A sponge city rain flood and waterlogging evolution resilience index system evaluation method

Abstract

The steps of the index system evaluation method for the evolution of sponge city rain flood waterlogging resilience are as follows: 1, collecting modeling basic data for modeling, obtaining indexes varying with rain flood time in bearing, adaptation and recovery stages; meanwhile, selecting indexes invariable in each stage, obtaining comprehensive indexes of rain flood waterlogging resilience evaluation of the research area in each stage; 2, establishing a directed topological network of comprehensive indexes in each stage; 3, based on the directed topological network, mapping the relationship of comprehensive indexes in each stage into effective one-dimensional dynamics respectively, predicting the response of the evolution of sponge city rain flood waterlogging resilience system to each index in the comprehensive index and positioning the index of the system losing resilience; 4, calculating the resilience centrality of each index; 5, cyclically executing steps 1-4 to predict the different disturbance response of the evolution of sponge city rain flood waterlogging resilience system to the comprehensive indexes of rain flood waterlogging resilience evaluation in bearing, adaptation and recovery stages. The present application can improve the accuracy of the resilience level evaluation of the sponge city.

Description

Technical Field

[0001] This invention belongs to the field of sponge city construction technology and relates to an index system evaluation method for the resilience of sponge cities in responding to the evolution of rainwater and urban flooding. Background Technology

[0002] Since the beginning of the 21st century, global climate change has been abnormal, extreme weather events have become more frequent, urbanization has accelerated, and urban flooding and waterlogging have become prominent problems, urgently requiring improvements in urban flood control capabilities. The resilience of sponge city systems refers to a city's ability to adjust its activities to maintain its basic functions in the face of environmental changes such as rainstorm disasters, and it is widely used to analyze, understand, and improve urban disaster response. While research on the conceptual connotation and extension of resilience is abundant, quantitative research is quite scarce. Existing resilience assessment methods can be divided into two categories: one is resilience analysis based on flood resilience indices, emphasizing the dynamic evolution within the system; the other is the indicator system method, which uses key variable indicators, meta-indicators, etc., to describe the system. The latter is the most typical method for resilience capacity assessment. However, the sponge city's stormwater and waterlogging evolution resilience system consists of multiple indicators, which participate in the global state through highly complex interaction patterns. Furthermore, the indicators change significantly over time during the resilience evolution process, making it a multidimensional dynamic process. Although multidimensional factors are carefully considered, current methods still focus more on static physical facilities, lacking process-based resilience considerations; or current dynamic analyses struggle to handle the complexity and nonlinear effects of the numerous interacting indicators in a multidimensional system. Summary of the Invention

[0003] To address the problems of the existing technologies, this invention provides a method for assessing the resilience of sponge cities in response to the evolution of stormwater and urban flooding, specifically addressing the limitations of the existing framework for assessing the resilience of sponge cities in handling multidimensional systems composed of numerous interacting components. The aim is to determine a comprehensive indicator system by combining domestic and international guidelines for selecting resilience indicators with the characteristics of the study area. The resilience assessment is divided into three stages according to the sub-storm flooding process: bearing capacity, adaptation, and recovery. Furthermore, it fully considers the multi-scale and complex interactions of the indicators during flood evolution, thereby enabling scientific quantitative guidance and improving the resilience of sponge city systems in controlling stormwater and urban flooding processes.

[0004] To achieve the above objectives, the specific solution of the present invention is as follows:

[0005] An index system assessment method for the resilience of sponge cities in responding to the evolution of urban flooding includes the following steps:

[0006] Step 1: Calculate the design rainfall with a return period of 0.25 years to 100 years for the study area and allocate the time history. Divide the study area into sub-catchments according to the watershed, community, and household scales. Collect the basic data for SWMM modeling. Couple the SWMM model and the LISFLOOD-FP model to obtain the stormwater resilience assessment index of the study area at the current urban level year during the carrying capacity, adaptation, and recovery stages, which varies with the stormwater time. Select and statistically analyze the stormwater resilience assessment index of the study area at the current urban level year during the carrying capacity, adaptation, and recovery stages, which does not vary with the stormwater time. Finally, obtain the comprehensive index of stormwater resilience assessment of the study area at the current urban level year during the carrying capacity, adaptation, and recovery stages.

[0007] Step 2: Examine the relationship between the comprehensive indicators of stormwater and urban flood resilience assessment in the carrying capacity, adaptation and recovery stages. Use the DEMATEL-ISM method to establish directed topological networks of the comprehensive indicators of stormwater and urban flood resilience assessment in the carrying capacity, adaptation and recovery stages respectively.

[0008] Step 3: Based on the directed topological network of the comprehensive indicators for stormwater and urban flood resilience assessment in Step 2 during the carrying, adaptation and recovery stages, the relationship between the comprehensive indicators for stormwater and urban flood resilience assessment in the carrying, adaptation and recovery stages is mapped into effective one-dimensional dynamics, predicting the response of the sponge city stormwater and urban flood resilience evolution system to the action of each indicator in the comprehensive indicators for stormwater and urban flood resilience assessment and locating the indicators in which the system loses resilience.

[0009] Step 4: Define the change in resilience of the sponge city stormwater and waterlogging evolution resilience system caused by the removal of indicators that have lost resilience from the comprehensive index of stormwater and waterlogging resilience assessment as resilience centrality, and calculate the resilience centrality of each indicator.

[0010] Step 5: Based on different target level years and different catchment areas in the study area, set resilience enhancement targets for the sponge city stormwater and urban flooding evolution resilience system. Execute steps 1-4 cyclically to predict the different disturbance responses of the sponge city stormwater and urban flooding evolution resilience system to the comprehensive indicators of stormwater and urban flooding resilience assessment in the carrying, adaptation, and recovery stages. Propose intervention strategies to avoid resilience loss, forming a feedback loop from the current situation to development and then to the target level for the sponge city stormwater and urban flooding evolution resilience system resilience enhancement process.

[0011] Furthermore, the comprehensive index for assessing stormwater and urban flooding resilience described in step 1 includes the following steps:

[0012] Step 11: The design rainfall for each return period is calculated using the urban calculation formula for the study area. The time history allocation is based on the Chicago rainfall pattern. The study area is divided into sub-catchment zones according to watershed, community, and household. The comprehensive information of hydrological and meteorological data, land use data of underlying surface, digital elevation model, drainage network and road network infrastructure data of the current urban level year of the study area is obtained and processed using ArcGIS software to obtain the SWMM model modeling parameters.

[0013] Step 12: Generate an .inp file from the SWMM modeling parameters and the design storm data with a return period of 0.25a-100a in Step 11. Open the .inp file with SWMM software and add a rain gauge in SWMM to complete the simulation of design rainfall with a return period of 0.25a-100a in the study area.

[0014] Step 13: Compile the simulation results of design rainfall over a return period of 0.25a-100a for the study area described in Step 12 into .ascii, .par, .bci, and .bdy files. The .ascii file is the terrain file, the .par file contains the required files and parameter files for the model, and the .bci and .bdy files contain the overflow node numbers and flow processes of the SWMM model. This completes the coupled modeling of the SWMM model and the LISFLOOD-FP model to obtain the urban current status level of the study area under the carrying, adaptation, and recovery stages, as measured by rainfall and flood time. These indicators include: under the carrying stage, road exposure index x1, building exposure level x2, inundation depth index x3, cumulative water depth index x4, flood flow velocity x5, drainage capacity of the pipe network x6, duration of flood events x7, and waterlogging rate index x8; under the adaptation stage, disaster loss rate x9, number of directly affected people x9, and other indicators. 11 Flood severity x 13 Total flood depth x 14 Total flood time x 15 Maximum flood flow velocity x 16 Pipeline drainage capacity x 17 and maximum water accumulation rate x 18 The persistence factor x during the recovery phase 25 ;

[0015] Step 14: Select an assessment index for urban flood resilience in the statistical study area that does not change with rainfall duration during the carrying, adaptation, and recovery phases; including the number of families with children in the adaptation phase. 10 Elderly population index x 12 Emergency shelter space during the recovery phase (x) 19 Public transportation service capacity x 20 Regional medical facility density x 21 Medical insurance coverage rate x 22 Road density x23 Subway station density x 24 The proportion of blue-green space area x 26 and considering the external discharge and storage volume x 27 .

[0016] Step 15, combining steps 13 and 14, finally obtains the comprehensive index x1 to x2, representing the urban current status level of the study area in the carrying, adaptation, and recovery stages, assessing its resilience to stormwater flooding. 27 .

[0017] Furthermore, the steps for establishing directed topological networks for the comprehensive index of stormwater flood resilience assessment in the carrying capacity, adaptation, and recovery stages using the DEMATEL-ISM method are as follows:

[0018] Step 21, determine the comprehensive index x for comparing stormwater and urban flooding resilience assessment. i For index x j The direct influence matrix A is obtained, and the normalized direct influence matrix B is obtained by normalizing the original relations; the comprehensive influence matrix T and the influence degree D of each indicator are calculated respectively. i Influence level C i Centrality M i and causal degree R i ;

[0019] Step 22: Combine the overall influence matrix T with the identity matrix I to determine the overall influence matrix E. Introduce a threshold λ to process the elements in matrix E and calculate the reachability matrix F.

[0020] Step 23, calculate the reachable level R(x) i ) and the antecedent set S(x) i If R(x) i ) and S(x i ) satisfies R(x) i )∩S(x i )=R(x i When ), it means R(x) i The corresponding indicator x in ) i All can be in S(x i The antecedent can be found in the indicator x. i For indicators at higher levels, the corresponding rows and columns in the reachable matrix are removed. Then, the highest-level indicator is extracted from the remaining matrix. This process is repeated until all rows and columns are removed. Based on the order in which the indicators are removed, a multi-level hierarchical directed topology graph of the sponge city stormwater and urban flooding evolution resilience system indicators is drawn.

[0021] Furthermore, the formula for the direct influence matrix is ​​as follows:

[0022]

[0023] Where: index x ij (i = 1, 2, ..., m; j = 1, 2, ..., n; i ≠ j) represents the index x. i For x j The direct impact; if i = j, then x ij =0;

[0024] The formula that directly affects matrix B according to the specification is as follows:

[0025]

[0026] The formula for the comprehensive influence matrix T is as follows:

[0027]

[0028] In the formula: I is the identity matrix;

[0029] The influence degree D of each indicator i Influence level C i Centrality M i and causal degree R i The calculation formulas are as follows;

[0030]

[0031]

[0032] M i =D i +C i

[0033] R i =D i -C i

[0034] In the formula: the influence degree Di is the sum of the values ​​in each row of T; the degree of influence Ci is the sum of the values ​​in each column of T;

[0035] The determination of the overall influence matrix E = [e ij ] n×n The calculation formula is:

[0036] E = I + T,

[0037] The reachability matrix F = [f ij ] n×n A threshold λ needs to be introduced to process the elements in matrix E; the value of this threshold will be determined by experts based on the specific circumstances. The matrix F = [f ij ] n×n The calculation formula is:

[0038] F = [f ij ]n×n ,

[0039]

[0040] The reachable level R(x) i The factor is obtained by using the column with a value of 1 in the i-th row of the reachability matrix F, as shown in the formula:

[0041] R(x i )={x i |F ij =1}

[0042] The preceding set S(x) i The factor is obtained by using the factors corresponding to the column with a value of 1 in the i-th column of the reachability matrix F, as shown in the formula:

[0043] S(x i )={x i |F ij =1}

[0044] Furthermore, the effective one-dimensional dynamic equation described in step 4 is as follows:

[0045]

[0046] In the formula: the average value x is used in the dimensionality reduction process. eff The effective state nearest neighbor activity of 27 indicators in the comprehensive resilience assessment index for sponge city stormwater and urban flooding evolution is calculated as follows: Weighted connection matrix A ij Capturing the positive interactions among comprehensive indicators for assessing stormwater and urban flooding resilience, representing the interaction between indicator x in a directed topological network. j To index x i The weight of a directed edge is 0 if there is no such edge; β eff It is an equivalent control parameter that measures the impact of the directed topological network structure formed by the comprehensive index of the resilience assessment of the sponge city's stormwater and urban flooding evolution resilience system on the resilience model of the sponge city's stormwater and urban flooding evolution resilience system. It is calculated as follows: Weighted connection matrix A ji Capturing the positive interactions among comprehensive indicators for assessing stormwater and urban flooding resilience, representing the interaction between indicator x in a directed topological network. i To index x j The weight of a directed edge is 0 if there is no such edge; F(x) eff ) and G(x eff ,x eff ) respectively represent the self-dynamics and interaction dynamics of each indicator in the comprehensive index for assessing the resilience of rainwater and urban flooding after dimensionality reduction.

[0047] Furthermore, the change in resilience of the sponge city stormwater flooding evolution resilience system caused by removing the indicators in step 5 is defined as resilience centrality. The specific steps for calculating the resilience centrality of each indicator in the comprehensive index of stormwater flooding resilience assessment using the GBB dimensionality reduction theory of system dynamics are as follows:

[0048] Step 51, removing the β caused by the comprehensive index of stormwater and urban flooding resilience assessment. eff Change is defined as resilience centrality, with the index x i resilience center for:

[0049]

[0050] Where: β eff and These represent the original network and the network with the metric x removed, respectively. i The original network,

[0051] Step 52, for β eff Normalizing the changes yields the resilience center R. i The formula is as follows:

[0052]

[0053] Step 53: Simplify using a first-order approximation of the Taylor expansion. The value of . Since the average degree of most networks is much greater than 1, under the assumption... In this case, the simplified form of resilience centrality is:

[0054]

[0055] Where: Weighted connection matrix A ij This indicates that in a directed topology network, from index x... j To index x i The weight of a directed edge is 0 if there is no such edge; the weighted connectivity matrix A ji This indicates that in a directed topology network, from index x... i To index x j The weight of a directed edge is 0 if there is no such edge. In a directed topology network, x represents a pointer to an index. i The number of edges; This indicates that in a directed topology network, from index x... i The number of edges indicated. In a directed topology network, x represents a pointer to an index. j The number of edges; This indicates that in a directed topology network, from index x... j The number of edges indicated.

[0056] Step 54: After adjusting the initial state of the comprehensive index for assessing the resilience of sponge city stormwater and urban flooding evolution system during the carrying capacity stage, delete the comprehensive index x for stormwater and urban flooding resilience assessment separately. i A new network is constructed, and the resilience centrality of each indicator is calculated.

[0057] Step 55: After adjusting the initial state of the comprehensive index for assessing the resilience of sponge city stormwater and urban flooding evolution system during the carrying capacity stage, delete the comprehensive index x for assessing the resilience of stormwater and urban flooding separately. i A new network was constructed to calculate the resilience centrality of each indicator, thereby quantifying the resilience of indicators in the sponge city stormwater and urban flooding evolution resilience system.

[0058] Advantages of the present invention

[0059] This invention provides an index system assessment method for the resilience of sponge cities in response to the evolution of stormwater and urban flooding. This method involves the hydrological and hydrodynamic mechanisms in the comprehensive assessment of sponge city resilience. The GBB dimensionality reduction theory maps the dynamics of high-dimensional systems into effective one-dimensional dynamics and fully considers the dynamic and complex interaction relationships of comprehensive evaluation indicators during flood evolution. It can not only accurately predict the response of the sponge city's stormwater and urban flooding resilience system to disturbances of each comprehensive stormwater and urban flooding resilience assessment index in each of the three stages of stormwater and urban flooding carrying capacity, adaptation, and recovery, but also quantify the resilience capacity of the indicators in the sponge city's stormwater and urban flooding resilience system. Furthermore, it can correctly locate the indicators in the sponge city's stormwater and urban flooding resilience system that have lost resilience. It has the role of providing scientific quantitative guidance and improving the resilience of sponge cities in controlling stormwater and urban flooding processes. Attached Figure Description

[0060] Figure 1 This is a flowchart of the evaluation method for the index system of sponge city resilience to the evolution of rainwater and urban flooding, as proposed in this invention.

[0061] Figure 2 yes Figure 1 Simulated runoff spatial distribution map of different return periods of design rainstorm scenarios in the central study area.

[0062] Figure 3 yes Figure 1 Simulated spatial distribution map of urban flooding under different return periods of design rainstorm scenarios in the central study area.

[0063] Figure 4 yes Figure 1 The directed topological network of comprehensive indicators for assessing the resilience of sponge city stormwater and urban flooding evolution in the central study area during the carrying, adaptation, and recovery stages.

[0064] Figure 5 yes Figure 1The network resilience of the carrying-stage in the stormwater and urban flooding evolution resilience system of sponge cities. Figure 5 The three-dimensional diagrams A, B, and C show the resilience planes of the comprehensive indicators for stormwater and urban flooding resilience assessment at the load-bearing stage, specifically the four indicators x1, x4, x6, and x7. Figure 5 The dynamic interaction of the four indicators x1, x4, x6, and x7 of D in practice, after applying the GBB theory dimensionality reduction method, combined with... Figure 5 The directed network topology of the bearer stage in the F-multidimensional system is composed of... Figure 5 The multidimensional manifolds shown in A, B, and C collapse as follows: Figure 5 A one-dimensional toughness function in the β space of E.

[0065] Figure 6 yes Figure 1 A schematic diagram of resilience centrality. (a) shows the directed topological network structure of the comprehensive index for the bearing stage of the stormwater and urban flooding resilience assessment in the sponge city stormwater and urban flooding evolution resilience system; (b) shows the resilience function of the directed topological network. The comprehensive index for stormwater and urban flooding resilience assessment is removed from (a) respectively, and the failure of each index is simulated to create a new network. The x-value of each network is then calculated. eff and β eff (c) Network mapping based on resilience centrality, where the magnitude of the index corresponds to its resilience centrality; (d) Performance of resilience centrality. Detailed Implementation

[0066] The present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. It should be noted that the specific embodiments are not intended to limit the scope of the present invention.

[0067] like Figure 1 As shown in the figure, a method for evaluating the resilience of sponge cities to the evolution of stormwater and urban flooding according to a specific embodiment includes the following steps: Step 1, obtaining the comprehensive index for stormwater and urban flooding resilience evaluation, includes the following steps:

[0068] Step 1: Using the latest urban storm intensity formula for the study area, calculate the design storms with return periods of 0.25 years to 50 years, and use the Chicago method to allocate the design storm time histories, obtaining the design storm process lines for each return period in the study area. Using ArcGIS software, acquire and process hydrological and meteorological data, land use data of the underlying surface, digital elevation model data, drainage network data, and road network infrastructure data for the current urban status year in the study area. This allows for the acquisition of SWMM model modeling parameters, enabling coupled modeling of the SWMM model and the LISFLOOD-FP model. This yields the stormwater resilience assessment index for the study area's current urban status year during the carrying capacity, adaptation, and recovery stages, varying with stormwater duration. Select and statistically analyze the stormwater resilience assessment index for the study area's current urban status year during the carrying capacity, adaptation, and recovery stages, which does not vary with stormwater duration. Finally, obtain the comprehensive stormwater resilience assessment index for the study area's current urban status year during the carrying capacity, adaptation, and recovery stages.

[0069] Step 11, this specific embodiment takes Nanning City as an example. The latest rainstorm intensity formula for Nanning City is as follows:

[0070]

[0071] In the formula: q represents the design rainfall intensity, L / (s*ha); P represents the design rainfall return period, y; t represents the design rainfall duration, min.

[0072] Design storms with return periods of 0.25a, ​​0.5a, 1a, 2a, 3a, 5a, 10a, 20a, 30a and 50a were calculated for the Zhupaichong watershed in Nanning City. The rainfall time series was distributed using the Chicago rainfall pattern with a duration of 120 minutes, and the 2-hour cumulative rainfall of the design storms for each return period was finally obtained.

[0073] Combining DEM hydrological analysis and high-definition remote sensing image manual identification, and taking into account the distribution of roads, buildings and pipelines on the underlying surface, the Zhupaichong watershed in Nanning City was divided into 124 sub-catchment zones, with the area of ​​each sub-catchment zone ranging from 8.19 to 179.19 hectares. Step 1 using ArcGIS software involves acquiring and processing comprehensive information on the urban status quo of the study area, including hydrological and meteorological data, land use data of the underlying surface, digital elevation model, drainage network data, and road network infrastructure data for the current year. This process yields information on the distribution of sub-catchments and the main drainage network in the study area, as well as key parameters for arranging stormwater pipes based on road elevation and slope. Specifically, the total length of the main stormwater pipeline in the study area is generalized to 141.95 km, comprising 476 pipe sections with an average length of 237.78 m. 476 stormwater wells are installed at a depth of 2.2 m. The main pipe diameter ranges from 800 mm to 2800 mm, and the pipe roughness coefficient is 0.013. A total of 48 drainage outlets are located in the study area, with an overall design storm return period of 2 years.

[0074] Step 12: Generate a .inp file using the SWMM modeling parameters obtained in Step 11 and the design rainfall data for various return periods (0.25a, ​​0.5a, 1a, 2a, 3a, 5a, 10a, 20a, 30a, 50a) for the study area. Open this file with SWMM software, add a rain gauge in SWMM, set the simulation options, and after modeling, simulate rainfall for different return periods for the entire study area. The simulated runoff spatial distribution of different return period design rainfall scenarios in the Zhupaichong watershed is shown below. Figure 2 As shown.

[0075] Step 13: Configure the design rainfall simulation results for each return period (0.25a, ​​0.5a, 1a, 2a, 3a, 5a, 10a, 20a, 30a, and 50a) of the study area, run using SWMM software in Step 12, into a LISFLOOD-FP .bdy file. Simultaneously, configure the .ascii, .bci, and .par files for the LISFLOOD-FP software in the Zhupaichong watershed. The .ascii file is the topographic file, the .par file contains the required model files and parameter files, and the .bci and .bdy files represent the overflow node numbers and flow processes of the SWMM model. After configuration, complete the LISFLOOD-FP modeling and coupling work, and conduct waterlogging simulations for the entire study area at different return periods to obtain stormwater waterlogging resilience assessment indices. The simulated waterlogging spatial distribution of the design storm scenarios for each return period (0.25a, ​​0.5a, 1a, 2a, 3a, 5a, 10a, 20a, 30a, and 50a) in the Zhupaichong watershed is shown below. Figure 3 As shown.

[0076] Step 14: Using the coupled SWMM and LISFLOOD-FP models from Steps 12 and 13, obtain the urban flood resilience assessment indicators for the study area at the current urban level, varying with rainfall time during the carrying, adaptation, and recovery stages. These indicators include: for the carrying stage: road exposure index x1, building exposure level x2, inundation depth index x3, cumulative water depth index x4, flood flow velocity x5, drainage capacity of the pipe network x6, duration of flood events x7, and waterlogging rate index x8; for the adaptation stage: disaster loss rate x9, number of directly affected people x1, and waterlogging rate x2, etc. 11 Flood severity x 13 Total flood depth x 14 Total flood time x 15 Maximum flood flow velocity x 16 Pipeline drainage capacity x 17 and maximum water accumulation rate x 18 The persistence factor x during the recovery phase 25 .

[0077] Step 15: Analyze the resilience evaluation index systems summarized by various countries for urban flooding problems. Considering the common problems of urban flooding in my country, and based on the guiding document for safe and resilient city evaluation in my country, "Guidelines for Safe and Resilient City Evaluation" (GB / T40947-2021), and the characteristics of the study area, select flood and waterlogging resilience assessment indicators that do not change with rainfall time in the three stages of carrying capacity, adaptation, and recovery in the current status of the study area. These indicators include the number of families with children in the adaptation stage. 10 Elderly population index x 12 Emergency shelter space during the recovery phase (x) 19 Public transportation service capacity x 20 Regional medical facility density x 21 Medical insurance coverage rate x 22 Road density x 23 Subway station density x 24 The proportion of blue-green space area x 26 and considering the external discharge and storage volume x 27 .

[0078] Step 16: Combining Steps 14 and 15, finally obtain the comprehensive index x1 to x2, representing the urban current status level of the study area during the carrying, adaptation, and recovery phases, to assess its resilience to urban flooding. 27 The comprehensive indicators for assessing the resilience of the Zhupaichong watershed to stormwater and urban flooding are shown in Table 1.

[0079] Table 1: Comprehensive Indicators for Assessing the Resilience of Sponge Cities in the Study Area During the Bearing, Adaptation, and Recovery Stages of Rainwater Flooding

[0080]

[0081]

[0082] The specific steps for establishing a directed topological network of comprehensive indicators for assessing urban resilience to stormwater flooding in the study area at the carrying capacity, adaptation, and recovery stages using the DEMATEL-ISM method are as follows:

[0083] Step 21, determine the comprehensive index x for comparing stormwater and urban flooding resilience assessment. i For index x j The direct influence matrix A is obtained, and the normalized direct influence matrix B is obtained by normalizing the original relations; the comprehensive influence matrix T and the influence degree D of each indicator are calculated respectively. i Influence level C i Centrality M i and causal degree R i ;

[0084] The formula for the directly influential matrix A is as follows:

[0085]

[0086] Where: index x ij (i = 1, 2, ..., m; j = 1, 2, ..., n; i ≠ j) represents the index x. i For x j The direct impact; if i = j, then x ij =0;

[0087] The formula that directly affects matrix B according to the specification is as follows:

[0088]

[0089] The formula for the comprehensive influence matrix T is as follows:

[0090]

[0091] In the formula: I is the identity matrix;

[0092] The influence degree D of each indicator i Influence level C i Centrality M i and causal degree R i The calculation formulas are as follows;

[0093]

[0094]

[0095] M i =D i +C i

[0096] R i =D i -C i

[0097] In the formula: the influence degree Di is the sum of the values ​​in each row of T; the degree of influence Ci is the sum of the values ​​in each column of T.

[0098] Step 22: Combine the overall influence matrix T with the identity matrix I to determine the overall influence matrix E. Introduce a threshold λ to process the elements in matrix E and calculate the reachability matrix F.

[0099] The determination of the overall influence matrix E = [e ij ] n×n The calculation formula is:

[0100] E = I + T

[0101] The reachability matrix F = [f ij ] n×nA threshold λ needs to be introduced to process the elements in matrix E; its value will be determined by experts based on the actual situation. The reachability matrix F = [f ij ] n×n The calculation formula is:

[0102] F = [f ij ] n×n ,

[0103]

[0104] Step 23, calculate the reachable level R(x) i ) and the antecedent set S(x) i If R(x) i ) and S(x i ) satisfies R(x) i )∩S(x i )=R(x i When ), it means R(x) i The corresponding indicator x in ) i All can be in S(x i The antecedent can be found in the indicator x. i For indicators at higher levels, the corresponding rows and columns in the reachable matrix are removed. Then, the highest-level indicator is extracted from the remaining matrix. This process is repeated until all rows and columns are removed. Based on the order in which the indicators are removed, a multi-level hierarchical directed topology graph of the sponge city stormwater and urban flooding evolution resilience system indicators is drawn.

[0105] The reachable level R(x) i The factor is obtained by using the column with a value of 1 in the i-th row of the reachability matrix F, as shown in the formula:

[0106] R(x i )={x i |F ij =1}

[0107] The preceding set S(x) i The factor is obtained by using the factors corresponding to the column with a value of 1 in the i-th column of the reachability matrix F, as shown in the formula:

[0108] S(x i )={x i |F ij =1}

[0109] Step 4: During the resilience evolution process, the interaction quantitative analysis of the comprehensive indicators of the current level of urban flooding resilience in the study area at the three stages of carrying capacity, adaptation, and recovery is carried out. Furthermore, the GBB dimensionality reduction theory of system dynamics is introduced to transform the high-dimensional system dynamics of 27 indicators in the three stages of carrying capacity, adaptation, and recovery into an equivalent control parameter β. effThe mapping is transformed into effective one-dimensional dynamics to predict the response of the sponge city's stormwater and urban flooding resilience system to each indicator and to correctly locate the indicators in which the system loses its resilience. The specific steps are as follows:

[0110] Step 41: The four components x = (x1, ..., x4) of the sponge city stormwater and urban flooding evolution resilience system under steady-state conditions, representing the four indicators x1, x4, x6, and x7. T To describe activities such as Figure 5 As shown in A, B, and C. Through traditional mathematical processing of the resilience of one-dimensional systems, the dimensionality reduction method considers a system composed of N indices, whose activities x = (x1, ..., x...). N ) T Following coupled nonlinear equations:

[0111]

[0112] In equation (13): F(x) i This describes a comprehensive index for assessing stormwater and urban flooding resilience, x. i Self-dynamics, G(x) i ,x j ) describes the index x i Interaction dynamics between indices interacting with a directed topological network; weighted connectivity matrix A ij Capturing the positive interactions among comprehensive indicators for assessing stormwater and urban flooding resilience, representing the interaction between indicator x in a directed topological network. j To index x i The weight of a directed edge is 0 if there is no such edge. The interaction process is as follows: Figure 5 As shown in D.

[0113] The resilience function of the sponge city's stormwater and urban flooding evolution resilience system satisfies a nonlinear dynamic equation, such as... Figure 5 As shown in F, the resilience centrality of the drainage capacity x6 of the pipeline network is the highest at 0.2134, while the resilience centrality of the flood event duration x7 is the lowest at 0.0834.

[0114] Step 42, use the average value x eff The effective state nearest neighbor activity of 27 indicators in the comprehensive resilience assessment index for sponge city stormwater and urban flooding evolution is used to characterize the resilience of the sponge city's stormwater and urban flooding evolution system. The specific formula is as follows:

[0115]

[0116] Step 43, use an equivalent control parameter β eff The influence of the directed topological network structure formed by the comprehensive index of the resilience assessment of the sponge city's stormwater and urban flooding evolution resilience system on the resilience pattern of the sponge city's stormwater and urban flooding evolution resilience system is as follows:

[0117]

[0118] Step 44: Map the dynamic characteristics of the original multidimensional sponge city stormwater and urban flooding evolution resilience system to a low-dimensional space to obtain the effective one-dimensional system dynamic equation:

[0119]

[0120] In the formula: F(x) eff ) and G(x eff ,x eff ) respectively represent the self-dynamics and interaction dynamics of each indicator in the comprehensive index for assessing the resilience of rainwater and urban flooding after dimensionality reduction.

[0121] Step 45: Numerically solve the directed topology network constructed in Step 3 and the comprehensive stormwater and flood resilience assessment index from Step 1. Test its performance by randomly deleting a small portion of the comprehensive stormwater and flood resilience assessment indexes, using a directed topology, or randomly adjusting the weights A of the comprehensive stormwater and flood resilience assessment indexes. ij To simulate the resilience of sponge cities during stormwater and flooding processes and to accurately identify the indicators of the loss of resilience in the evolution of sponge city stormwater and flooding resilience systems.

[0122] Step 5: Define the change in system resilience caused by removing an indicator as resilience centrality. Further use the GBB dimensionality reduction theory of system dynamics to calculate the resilience centrality of each indicator, quantifying the capacity of each indicator in the sponge city stormwater and urban flooding evolution resilience system. The specific steps are as follows:

[0123] Step 51, removing the β caused by the comprehensive index of stormwater and urban flooding resilience assessment. eff Change is defined as resilience centrality, which is used to quantify the ability of an indicator to influence the resilience of a system. The indicator is x. i resilience center for:

[0124]

[0125] In equation (17): β eff and These represent the original network and the network with the metric x removed, respectively. i The original network,

[0126] Step 52, for β eff Normalizing the changes yields the resilience center R. i The formula is as follows:

[0127]

[0128] Step 53: Simplify using a first-order approximation of the Taylor expansion. The value of . Since the average degree of most networks is much greater than 1, under the assumption... In this case, the simplified form of resilience centrality is:

[0129]

[0130] In equation (19): the weighted connection matrix A ij This indicates that in a directed topology network, from index x... j To index x i The weight of a directed edge is 0 if there is no such edge; the weighted connectivity matrix A ji This indicates that in a directed topology network, from index x... i To index x j The weight of a directed edge is 0 if there is no such edge. In a directed topology network, x represents a pointer to an index. i The number of edges; This indicates that in a directed topology network, from index x... i The number of edges indicated; In a directed topology network, x represents a pointer to an index. j The number of edges; This indicates that in a directed topology network, from index x... j The number of edges indicated.

[0131] Step 54: After adjusting the initial state of the comprehensive index for assessing the resilience of the sponge city's stormwater and urban flooding evolution stage, the initial state of the sponge city's stormwater and urban flooding evolution stage is as follows: Figure 6 As shown in (b), the comprehensive index x for stormwater flood resilience assessment was removed separately. i A new network was constructed to calculate the resilience centrality of each indicator, quantifying the resilience of the indicators in the sponge city stormwater and urban flooding evolution resilience system. The resilience centrality of each indicator in the Zhupaichong watershed sponge city stormwater and urban flooding evolution resilience system is shown below. Figure 6 As shown in (c), a failure in the drainage capacity x6 of the pipeline network led to system collapse, indicating that the drainage capacity x6 has a stronger impact on system resilience than other indicators. The resilience centrality of each indicator is as follows: Figure 6 As shown in (d), the resilience centrality of the drainage capacity of the pipeline network x6 is the highest, while the resilience centrality of the flood event duration x7 is the lowest.

[0132] Step 6: In this specific embodiment, different resilience enhancement targets for the sponge city stormwater and urban flooding evolution resilience system are set according to different target level years and different regional scale catchment zones in the study area. Steps 1 to 5 are executed cyclically to predict the response of the sponge city stormwater and urban flooding evolution resilience system to each indicator at each stage, propose potential intervention strategies to avoid resilience loss, and summarize the resilience enhancement process of the sponge city stormwater and urban flooding evolution resilience system from the current situation to development and then to the target level feedback loop, thereby enhancing the resilience of the sponge city.

Claims

1. A method for evaluating the resilience of sponge cities in responding to the evolution of stormwater and urban flooding, characterized in that, Includes the following steps: Step 1: Calculate the design storms with a return period of 0.25a to 100a in the study area and allocate them by time history. Divide the study area into sub-catchment zones according to the watershed, community and household scales. Obtain the modeling parameters of the SWMM model and perform coupled modeling of the SWMM model and the LISFLOOD-FP model to obtain the stormwater resilience assessment index of the study area as the urban status level changes with the time of stormwater in the carrying, adaptation and recovery stages. We selected an indicator for assessing the resilience of urban waterlogging in the study area that does not change with the duration of rainfall and flood during the carrying, adaptation, and recovery stages of the current urban status in the study area. Finally, we obtained a comprehensive indicator for assessing the resilience of urban waterlogging in the study area during the carrying, adaptation, and recovery stages of the current urban status in the study area. Step 2: Examine the relationship between the comprehensive indicators of stormwater and urban flood resilience assessment in the carrying capacity, adaptation and recovery stages. Use the DEMATEL-ISM method to establish directed topological networks of the comprehensive indicators of stormwater and urban flood resilience assessment in the carrying capacity, adaptation and recovery stages respectively. Step 3: Based on the directed topological network of the comprehensive indicators for stormwater and urban flood resilience assessment in Step 2 during the carrying, adaptation and recovery stages, the relationship of the comprehensive indicators for stormwater and urban flood resilience assessment in the carrying, adaptation and recovery stages is mapped into effective one-dimensional dynamics, predicts the response of the sponge city stormwater and urban flood resilience evolution system to the action of each indicator in the comprehensive indicators for stormwater and urban flood resilience assessment, and locates the indicators in which the sponge city stormwater and urban flood resilience evolution system loses its resilience. Step 4: Define the change in resilience of the sponge city stormwater and waterlogging evolution resilience system caused by the removal of indicators that have lost resilience from the comprehensive index of stormwater and waterlogging resilience assessment as resilience centrality, and calculate the resilience centrality of each indicator. Step 5: Based on different target level years and different catchment areas in the study area, set resilience enhancement targets for the sponge city stormwater and urban flooding evolution resilience system. Execute steps 1-4 iteratively to predict the different disturbance responses of the sponge city stormwater and urban flooding evolution resilience system to the comprehensive indicators of stormwater and urban flooding resilience assessment in the carrying, adaptation, and recovery stages. Propose intervention strategies to avoid resilience loss, forming a resilience enhancement process for the sponge city stormwater and urban flooding evolution resilience system that feedback loops from the current situation to development and then to the target level.

2. The evaluation method for the index system of sponge city resilience to the evolution of stormwater and urban flooding as described in claim 1, characterized in that, Step 1, which describes obtaining the comprehensive index for assessing stormwater and urban flooding resilience, includes the following steps: Step 11: The design rainfall for each return period is calculated using the urban calculation formula for the study area. The time history allocation is based on the Chicago rainfall pattern. The study area is divided into sub-catchment zones according to watershed, community, and household. The comprehensive information of hydrological and meteorological data, land use data of underlying surface, digital elevation model, drainage network and road network infrastructure data of the current urban level year of the study area is obtained and processed using ArcGIS software to obtain the SWMM model modeling parameters. Step 12: Generate an .inp file from the SWMM modeling parameters of Step 11 and the design rainfall data for the 0.25a-100a return period in the study area. Open the .inp file with SWMM software and add a rain gauge in SWMM to complete the simulation of the design rainfall for the 0.25a-100a return period in the study area. Step 13: Compile the simulation results of design rainfall over a return period of 0.25a-100a for the study area described in Step 12 into .ascii, .par, .bci, and .bdy files. The .ascii file is the terrain file, the .par file contains the required files and parameter files for the model, and the .bci and .bdy files contain the overflow node numbers and flow processes of the SWMM model. This completes the coupled modeling of the SWMM model and the LISFLOOD-FP model to obtain the urban current status level of the study area under the carrying capacity, adaptation, and recovery stages, as measured by the temporal variation of rainfall and flooding. These indicators include: under the carrying capacity stage, road exposure index x1, building exposure level x2, inundation depth index x3, cumulative water depth index x4, flood flow velocity x5, drainage capacity of the pipe network x6, duration of flood events x7, and waterlogging rate index x8; under the adaptation stage, disaster loss rate x9, number of directly affected people x9, and other indicators. 11 Flood severity x 13 Total flood depth x 14 Total flood time x 15 Maximum flood flow velocity x 16 Pipeline drainage capacity x 17 and maximum water accumulation rate x 18 The persistence factor x during the recovery phase 25 ; Step 14: Select an assessment index for urban flood resilience in the statistical study area that does not change with rainfall duration during the carrying, adaptation, and recovery phases. This index includes the number of families with children in the adaptation phase. 10 Elderly population index x 12 Emergency shelter space during the recovery phase (x) 19 Public transportation service capacity x 20 Regional medical facility density x 21 Medical insurance coverage rate x 22 Road density x 23 Subway station density x 24 The proportion of blue-green space area x 26 and considering the external discharge and storage volume x 27 ; Step 15, combining steps 13 and 14, finally obtains the comprehensive index x1 to x2, representing the urban current status level of the study area in the carrying, adaptation, and recovery stages, assessing its resilience to stormwater flooding. 27 .

3. The evaluation method for the index system of sponge city resilience to the evolution of stormwater and urban flooding as described in claim 1, characterized in that, The steps in step 2, which involve establishing directed topological networks for the comprehensive index of stormwater and urban flooding resilience assessment in the carrying capacity, adaptation, and recovery stages using the DEMATEL-ISM method, are as follows: Step 21, determine the comprehensive index x for comparing stormwater and urban flooding resilience assessment. i For index x j The direct influence matrix A is obtained, and the normalized direct influence matrix B is obtained by normalizing the original relations; the comprehensive influence matrix T and the influence degree D of each indicator are calculated respectively. i Influence level C i Centrality M i and causal degree R i ; Step 22: Combine the overall influence matrix T with the identity matrix I to determine the overall influence matrix E. Introduce a threshold λ to process the elements in matrix E and calculate the reachability matrix F. Step 23, calculate the reachable level R(x) i ) and the antecedent set S(x) i If R(x) i ) and S(x i ) satisfies R(x) i )∩S(x i )=R(x i When ), it means R(x) i The corresponding indicator x in ) i All can be in S(x i The antecedent can be found in the indicator x. i For indicators at higher levels, the corresponding rows and columns in the reachable matrix are removed. Then, the highest-level indicator is extracted from the remaining matrix. This process is repeated until all rows and columns are removed. Based on the order in which the indicators are removed, a multi-level hierarchical directed topology graph of the sponge city stormwater and urban flooding evolution resilience system indicators is drawn.

4. The evaluation method for the index system of sponge city resilience to the evolution of stormwater and urban flooding as described in claim 3, characterized in that, The formula for the direct influence matrix is ​​as follows: Where: index x ij (i = 1, 2, ..., m; j = 1, 2, ..., n; i ≠ j) represents the index x. i For x j The direct impact; if i = j, then x ij =0; The formula that directly affects matrix B according to the specification is as follows: The formula for the comprehensive influence matrix T is as follows: In the formula: I is the identity matrix; The influence degree D of each indicator i Influence level C i Centrality M i and causal degree R i The calculation formulas are as follows; M i =D i +C i R i =D i -C i In the formula: the influence degree Di is the sum of the values ​​in each row of T; the degree of influence Ci is the sum of the values ​​in each column of T; The determination of the overall influence matrix E = [e ij ] n×n The calculation formula is: E = I + T, The reachability matrix F = [f ij ] n×n A threshold λ needs to be introduced to process the elements in matrix E, and the value of the threshold λ is determined by experts based on the actual situation. Reachability matrix F = [f ij ] n×n The calculation formula is: F=[f ij ] n×n , The reachable level R(x) i The factor is obtained by using the column with a value of 1 in the i-th row of the reachability matrix F, as shown in the formula: R(x i )={x i |F ij =1} The preceding set S(x) i The factors are obtained by using the i-th column of the reachability matrix F, where the value is 1. The formula is: S(x i )={x i |F ij =1}。 5. The evaluation method for the index system of sponge city resilience to the evolution of stormwater and urban flooding as described in claim 1, characterized in that, The effective one-dimensional dynamic equation described in step 3 is as follows: In the formula: the average value x is used in the dimensionality reduction process. eff The effective state nearest neighbor activity of 27 indicators in the comprehensive resilience assessment index for sponge city stormwater and urban flooding evolution is calculated as follows: Weighted connection matrix A ij Capturing the positive interactions among comprehensive indicators for assessing stormwater and urban flooding resilience, representing the interaction between indicator x in a directed topological network. j To index x i The weight of a directed edge is 0 if there is no such edge; β eff It is an equivalent control parameter that measures the impact of the directed topological network structure formed by the comprehensive index of the resilience assessment of the sponge city's stormwater and urban flooding evolution resilience system on the resilience model of the sponge city's stormwater and urban flooding evolution resilience system. It is calculated as follows: Weighted connection matrix A ji Capturing the positive interactions among comprehensive indicators for assessing stormwater and urban flooding resilience, representing the interaction between indicator x in a directed topological network. i To index x j The weight of a directed edge is 0 if there is no such edge; F(x) eff ) and G(x eff ,x eff ) respectively represent the self-dynamics and interaction dynamics of each indicator in the comprehensive index for assessing the resilience of rainwater and urban flooding after dimensionality reduction.

6. The evaluation method for the index system of sponge city resilience to the evolution of stormwater and urban flooding as described in claim 1, characterized in that, Step 4 describes the resilience centrality R of each indicator. i The calculation formula is as follows: Where: weighted connection matrix A ij This indicates that in a directed topology network, from index x... j To index x i The weight of a directed edge is 0 if there is no such edge; the weighted connectivity matrix A ji This indicates that in a directed topology network, from index x... i To index x j The weight of a directed edge is 0 if there is no such edge. In a directed topology network, x represents a pointer to an index. i The number of edges; This indicates that in a directed topology network, from index x... i The number of edges indicated; In a directed topology network, x represents a pointer to an index. j The number of edges; This indicates that in a directed topology network, from index x... j The number of edges indicated.

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