according to the population distribution of each space unit of the target city at the target moment. The method aims at improving the accuracy of population exposure calculation.

Description

Technical Field

[0001] This application relates to the field of flood disaster technology, specifically to a method and system for calculating population exposure to flood disasters based on spatial constraints. Background Technology

[0002] Against the backdrop of intensifying global climate change and continuous urbanization, the frequency and intensity of urban rainstorms and floods are increasing, posing serious threats to urban infrastructure safety and human life. Compared to relatively static factors such as infrastructure, urban residents, as a major victim of floods, are characterized by their large numbers, dispersed spatial distribution, and significant differences in behavioral decisions. During floods, their movement paths, evacuation choices, and response timing directly affect their exposure risk and the consequences of the disaster. However, both floods and population evacuation exhibit significant spatiotemporal dynamics, and static analysis of water accumulation or physical processes alone is insufficient to characterize the actual changes in risk to individuals during the evolution of the disaster. Summary of the Invention

[0003] In view of this, this application provides a method and system for calculating population exposure to flood disasters based on spatial constraints. It aims to solve or partially solve the problems existing in the background technology.

[0004] The first aspect of this application provides a method for calculating population exposure to flood disasters based on spatial constraints, the method comprising: Based on the rainfall observation sequence obtained from monitoring, the current spatial distribution of water accumulation mask in the target city is determined. The spatial distribution of water accumulation mask refers to the range and depth of water accumulation in the target city at the corresponding time. Each resident's current multivariate state information is input into a pre-trained reinforcement learning model. Based on the reinforcement learning model's estimation of the state transition probability distribution, the model predicts and outputs the risk avoidance actions that each resident will currently perform. The resident's current multivariate state information includes their spatial location, mobility speed, risk tolerance, and information perception intensity. Based on the risk avoidance actions currently performed by each resident as predicted, determine the spatial location of each resident at the next moment; Based on the spatial location of each resident at the next moment, determine the population distribution of each spatial unit of the target city at the next moment; Based on the population distribution of each spatial unit of the target city at the target time, determine the flood disaster population exposure value of the target city at the target time; The expression for the state transition probability is:

[0005]

[0006] in, Let be the state transition probability of the i-th resident performing the m-th action at time t; For the i-th resident performing the m-th action at time t, the spatial risk-benefit ratio action score is given. The safety utility of the spatial unit where the i-th resident is located at time t; The flood risk level is the spatial location of the i-th resident at time t, and the flood risk level is obtained based on the spatial distribution of the water accumulation mask. Let λ be the movement cost of the i-th resident performing the m-th action at the current spatial location at time t; λ is the spatial cost weight; and η is the theoretical intensity parameter used to control the individual's sensitivity to action rating. Let represent the action space of the i-th resident, which includes all actions that the i-th resident can perform.

[0007] Optionally, based on the population distribution of each spatial unit of the target city at the target time, the flood disaster population exposure value of the target city at the target time is determined, including: Based on the population distribution and surface inundation depth of the j-th spatial unit of the target city at the m-th time before the target time, determine the population exposure load of the j-th spatial unit at the m-th time, where j takes values ​​from 1 to J and m takes values ​​from 1 to M. Based on the population exposure load of the j-th spatial unit at all times before the target time, determine the cumulative population exposure of the j-th spatial unit at the target time; Based on the cumulative population exposure of all spatial units in the target city at the target time, the flood disaster population exposure value of the target city at the target time is determined.

[0008] Optionally, the method further includes: Based on the evacuation trajectories of residents from the starting time to the target time, the length of the evacuation path of the residents is determined; The evacuation efficiency of the residents is determined based on the length of their evacuation routes and the time they first enter the refuge area. The total risk avoidance efficiency of the target city before the target time is determined based on the risk avoidance efficiency of all residents in the target city before the target time.

[0009] Optionally, the method further includes: Based on the current spatial location of each resident in the target city and the current spatial distribution of the water accumulation mask, determine the current danger perception index of each resident. Based on the relationship between each resident's current risk perception index and risk perception threshold, target residents who will currently take evasive action are identified from all residents. By inputting the current multivariate state information of the target resident into a pre-trained reinforcement learning model, and based on the estimation of the state transition probability distribution by the reinforcement learning model, the risk avoidance action to be performed by the target resident is predicted and output.

[0010] Optionally, a trained reinforcement learning model can be obtained by training the initial reinforcement learning model, including: Based on the historical rainfall observation sequence obtained within a specified time period, the spatial distribution of water accumulation mask in the target city at each moment within the specified time period is generated. The multivariate state information of each resident at the nth time within the specified time period is input into the initial reinforcement learning model. Based on the current estimate of the state transition probability distribution by the initial reinforcement learning model, the risk avoidance actions to be performed by each resident are predicted and output. Based on the risk avoidance actions performed by each resident as predicted, the spatial location of each resident at the (n+1)th moment within the specified time period is predicted. Based on the predicted spatial location of each resident at the (n+1)th moment within the specified time period, the population distribution of each spatial unit of the target city at the (n+1)th moment within the specified time period is predicted. Based on the difference between the actual population distribution of the target city and the predicted population distribution of the target city, the parameters of the initial reinforcement learning model are updated to obtain the trained reinforcement learning model.

[0011] Optionally, based on the difference between the actual population distribution of the target city and the predicted population distribution of the target city, the parameters of the initial reinforcement learning model are updated to obtain a trained reinforcement learning model, including: The first loss value is obtained by substituting the difference between the actual population distribution of the target city and the predicted population distribution of the target city into the first loss function; Based on the first loss value, the parameters of the initial reinforcement learning model are updated to obtain the trained reinforcement learning model. The expression for the first loss function is:

[0012] in, Let be the population distribution error index at time t. The value range is [0,1]; The weight of the k-th spatial unit. Let N be the total population within the k-th spatial unit, and N be the total number of spatial units. The relative deviation of population distribution in the k-th spatial unit at time t. Let be the predicted population size of the k-th spatial unit at time t. Let ε be the actual population of the k-th spatial unit at time t, and let ε be a constant to prevent the denominator from being zero.

[0013] Optionally, based on the difference between the actual population distribution of the target city and the predicted population distribution of the target city, the parameters of the initial reinforcement learning model are updated to obtain a trained reinforcement learning model, including: The second loss value is obtained by substituting the difference between the actual population distribution of the target city and the predicted population distribution of the target city into the second loss function; Based on the second loss value, the parameters of the initial reinforcement learning model are updated to obtain the trained reinforcement learning model. The expression for the second loss function is:

[0014] in, A comprehensive population distribution error index for a specified time period; Let be the population distribution error index at time t. The value range is [0,1]; T represents the total number of spatial units.

[0015] Optionally, based on the rainfall observation sequences obtained from monitoring, the current spatial distribution of waterlogged areas in the target city can be determined, including: The rainfall observation sequences obtained from monitoring are input into the surface flood model and the underground drainage network model, respectively; The surface flood model was used to simulate the two-dimensional flood inundation distribution data at each time step, and the underground drainage network model was used to simulate the water depth data of the network nodes and the flow rate data of the pipe segments at each time step. The outputs of the surface flood model and the underground drainage network model are coupled and simulated to obtain the current spatial distribution of water accumulation mask in the target city.

[0016] Optionally, the target city is divided into spatial units to obtain the spatial unit division results of the target city, including: Based on the urban traffic network data of the target city, a topology connection graph is constructed, wherein the topology connection graph uses road intersections as nodes and road segments as edges; Based on the regional service main function data of the target city, obtain the dominant service function type code of each geographic grid; The city is divided into initial units by spatial gridding, the connection density of the transportation network in each initial unit is calculated, and adjacent initial units with connection densities higher than a set threshold are merged to form basic transportation units. According to the preset functional aggregation rules, spatially adjacent transportation infrastructure units are iteratively merged. The functional aggregation rules are: when the dominant service function type codes of two adjacent transportation infrastructure units are consistent, they are merged into a new functional area. Each functional area obtained at the end will be used as a spatial unit for urban analysis.

[0017] A second aspect of this application provides a spatially constrained system for calculating population exposure to flood disasters, the system comprising: The water accumulation mask spatial distribution determination module is used to determine the current water accumulation mask spatial distribution of the target city based on the rainfall observation sequence obtained from monitoring. The water accumulation mask spatial distribution refers to the water accumulation range and depth of the target city at the corresponding time. The risk avoidance action determination module is used to input the current multivariate state information of each resident into a pre-trained reinforcement learning model. Based on the estimation of the state transition probability distribution by the reinforcement learning model, it predicts and outputs the risk avoidance action to be performed by each resident. The current multivariate state information of the residents includes their spatial location, mobility speed, risk tolerance, and information perception intensity. The spatial location determination module is used to determine the spatial location of each resident at the next moment based on the risk avoidance actions currently performed by each resident as predicted. The population distribution determination module is used to determine the population distribution of each spatial unit of the target city at the next moment based on the spatial location of each resident at the next moment. The population exposure determination module is used to determine the flood disaster population exposure value of the target city at the target time based on the population distribution of each spatial unit of the target city at the target time; The expression for the state transition probability is:

[0018]

[0019] in, Let be the state transition probability of the i-th resident performing the m-th action at time t; For the i-th resident performing the m-th action at time t, the spatial risk-benefit ratio action score is given. The safety utility of the spatial unit where the i-th resident is located at time t; Let be the flood risk level of the i-th resident at time t. Let λ be the movement cost of the i-th resident performing the m-th action at the current spatial location at time t; λ is the spatial cost weight; and η is the theoretical intensity parameter used to control the individual's sensitivity to action rating. Let represent the action space of the i-th resident, which includes all actions that the i-th resident can perform.

[0020] The spatially constrained method for calculating population exposure to flood disasters provided in this application has the following advantages: This application provides a spatially constrained method for calculating population exposure to flooding. Based on monitored rainfall observation sequences, the spatial distribution of the flood cover in the target city is determined, where the distribution refers to the extent and depth of flooding in the target city at a given time. The current multivariate state information of each resident is input into a pre-trained reinforcement learning model. Based on the model's estimation of the state transition probability distribution, the method predicts the evacuation actions to be taken by each resident. The multivariate state information includes the resident's spatial location, mobility speed, risk tolerance, and information perception intensity. Based on the predicted evacuation actions, the spatial location of each resident at the next time step is determined. Based on the spatial location of each resident at the next time step, the population distribution of each spatial unit in the target city at the next time step is determined. Based on the population distribution of each spatial unit in the target city at the target time step, the flood exposure value of the target city at the target time step is determined.

[0021] The spatially constrained flood disaster population exposure calculation method provided in this application pre-trains a deployable reinforcement learning model. This application introduces population distribution error constraints, embedding the observed spatial distribution of the population in historical flood scenarios as a quantitative indicator into the dynamic modeling and reinforcement learning process. This allows simulation results to no longer rely solely on preset behavioral rules, but rather to adaptively calibrate using population distribution characteristics as the optimization objective, thereby significantly reducing the structural deviation between the model and reality.

[0022] Meanwhile, by comparing the real-world population distribution with the simulated population distribution in a grid and constructing a consistency evaluation index system, this application enables the model calibration process to have a more explicit mathematical objective function (such as the first loss function and the second loss function mentioned above), avoiding the uncertainty and subjectivity caused by relying on expert experience to adjust parameters in traditional methods, and ensuring the accuracy and verifiability of the simulation results.

[0023] By simultaneously characterizing the evolution of land inundation and the dynamic distribution of population at both the street and grid scales (such as constructing a topological connection map based on urban traffic network data of the target city and dividing it into spatial units), this application can output high spatiotemporal resolution results of population exposure distribution and refuge routes, reducing the error of existing methods in accurately characterizing population risk at the microscale. Attached Figure Description

[0024] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 A flowchart illustrating a spatially constrained method for calculating population exposure to flood disasters, as shown in one embodiment of this application; Figure 2 This is a schematic diagram illustrating the division of spatial units in a spatially constrained method for calculating population exposure to flood disasters, as shown in one embodiment of this application. Figure 3 This is a schematic diagram of population distribution in a spatially constrained method for calculating population exposure to flood disasters, as illustrated in one embodiment of this application. Figure 4 This is a schematic diagram illustrating the reward change of a reinforcement learning model in a spatially constrained method for calculating population exposure to flood disasters, as shown in one embodiment of this application. Figure 5 This is a schematic diagram illustrating a spatially constrained flood disaster population exposure calculation system, as shown in one embodiment of this application. Detailed Implementation

[0026] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0027] refer to Figure 1 , Figure 1 This is a flowchart illustrating a spatially constrained method for calculating population exposure to flood disasters, as shown in one embodiment of this application. Figure 1 As shown, the method includes: Step S01: Based on the rainfall observation sequence obtained from monitoring, determine the current spatial distribution of water accumulation mask in the target city. The spatial distribution of water accumulation mask refers to the range and depth of water accumulation in the target city at the corresponding time.

[0028] In this embodiment, for the target city to be analyzed, the rainfall observation sequence of the target city, which records the rainfall process data of the target city in chronological order, is used as input. Then, this rainfall observation sequence is input into a surface flood model (such as the Lisflood-FP model) and an underground drainage network model (such as the SWMM model) for coupled simulation to obtain the current spatial distribution of water accumulation mask in the target city. This spatial distribution of water accumulation mask records the water accumulation range and depth of the target city at various corresponding times in the past.

[0029] In this application, step S01 specifically includes the following sub-steps: Step S01_1: Input the obtained rainfall observation sequence into the surface flood model and the underground drainage network model respectively.

[0030] In this embodiment, the rainfall observation sequence of the target city up to the present time is first used as the input condition, and then the surface flood model and the underground drainage network model are input respectively.

[0031] Step S01_2: Simulate the two-dimensional flood inundation distribution data at each time step using the surface flood model, and simulate the water depth data of the pipe network nodes and the flow rate data of the pipe segments at each time step using the underground drainage pipe network model.

[0032] In this embodiment, during the coupled simulation of the surface flood model and the underground drainage network model, the surface flood model is used to simulate the surface flood inundation process within the city and watershed. Based on the urban topography, the flow path and water depth of the runoff formed by rainfall on the surface are accurately calculated to obtain two-dimensional flood inundation distribution data at each time step in the target city.

[0033] The underground drainage network model, based on the network structure, diameter, slope, and node characteristics of the urban drainage system, simulates the flow, inflow, and overflow of rainwater through the drainage network, enabling response analysis of the urban drainage system during flood events. This allows for the acquisition of network node water depth data and pipe segment flow data at each time step in the target city.

[0034] Step S01_3: Couple the output results of the surface flood model and the underground drainage network model to obtain the current spatial distribution of water accumulation mask in the target city.

[0035] In this embodiment, through the aforementioned coupled simulation method, this application can achieve a two-dimensional evolution simulation of the entire process of urban surface flooding, from rainfall formation, confluence, water accumulation to drainage. After the simulation is completed, the spatial distribution results of the water accumulation mask corresponding to each time step within the simulation period are further generated. These spatial distribution results reflect the water accumulation range and depth of the target city at different time points, providing a quantitative basis for urban flood risk assessment, drainage planning, and emergency evacuation decisions.

[0036] Step S02: Input the current multivariate state information of each resident into the pre-trained reinforcement learning model. Based on the estimation of the state transition probability distribution by the reinforcement learning model, predict and output the risk avoidance action to be performed by each resident. The current multivariate state information of each resident includes their spatial location, mobility speed, risk tolerance, and information perception intensity. The expression for the state transition probability is:

[0037]

[0038] in, Let be the state transition probability of the i-th resident performing the m-th action at time t; For the i-th resident performing the m-th action at time t, the spatial risk-benefit ratio action score is given. The safety utility of the spatial unit where the i-th resident is located at time t; The flood risk level is the spatial location of the i-th resident at time t, and the flood risk level is obtained based on the spatial distribution of the water accumulation mask. Let λ be the movement cost of the i-th resident performing the m-th action at the current spatial location at time t; λ is the spatial cost weight; and η is the theoretical intensity parameter used to control the individual's sensitivity to action rating. Let represent the action space of the i-th resident, which includes all actions that the i-th resident can perform.

[0039] In this embodiment, a deployable reinforcement learning model is pre-trained. By inputting the current multivariate state information of each resident in the target city into the pre-trained reinforcement learning model, the model predicts the avoidance actions to be taken by each resident based on its own estimation of the state transition probability distribution obtained during training. For example, resident A might move to the left from its current location to move to a safe haven (or low-risk area) on the left. In other words, the reinforcement learning model predicts which location each resident will move to in the future to avoid danger based on their current state, thereby predicting the future resident aggregation situation in each spatial unit.

[0040] The diverse status information of residents includes their spatial location, mobility speed, risk tolerance, and information perception intensity. Mobility speed is influenced by resident type; for example, adult men move faster, while adult women move slower. Residents' risk tolerance reflects their sensitivity to flood hazards (such as water depth and flow velocity) or their psychological resilience. Individual risk tolerance is set based on age and gender; for example, adult men have higher risk tolerance, adult women have lower risk tolerance, and the elderly have even lower risk tolerance, but elderly men tend to have higher risk tolerance than elderly women. Residents' information perception intensity describes their ability to acquire and process information about surrounding environmental risks and evacuation guidance, determined based on whether the individual has received flood warnings and their level of education. Let's assume that at time t, there are a total of [number missing] people in the city. There are i residents, and the state of the i-th resident is defined as follows: ,in,( () represents the spatial location of the i-th resident at time t. This represents the movable speed of the i-th resident at time t. This represents the risk tolerance of the i-th resident at time t. Let represent the information perception intensity of the i-th resident at time t.

[0041] The expression for the state transition probability in this reinforcement learning model is as follows:

[0042]

[0043] in, Let be the state transition probability of the i-th resident performing the m-th action at time t; For the i-th resident performing the m-th action at time t, the spatial risk-benefit ratio action score is given. The safety utility of the spatial unit where the i-th resident is located at time t; The flood risk level is the spatial location of the i-th resident at time t, and the flood risk level is obtained based on the spatial distribution of the water accumulation mask. Let λ be the movement cost of the i-th resident performing the m-th action at the current spatial location at time t; λ is the spatial cost weight, representing the regional cost weight that considers spatial distribution when selecting actions; η is the theoretical intensity parameter, used to control the individual's sensitivity to action ratings. Let represent the action space of the i-th resident, which includes all actions that the i-th resident can perform.

[0044] The safety utility in the expression for the state transition probability is affected by the maximum capacity of the spatial unit. Buildings have a man-made maximum capacity; as the number of people in the building increases, the spatial unit becomes crowded. When the spatial unit exceeds its maximum capacity, it cannot protect more residents seeking refuge. For residents seeking refuge, the safety utility of the spatial unit is 0, and they will no longer seek refuge there. That is, this application determines the safety utility of a spatial unit based on the relationship between its current capacity and its maximum capacity. When the current capacity of a spatial unit is close to its maximum capacity, the safety utility of that spatial unit is close to 0.

[0045] The flood risk in the expression for the state transition probability is represented by the mask depth, with greater depth indicating greater risk. Specifically, areas with a flood depth of less than 0.25 meters are considered to have no flood exposure risk and are not considered in the hierarchical statistical analysis of exposed subjects; areas with a water depth exceeding 0.25 meters but less than 0.75 meters are considered to have a slight exposure risk; areas with a water depth between 0.75 meters and 1.5 meters are considered to have a moderate exposure risk; and areas with a water depth between 1.5 meters and 2.5 meters are considered to have a severe exposure risk. Furthermore, any area with a water depth greater than 2.5 meters is considered to have an extremely severe flood exposure risk. In the actual prediction phase of the reinforcement learning model, the flood risk of each resident at a given time is determined based on the depth information recorded in the spatial distribution results of the flood mask in the target city over a period of time up to the present, obtained in step S01. For example, the flood risk of the i-th resident at time t is determined based on the spatial distribution of the flood mask at time t recorded in the spatial distribution results of the flood mask in the target city over a period of time up to the present.

[0046] The movement cost in the expression for the state transition probability is affected by the flooding depth before and after the movement. The deeper the flooding depth at the new location compared to the original location, the greater the movement cost. It can be calculated by dividing the flooding depth at the new location by the flooding depth at the current location.

[0047] Step S03: Based on the risk avoidance actions currently performed by each resident as predicted, determine the spatial location of each resident at the next moment.

[0048] In this embodiment, after predicting the current avoidance action of each resident based on their current multivariate state information in step S02, for any resident, the spatial location of that resident in the next moment can be obtained based on their current location and the predicted avoidance action. The spatial location of each resident in the next moment can be obtained in the same way. This application projects the spatial locations of residents at each moment during the simulation onto the corresponding locations in the target city to obtain the population spatial location information and distribution density characteristics of each spatial unit in the target city.

[0049] Step S04: Determine the population distribution of each spatial unit of the target city at the next moment based on the spatial location of each resident at the next moment.

[0050] In this embodiment, after obtaining the spatial location of each resident at the next moment through step S03, the spatial location of each resident at the next moment is statistically analyzed to obtain the population distribution of each spatial unit in the target city at the next moment. For example, based on the spatial location of each resident at the next moment, it is determined that 5028 people will gather in spatial unit a and 8032 people will gather in spatial unit b in the next moment.

[0051] Step S05: Based on the population distribution of each spatial unit of the target city at the target time, determine the flood disaster population exposure value of the target city at the target time.

[0052] In this embodiment, since the model can predict the spatial location of a resident at the next moment based on the input resident's state, the resident's state at that next moment is also predicted after the spatial location is predicted. By continuing to input the predicted state at the next moment into the model, the model can further predict the resident's state at the next even later moment. This process is repeated, and the model can predict the resident's state multiple time steps in the future based on the resident's state at the current moment. Since predictions at multiple time steps accumulate prediction errors, this application limits the maximum number of time steps that can be predicted. When the time step is 5 minutes, the maximum number of time steps is preferably 6, meaning that it can predict the resident's state at most one moment and its state at various moments in the next half hour.

[0053] For example, with a time step of 5 minutes and the current time being time t, based on the state of a resident at time t, the model can predict the state of the resident at the next time t+5 based on the state of the resident at time t. Then, based on the predicted state at time t+5, it can further predict the state at time t+10, and so on. The model can predict the state of a resident at a future time t+5n based on the state of the resident at time t.

[0054] In this embodiment, through steps S01 to S04, the population distribution of each spatial unit in the target city at multiple future time steps starting from the current time can be obtained. For example, if the current time is t, and the multiple future time steps include t+5n, where n takes values ​​of 1, 2, 3, 4, 5, and 6, then the population distribution of each spatial unit in the target city at six future time steps starting from the current time can be obtained. One of the time steps is selected as the target time, and then, based on the population distribution of each spatial unit in the target city at the target time, the flood exposure value of the target city at that target time is calculated.

[0055] The method provided in this application, under a given rainstorm-type flood disaster scenario, deploys a reinforcement learning model calibrated through reinforcement learning to dynamically simulate population behavior at different time stages after the flood occurs. In each simulation time step, each population agent autonomously determines whether to depart, its direction of movement, and its speed of movement based on its current location, the surrounding flooding status, accessible evacuation points, and individual decision-making strategies, thus forming a population migration, aggregation, and evacuation evolution process at the group scale. This process yields the temporal and spatial trajectory set and staged distribution status of the population throughout the disaster process, providing fundamental data for evacuation path analysis and exposure quantification.

[0056] In this application, a basic initial reinforcement learning model is first constructed. The process of training the initial reinforcement learning model to obtain a trained reinforcement learning model includes the following sub-steps: Step S001: Based on the historical rainfall observation sequence obtained within the specified time period, generate the spatial distribution of water accumulation mask in the target city at each moment within the specified time period.

[0057] In this embodiment, historical rainfall observation sequences within the time period of past urban flooding events are obtained based on these events. Using the same simulation method as described above, the spatial distribution of water accumulation masks in the city at various times within this specified time period (i.e., the time period of the flooding event) is obtained.

[0058] Step S002: Input the multivariate state information of each resident at the nth time within the specified time period into the initial reinforcement learning model. Based on the current estimate of the state transition probability distribution by the initial reinforcement learning model, predict and output the risk avoidance actions to be performed by each resident.

[0059] In this embodiment, the past flooding event in the city mentioned in step S001 is still used as the basis. In this flooding event, the multivariate state information of each resident in the city at the nth time within the specified time period (i.e., the time period during which the flood occurred) is obtained and input into the initial reinforcement learning model. Based on the current estimation of the state transition probability distribution by the initial reinforcement learning model, the avoidance actions to be performed by each resident are predicted and output. During the first training, since the model training has just begun, no state transition probability distribution has been estimated yet, and the state transition probability distribution at this time is the initial distribution state.

[0060] Step S003: Based on the risk avoidance actions performed by each resident as predicted, predict the spatial location of each resident at the (n+1)th moment within the specified time period.

[0061] In this embodiment, after predicting the avoidance action of each resident at the nth time based on the multivariate state information of each resident at the nth time through step S002, the spatial location of any resident at the (n+1)th time can be obtained based on the resident's location at the nth time and the predicted avoidance action at the nth time.

[0062] Step S004: Based on the predicted spatial location of each resident at the (n+1)th moment within the specified time period, predict the population distribution of each spatial unit of the target city at the (n+1)th moment within the specified time period.

[0063] In this embodiment, after obtaining the spatial location of each resident at time n+1 through step S003, the spatial location of each resident at time n+1 is statistically analyzed to obtain the population distribution of each spatial unit in the target city at time n+1.

[0064] Step S005: Based on the difference between the actual population distribution of the target city and the predicted population distribution of the target city, update the parameters of the initial reinforcement learning model to obtain the trained reinforcement learning model.

[0065] In this embodiment, the predicted population distribution of each spatial unit in the target city at each time point within the specified time period is compared with the corresponding actual population distribution to obtain the deviation between the predicted and actual population distribution results. Based on this deviation, the parameters of the initial reinforcement learning model are updated until the trained reinforcement learning model is obtained.

[0066] For example, the target city's spatial units include spatial units a and b, and the various moments within a specified time period include two moments: moment 1 and moment 2. The predicted population distribution of spatial unit a at moment 1 is compared with its actual population distribution at moment 1; simultaneously, the predicted population distribution of spatial unit a at moment 2 is compared with its actual population distribution at moment 2; and so on. Based on these four comparisons, the deviation between the predicted and actual population distribution results is determined.

[0067] To achieve temporal consistency between predicted population distribution data based on historical flood events and actual population distribution data from those historical flood events, the simulation data is resampled according to the time step set by the flood scenario. This resampling process adjusts the temporal resolution of the simulation data, ensuring it corresponds to the historical actual population distribution data at each time point. This synchronization of the two types of data across time scales provides a comparable basis for subsequent evacuation behavior analysis and flood risk assessment. In other words, the statistical time for the actual population distribution data from past flood events is fixed; for example, the actual population distribution data in the city is collected 10 minutes, 20 minutes, and 30 minutes after the historical flood event. Therefore, the final predicted population distribution data is also selected from the predicted population distribution data 10 minutes, 20 minutes, and 30 minutes after the historical flood event.

[0068] In this application, step S05 may include sub-steps S05_1 to S05_3: Step S05_1: Based on the population distribution and surface inundation depth of the j-th spatial unit of the target city at the m-th time before the target time, determine the population exposure load of the j-th spatial unit at the m-th time, where j takes the value from 1 to J and m takes the value from 1 to M.

[0069] In this embodiment, this application provides an optional method for calculating population exposure to flood disasters, as follows: Based on the population distribution and surface inundation depth predicted for the j-th spatial unit in the target city at the m-th time prior to the target time, the population exposure load of the j-th spatial unit at the m-th time is determined, where j ranges from 1 to J and m ranges from 1 to M. The expression for calculating the population exposure load is: ,in, This represents the predicted population size of the j-th spatial unit at the m-th time before the target time. This represents the surface inundation depth of the j-th spatial unit at the m-th time before the target time. This is a flood impact function used to characterize the amplification effect of surface inundation depth on exposure risk. Parameters for adjusting the impact of floods.

[0070] Step S05_2: Determine the cumulative population exposure of the j-th spatial unit at the target time based on the population exposure load of the j-th spatial unit at all times before the target time.

[0071] In this embodiment, after calculating the population exposure load of each spatial unit in the target city at each time point before the target time through step S05_1, the cumulative population exposure of the j-th spatial unit at the target time is calculated based on the population exposure load of the j-th spatial unit at all times before the target time. Through the same implementation method, each spatial unit can calculate its own corresponding cumulative population exposure. The expression for calculating the cumulative population exposure is: ,in, This represents the population exposure load of the j-th spatial unit at the m-th time before the target time. Z(j) represents the duration of the time step between two adjacent moments, such as 5 minutes as mentioned above, and Z(j) represents the cumulative population exposure of the j-th spatial unit.

[0072] Step S05_3: Based on the cumulative population exposure of all spatial units in the target city at the target time, determine the flood disaster population exposure value of the target city at the target time.

[0073] In this embodiment, after calculating the cumulative population exposure of all spatial units in the target city at the target time, the flood disaster population exposure value of the target city at that target time is calculated. The expression for calculating flood disaster population exposure value is: Where Z(j) represents the cumulative population exposure of the j-th spatial unit, and J represents the set of spatial units in the target city. This indicates the population exposure rate during floods.

[0074] In this application, the spatially constrained method for calculating population exposure to flood disasters also includes: Step S06: Determine the length of the evacuation path of the residents based on their evacuation trajectory from the starting time to the target time.

[0075] In this embodiment, the evacuation path length of each resident is calculated based on their evacuation trajectory from the start time to the target time. The predicted trajectory of the a-th resident is: ,in, Let represent the coordinates of the 'a'-th resident at time t. The expression for calculating the length of the evacuation path is:

[0076] Step S07: Determine the evacuation efficiency of the residents based on the length of their evacuation routes and the time they first enter the refuge point.

[0077] In this embodiment, the spatial locations of various refuge points in the target city are predefined. Based on the evacuation path length of a resident and the time of their first entry into a refuge point, the evacuation efficiency of that resident is calculated. Using the same implementation method, a corresponding evacuation efficiency can be calculated for each resident entering a refuge point. The calculation expression for evacuation efficiency is: ,in, Let be the length of the evacuation route for the 'a'th resident. Let α be the time when the a-th resident first enters any refuge point, α be the weighting coefficient of the path length and β be the weighting coefficient of the refuge time.

[0078] Step S08: Determine the total risk avoidance efficiency of the target city before the target time based on the risk avoidance efficiency of all residents in the target city before the target time.

[0079] In this embodiment, the total evacuation efficiency of the target city before the target time is calculated based on the evacuation efficiency of all residents in the target city before the target time. Residents who did not enter a refuge point before the target time will not have a corresponding evacuation efficiency value. The expression for calculating the total evacuation efficiency is: ,in, Let denot be the evacuation efficiency of the a-th resident. In the model application, resident evacuation efficiency will serve as a derived indicator of the simulation results, similar in function to the resident exposure indicator at each time step. Exposure is used to assess the impact of flood disasters on residents, while evacuation efficiency is used to assess the residents' response speed to flood disasters.

[0080] In this application, the spatially constrained method for calculating population exposure to flood disasters also includes: Step S02_01: Based on the current spatial location of each resident in the target city and the current spatial distribution of the water accumulation mask, determine the current danger perception index of each resident.

[0081] In this embodiment, to more accurately predict residents' evacuation actions, this application provides another evacuation action prediction method. In this method, the application assesses the danger perception index of each resident. For residents with a low danger perception index, it is determined that they will not perform evacuation actions and will remain in their current spatial location. Specifically, the current danger perception index of each resident is first calculated based on their current spatial location in the target city and the current spatial distribution of flooded shelters. Through the same implementation method, a corresponding danger perception index can be calculated for each resident.

[0082] The formula for calculating the danger perception index is: ,in, This represents the surface inundation depth at the spatial location of the i-th resident at time t. This represents the information perception intensity of the i-th resident. The danger perception index quantifies the strength of an individual's willingness to migrate from their current location. Based on the danger perception index, agent risk avoidance modeling is performed. When the danger perception index of the agent's location exceeds a threshold, the agent will travel along the road network to the nearest safe building for risk avoidance.

[0083] Step S02_02: Based on the relationship between each resident's current danger perception index and danger perception threshold, identify the target resident who will currently take avoidance actions from all residents.

[0084] In this embodiment, a hazard perception threshold is predefined. This threshold can be set according to the actual scenario and is not specifically limited here. Each resident's current hazard perception index is compared with the hazard perception threshold. Residents whose hazard perception index is greater than or equal to the threshold are identified as target residents who will currently take hazard avoidance actions. Using the same implementation method, all target residents in the target city can be identified.

[0085] In step S02_03: The current multivariate state information of the target resident is input into the pre-trained reinforcement learning model. Based on the estimation of the state transition probability distribution by the reinforcement learning model, the risk avoidance action to be performed by the target resident is predicted and output.

[0086] In this embodiment, the current multivariate state information of each target resident in the target city is finally input into the pre-trained reinforcement learning model. Based on the estimation of the state transition probability distribution by the reinforcement learning model, the risk avoidance action currently performed by each target resident is predicted and output.

[0087] For residents in the target city who are not currently part of the target population, it is determined that they will not take any evasive action at this time, and their spatial location will remain unchanged in the next moment. However, if, in the next moment, the danger perception index of these other residents begins to be greater than or equal to the danger perception threshold, then in subsequent predictions, their current multi-state information will be input into the pre-trained reinforcement learning model to predict evasive actions.

[0088] In this application, step S005 may include: calculating a first loss value by substituting the difference between the actual population distribution of the target city and the predicted population distribution of the target city into a first loss function; Based on the first loss value, the parameters of the initial reinforcement learning model are updated to obtain the trained reinforcement learning model. The expression for the first loss function is:

[0089] in, This is the population distribution error index at time t, used to quantify the degree of consistency between the predicted population distribution and the actual population distribution at different time steps. The value range is [0,1]; The weight of the k-th spatial unit. Let N be the total population within the k-th spatial unit, and N be the total number of spatial units. The relative deviation of population distribution in the k-th spatial unit at time t. Let be the predicted population size of the k-th spatial unit at time t. Let ε be the actual population of the k-th spatial unit at time t, and let ε be a constant to prevent the denominator from being zero.

[0090] In this embodiment, in one optional implementation, this application defines a first loss function. This first loss function is used to calculate the deviation between the actual population distribution and the predicted population distribution of the target city in each training round, obtaining a corresponding first loss value. Then, based on the obtained first loss value, the parameters of the initial reinforcement learning model are updated until a trained reinforcement learning model is obtained. In another optional implementation, when the deviation between the actual population distribution and the predicted population distribution of the target city in one training round is lower than a preset deviation threshold, the training is considered complete, and the reinforcement learning model can be directly deployed and applied.

[0091] This application uses vectorization to represent the actual and predicted populations of the divided spatial units. Let the actual population of the k-th spatial unit at time t be... The projected population is Then the population distribution vector is represented as:

[0092]

[0093] Where N is the number of spatial grid cells.

[0094] In this application, step S005 may include: calculating a second loss value by substituting the difference between the actual population distribution of the target city and the predicted population distribution of the target city into a second loss function; Based on the second loss value, the parameters of the initial reinforcement learning model are updated to obtain the trained reinforcement learning model. The expression for the second loss function is:

[0095] in, The comprehensive population distribution error index for a specified time period is used to quantify the overall degree of conformity between the predicted population distribution during the entire flood process and the actual population distribution in historical flood events. It serves as a constraint objective for population risk avoidance decision optimization and reinforcement learning training. Let be the population distribution error index at time t. The value range is [0,1]; T represents the total number of spatial units.

[0096] In this embodiment, in another optional implementation, this application defines a second loss function. This second loss function is used to calculate the deviation between the actual population distribution and the predicted population distribution of the target city in each training round, obtaining a corresponding second loss value. Then, based on the obtained second loss value, the parameters of the initial reinforcement learning model are updated until a trained reinforcement learning model is obtained. An optional implementation is that when the deviation between the actual population distribution and the predicted population distribution of the target city in one training round is lower than a preset deviation threshold, the training is complete, and the reinforcement learning model can be directly deployed and applied. Wherein, the second loss function... That is, the expression for the first loss function.

[0097] In this application, the target city is divided into spatial units to obtain the spatial unit division results of the target city, including: Step S01_01: Based on the urban traffic network data of the target city, construct a topology connection graph, wherein the topology connection graph uses road intersections as nodes and road segments as edges.

[0098] In this embodiment, urban traffic network data of the target city is obtained, and a topological connection graph with road intersections as nodes and road segments as edges is constructed based on the urban traffic network data.

[0099] Step S01_02: Based on the regional service main function data of the target city, obtain the dominant service function type code of each geographic raster.

[0100] In this embodiment, regional service main function data of the target city is obtained, and based on the regional service main function data, the dominant service function type code of each geographic grid in the target city is obtained.

[0101] Step S01_03: Divide the city into initial units through spatial gridding, calculate the connection density of the traffic network in each initial unit, and merge adjacent initial units with connection densities higher than a set threshold to form basic traffic units.

[0102] In this embodiment, the city is divided into initial units using a conventional spatial gridding basis. Then, the connection density of the transportation network within each initial unit is calculated, and adjacent initial units with a connection density higher than a set threshold are merged to form basic transportation units.

[0103] Step S01_04: According to the preset functional aggregation rules, spatially adjacent traffic infrastructure units are iteratively merged. The functional aggregation rules are: when the dominant service function type codes of two adjacent traffic infrastructure units are consistent, they are merged into a new functional area.

[0104] In this embodiment, the present application predefines a functional aggregation rule, which stipulates that when two adjacent traffic infrastructure units have the same dominant service function type code, they are merged into a new functional area. Then, based on the preset functional aggregation rule, spatially adjacent traffic infrastructure units are iteratively merged to form functional areas.

[0105] Step S01_05: Use each functional area obtained at the end as a spatial unit for urban analysis.

[0106] In this embodiment, each functional area obtained by merging is determined as a spatial unit for urban analysis, that is, one functional area is one spatial unit.

[0107] This application presents a spatially constrained method for calculating population exposure during floods, specifically for urban rainstorm and flood scenarios. Addressing the complexity and dynamism of population evacuation behavior at the micro-spatial scale, it constructs an evacuation simulation and decision optimization method centered on individual populations. Under spatiotemporal constraints within an urban street environment, this method dynamically simulates the population evacuation process and characterizes exposure risks. It enables the calibration and optimization of population evacuation decisions based on spatial distribution constraints, effectively improving the consistency between simulated evacuation behavior results and actual scenarios. This provides refined and quantifiable technical support for population evacuation risk assessment and emergency decision-making under urban flood disaster conditions.

[0108] The spatially constrained flood disaster population exposure calculation method provided in this application pre-trains a deployable reinforcement learning model. This application introduces population distribution error constraints, embedding the observed spatial distribution of the population in historical flood scenarios as a quantitative indicator into the dynamic modeling and reinforcement learning process. This allows simulation results to no longer rely solely on preset behavioral rules, but rather to adaptively calibrate using population distribution characteristics as the optimization objective, thereby significantly reducing the structural deviation between the model and reality.

[0109] Meanwhile, by comparing the real-world population distribution with the simulated population distribution in a grid and constructing a consistency evaluation index system, this application enables the model calibration process to have a more explicit mathematical objective function (such as the first loss function and the second loss function mentioned above), avoiding the uncertainty and subjectivity caused by relying on expert experience to adjust parameters in traditional methods, and ensuring the accuracy and verifiability of the simulation results.

[0110] By simultaneously characterizing the evolution of land inundation and the dynamic distribution of population at both the street and grid scales (such as constructing a topological connection map based on urban traffic network data of the target city and dividing it into spatial units), this application can output high spatiotemporal resolution results of population exposure distribution and refuge routes, reducing the error of existing methods in accurately characterizing population risk at the microscale.

[0111] This application uses population distribution error constraints as the core calibration mechanism. Its model parameters are no longer strongly bound to a specific region or single scenario, allowing for retraining and transfer using historical population data from different cities, thus possessing stronger cross-regional applicability. Specifically, a reinforcement learning model trained based on relevant data from historical flooding events in a city can be used to predict residents' evacuation actions for that city.

[0112] The following example illustrates the spatially constrained method for calculating population exposure to floods provided in this application.

[0113] First, based on urban transportation network data and regional service function data, the city is divided into spatial units, resulting in, for example: Figure 2 The spatial unit division results are shown.

[0114] To obtain population spatial distribution data at various points in time during a historical flood event in the city, this study aims to determine the population density information of each spatial unit within the city at each time point. Figure 3 As shown, Figure 3 This illustration shows the population distribution in various spatial units within a city at different times during a historical flood event.

[0115] Based on urban road network, building distribution, and initial population location data, a population intelligence agent set is constructed for the city. Each individual is assigned attributes such as location, mobility, risk tolerance, and information perception intensity, forming a population state expression system. Based on the flood inundation depth of this historical flood event, the flood hazard field is mapped to spatial units to drive the calculation of the population's risk avoidance intentions. At each simulation time step, the risk perception index of each population intelligence agent at its current location is calculated. When the risk perception intensity exceeds a set threshold, the corresponding population intelligence agent triggers risk avoidance behavior. The risk avoidance choices of the population intelligence agents are modeled as Markov decision processes, with their action space consisting of reachable road nodes or refuge building units.

[0116] By inputting multi-state information of population agents triggering evacuation behavior into a reinforcement learning model for simulation prediction, the spatial distribution of the population at each time step obtained from the simulation prediction is statistically analyzed and vectorized. Based on the comparison between the predicted population distribution and the actual population distribution, loss functions (such as the first loss function and the second loss function) are used as feedback signals for multi-agent reinforcement learning to iteratively optimize the initial departure time, evacuation target selection, and movement path of the population agents. Through this reinforcement learning training process, the decision-making strategy parameters of the population agents are continuously adjusted, so that the spatial distribution of the simulated population during the flood process gradually approximates the actual population distribution in a real flood event, ultimately obtaining a qualified reinforcement learning model. Figure 4 The diagram schematically illustrates the training rounds and model reward changes of the reinforcement learning model of this application. The loss function in the diagram is the second loss function mentioned above. The loss smoothing result is a smoothing result based on the distribution of the line graph loss function, used to show the overall trend of change.

[0117] The reinforcement learning model, calibrated through reinforcement learning, was applied to a rainstorm-induced flood disaster scenario to dynamically simulate the entire flood event. At each time step, each population agent autonomously executed departure, movement, and evacuation behaviors based on its location's inundation depth, accessible evacuation points, and its own decision-making strategy, forming a continuous spatiotemporal migration trajectory of the population. Based on the prediction simulation results, the evacuation path length and arrival time of each agent were extracted, and the population evacuation efficiency at the city scale was calculated. Simultaneously, population distribution and flood inundation distribution were coupled within a unified grid, and the population exposure load of each unit at different times was statistically analyzed and accumulated over time to obtain the spatial distribution results of population exposure at the city scale, which were used to evaluate the evacuation effectiveness and population risk level under different flood scenarios.

[0118] Based on the same inventive concept, this application provides a spatially constrained flood disaster population exposure calculation system, such as... Figure 5 As shown, the system 500 includes: The water accumulation mask spatial distribution determination module 501 is used to determine the current water accumulation mask spatial distribution of the target city based on the rainfall observation sequence obtained by monitoring. The water accumulation mask spatial distribution refers to the water accumulation range and depth of the target city at the corresponding time. The risk avoidance action determination module 502 is used to input the current multivariate state information of each resident into a pre-trained reinforcement learning model, and predict and output the risk avoidance action to be performed by each resident based on the estimation of the state transition probability distribution by the reinforcement learning model; wherein, the current multivariate state information of the resident includes its own spatial location, mobility speed, risk tolerance and information perception intensity. The spatial location determination module 503 is used to determine the spatial location of each resident at the next moment based on the risk avoidance actions currently performed by each resident as predicted. The population distribution determination module 504 is used to determine the population distribution of each spatial unit of the target city at the next moment based on the spatial location of each resident at the next moment. The population exposure determination module 505 is used to determine the flood disaster population exposure value of the target city at the target time based on the population distribution of each spatial unit of the target city at the target time; The expression for the state transition probability is:

[0119]

[0120] in, Let be the state transition probability of the i-th resident performing the m-th action at time t; For the i-th resident performing the m-th action at time t, the spatial risk-benefit ratio action score is given. The safety utility of the spatial unit where the i-th resident is located at time t; Let be the flood risk level of the i-th resident at time t. Let λ be the movement cost of the i-th resident performing the m-th action at the current spatial location at time t; λ is the spatial cost weight; and η is the theoretical intensity parameter used to control the individual's sensitivity to action rating. Let represent the action space of the i-th resident, which includes all actions that the i-th resident can perform.

[0121] It should be noted that, for the sake of simplicity, the method embodiments are all described as a series of actions. However, those skilled in the art should understand that the embodiments of this application are not limited to the described order of actions, because according to the embodiments of this application, some steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also understand that the embodiments described in the specification are all preferred embodiments, and the actions involved are not necessarily necessary for the embodiments of this application.

[0122] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0123] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, embodiments of this application can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of this application can take the form of computer program products implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0124] This application describes embodiments with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0125] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0126] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0127] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0128] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0129] The above provides a detailed description of the method and system for calculating population exposure to flood disasters based on spatial constraints. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for calculating population exposure to flood disasters based on spatial constraints, characterized in that, The method includes: Based on the rainfall observation sequence obtained from monitoring, the current spatial distribution of water accumulation mask in the target city is determined. The spatial distribution of water accumulation mask refers to the range and depth of water accumulation in the target city at the corresponding time. Each resident's current multivariate state information is input into a pre-trained reinforcement learning model. Based on the reinforcement learning model's estimation of the state transition probability distribution, the model predicts and outputs the risk avoidance actions that each resident will currently perform. The resident's current multivariate state information includes their spatial location, mobility speed, risk tolerance, and information perception intensity. Based on the risk avoidance actions currently performed by each resident as predicted, determine the spatial location of each resident at the next moment; Based on the spatial location of each resident at the next moment, determine the population distribution of each spatial unit of the target city at the next moment; Based on the population distribution of each spatial unit of the target city at the target time, determine the flood disaster population exposure value of the target city at the target time; The expression for the state transition probability is: in, Let be the state transition probability of the i-th resident performing the m-th action at time t; For the i-th resident performing the m-th action at time t, the spatial risk-benefit ratio action score is given. The safety utility of the spatial unit where the i-th resident is located at time t; The flood risk level is the spatial location of the i-th resident at time t, and the flood risk level is obtained based on the spatial distribution of the water accumulation mask. Let λ be the movement cost of the i-th resident performing the m-th action at the current spatial location at time t; λ is the spatial cost weight; and η is the theoretical intensity parameter used to control the individual's sensitivity to action rating. Let represent the action space of the i-th resident, which includes all actions that the i-th resident can perform.

2. The method for calculating population exposure to flood disasters based on spatial constraints according to claim 1, characterized in that, Based on the population distribution of each spatial unit of the target city at the target time, determine the flood exposure value of the target city at the target time, including: Based on the population distribution and surface inundation depth of the j-th spatial unit of the target city at the m-th time before the target time, determine the population exposure load of the j-th spatial unit at the m-th time, where j takes values ​​from 1 to J and m takes values ​​from 1 to M. Based on the population exposure load of the j-th spatial unit at all times before the target time, determine the cumulative population exposure of the j-th spatial unit at the target time; Based on the cumulative population exposure of all spatial units in the target city at the target time, the flood disaster population exposure value of the target city at the target time is determined.

3. The method for calculating population exposure to flood disasters based on spatial constraints according to claim 1, characterized in that, The method further includes: Based on the evacuation trajectories of residents from the starting time to the target time, the length of the evacuation path of the residents is determined; The evacuation efficiency of the residents is determined based on the length of their evacuation routes and the time they first enter the refuge area. The total risk avoidance efficiency of the target city before the target time is determined based on the risk avoidance efficiency of all residents in the target city before the target time.

4. The method for calculating population exposure to flood disasters based on spatial constraints according to claim 1, characterized in that, The method further includes: Based on the current spatial location of each resident in the target city and the current spatial distribution of the water accumulation mask, determine the current danger perception index of each resident. Based on the relationship between each resident's current risk perception index and risk perception threshold, target residents who will currently take evasive action are identified from all residents. By inputting the current multivariate state information of the target resident into a pre-trained reinforcement learning model, and based on the estimation of the state transition probability distribution by the reinforcement learning model, the risk avoidance action to be performed by the target resident is predicted and output.

5. The method for calculating population exposure to flood disasters based on spatial constraints according to claim 1, characterized in that, By training the initial reinforcement learning model, a trained reinforcement learning model is obtained, including: Based on the historical rainfall observation sequence obtained within a specified time period, the spatial distribution of water accumulation mask in the target city at each moment within the specified time period is generated. The multivariate state information of each resident at the nth time within the specified time period is input into the initial reinforcement learning model. Based on the current estimate of the state transition probability distribution by the initial reinforcement learning model, the risk avoidance actions to be performed by each resident are predicted and output. Based on the risk avoidance actions performed by each resident as predicted, the spatial location of each resident at the (n+1)th moment within the specified time period is predicted. Based on the predicted spatial location of each resident at the (n+1)th moment within the specified time period, the population distribution of each spatial unit of the target city at the (n+1)th moment within the specified time period is predicted. Based on the difference between the actual population distribution of the target city and the predicted population distribution of the target city, the parameters of the initial reinforcement learning model are updated to obtain the trained reinforcement learning model.

6. The method for calculating population exposure to flood disasters based on spatial constraints according to claim 5, characterized in that, Based on the difference between the actual population distribution and the predicted population distribution of the target city, the parameters of the initial reinforcement learning model are updated to obtain a trained reinforcement learning model, including: The first loss value is obtained by substituting the difference between the actual population distribution of the target city and the predicted population distribution of the target city into the first loss function; Based on the first loss value, the parameters of the initial reinforcement learning model are updated to obtain the trained reinforcement learning model. The expression for the first loss function is: in, Let be the population distribution error index at time t. The value range is [0,1]; The weight of the k-th spatial unit. Let N be the total population within the k-th spatial unit, and N be the total number of spatial units. The relative deviation of population distribution in the k-th spatial unit at time t. Let be the predicted population size of the k-th spatial unit at time t. Let ε be the actual population of the k-th spatial unit at time t, and let ε be a constant to prevent the denominator from being zero.

7. The method for calculating population exposure to flood disasters based on spatial constraints according to claim 5, characterized in that, Based on the difference between the actual population distribution and the predicted population distribution of the target city, the parameters of the initial reinforcement learning model are updated to obtain a trained reinforcement learning model, including: The second loss value is obtained by substituting the difference between the actual population distribution of the target city and the predicted population distribution of the target city into the second loss function; Based on the second loss value, the parameters of the initial reinforcement learning model are updated to obtain the trained reinforcement learning model. The expression for the second loss function is: in, A comprehensive population distribution error index for a specified time period; Let be the population distribution error index at time t. The value range is [0,1]; T represents the total number of spatial units.

8. The method for calculating population exposure to flood disasters based on spatial constraints according to claim 1, characterized in that, Based on the rainfall observation sequences obtained from monitoring, the current spatial distribution of waterlogging cover in the target city is determined, including: The rainfall observation sequences obtained from monitoring are input into the surface flood model and the underground drainage network model, respectively; The surface flood model was used to simulate the two-dimensional flood inundation distribution data at each time step, and the underground drainage network model was used to simulate the water depth data of the network nodes and the flow rate data of the pipe segments at each time step. The outputs of the surface flood model and the underground drainage network model are coupled and simulated to obtain the current spatial distribution of water accumulation mask in the target city.

9. The method for calculating population exposure to flood disasters based on spatial constraints according to claim 1, characterized in that, The target city is divided into spatial units to obtain the spatial unit division results, including: Based on the urban traffic network data of the target city, a topology connection graph is constructed, wherein the topology connection graph uses road intersections as nodes and road segments as edges; Based on the regional service main function data of the target city, obtain the dominant service function type code of each geographic grid; The city is divided into initial units by spatial gridding, the connection density of the transportation network in each initial unit is calculated, and adjacent initial units with connection densities higher than a set threshold are merged to form basic transportation units. According to the preset functional aggregation rules, spatially adjacent transportation infrastructure units are iteratively merged. The functional aggregation rules are: when the dominant service function type codes of two adjacent transportation infrastructure units are consistent, they are merged into a new functional area. Each functional area obtained at the end will be used as a spatial unit for urban analysis.

10. A spatially constrained system for calculating population exposure to flood disasters, characterized in that, The system includes: The water accumulation mask spatial distribution determination module is used to determine the current water accumulation mask spatial distribution of the target city based on the rainfall observation sequence obtained from monitoring. The water accumulation mask spatial distribution refers to the range and depth of water accumulation in the target city at the corresponding time. The risk avoidance action determination module is used to input the current multivariate state information of each resident into a pre-trained reinforcement learning model, and predict and output the risk avoidance action to be performed by each resident based on the estimation of the state transition probability distribution by the reinforcement learning model; wherein, the current multivariate state information of the resident includes its own spatial location, mobility speed, risk tolerance and information perception intensity. The spatial location determination module is used to determine the spatial location of each resident at the next moment based on the risk avoidance actions currently performed by each resident as predicted. The population distribution determination module is used to determine the population distribution of each spatial unit of the target city at the next moment based on the spatial location of each resident at the next moment. The population exposure determination module is used to determine the flood disaster population exposure value of the target city at the target time based on the population distribution of each spatial unit of the target city at the target time; The expression for the state transition probability is: in, Let be the state transition probability of the i-th resident performing the m-th action at time t; For the i-th resident performing the m-th action at time t, the spatial risk-benefit ratio action score is given. The safety utility of the spatial unit where the i-th resident is located at time t; Let be the flood risk level of the i-th resident at time t. Let λ be the movement cost of the i-th resident performing the m-th action at the current spatial location at time t; λ is the spatial cost weight; and η is the theoretical intensity parameter used to control the individual's sensitivity to action rating. Let represent the action space of the i-th resident, which includes all actions that the i-th resident can perform.

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