Urban Stormwater Resilience Assessment Method Based on Cloud Model and TOPSIS

4.1. Cloud Model Combines with Delphi Method to Calculate the Weight of Indicators

The traditional index weight determination method is is is highly subjective . To reduce the subjectivity of weight determination , the cloud weight ( Ex , En , He ) method is select in this paper to soften the traditional weight . Ex is expect to be the traditional weight , and entropy En and hyperentropy He is are are the parameter used to soften the weight .

(1) Delphi method

relevant professional and mostly expert and scholar were invite to weigh the indicator in the evaluation index system of urban rainwater toughness , and the importance of the low index ( such as the index layer ) to the upper index ( such as the criterion layer ) was give a score base on 0–1 .

( 2 ) Cloud weight solution and correction

A reverse cloud generator algorithm is used to process the expert rating results to obtain the cloud weight corresponding to each index and generate the corresponding cloud map. The thicker the cloud in the cloud map, the higher the superentropy value and the greater the dispersion of cloud droplets, which indicates that the experts’ scoring results differ greatly, and the persuasion is low. Suggestions should be put forward on the experts’ scoring results and a new round of grading revision should be carried out to modify the index cloud weight. According to the procedure of “expert rating—result collection—cloud image judgment—opinion feedback—expert rating”, the cloud image is constantly improved to reduce the dispersion of cloud droplets, reduce the subjectivity of index cloud weight, and improve the accuracy and scientificity of evaluation results.

(3) Weight normalization processing

After calculating the index cloud weights of each layer of the urban stormwater toughness evaluation index system, it is necessary to normalize the index cloud weights of the same layer according to Equation (9).

$W_{ij}=\frac{w_{ij}}{{\sum }_{j=1}^n{w}_{ij}}$

(9)

$w_{ij}$

is the cloud weight of indicators at each layer,

${\sum }_{j=1}^n{w}_{ij}$

is the sum of the cloud weight of indicators at the same layer, and

$w_{ij}$

is the indicator weight after normalization.

The steps to determine the weight of each index by combining the cloud model and the Delphi method are as follows:

accord to the step to determine the weight of urban rainwater resilience assessment indicator in the previous section , 10 expert in the industry were invite to score the importance of the low level indicator relative to the upper level , that is , the importance of b_i( i = 1 , 2 , 3 ) relative to A , and C_i relative to B_I. Ten point of the expert weight scoring table were issue and , ten copy were recycle . finally , the cloud model is used to reverse the cloud generator to obtain the cloud weight of the low layer relative to the upper index .

The evaluation index system is involves of urban rainwater resilience involve a total of 18 index , which will not be describe in this paper due to space limitation . Here , the determination process of the cloud weight between the resistance index of the criterion layer and the target layer is take as an example to illustrate . The expert grading table is show in

Table 2

.

Python programming language is used to implement reverse cloud generator algorithm, and the weight scoring results of B1 are processed to obtain the first score result’s cloud weight (0.9180, 0.0421, 0.0170). At the same time, the forward generator is used to generate the cloud map of the weight of B

₁

cloud, as shown in

figure 2

. According to the weighted cloud map of B

₁

cloud, it can be seen that the cloud is thicker and the cloud drops are more dispersed, which means that there are big differences among experts when evaluating the importance of resistance relative to the toughness of urban rainwater in the scoring process. To improve the consistency of experts’ recognition of the cloud weight scoring results and reduce the subjective randomness of the scoring results, experts were invited to score again. After repeated feedback and correction, the cloud drop layer thickness in

figure 2

is obviously get small and small , and the expert opinion are gradually unified . The cloud weight is is of resistance relative to urban stormwater resilience is ( 0.9230 , 0.0163 , 0.0065 ) .

The above process is repeated to determine the index cloud weights of each layer of the urban storm flood resilience assessment index system and continuously revise them. Finally, the normalization process is conducted to obtain the index cloud weights of each layer of the urban storm flood resilience assessment index system, as shown in

Table 3

.

The index weight of each layer in the urban stormwater resilience assessment index system are summarize as show in

Table 4

.

4.2 . The Indicator Closeness Degree Was calculate by TOPSIS Method

4.2.1. Fuzzy Description of Resilience Indicator Grade

Because the units and orders of magnitude of each indicator are inconsistent, we set four ranges for each three-level indicator by referring to the standard ranges of each indicator in various provinces in China and assign corresponding scores to each range. Among them, 1 indicates that the index is lower than the national average, 2 and 3 indicate that the index is around the national average, and 4 indicates that the index is higher than the national average. We divided the fuzzy grade description of each resilience indicator into four levels, among which the first level indicates that the city has the lowest level of storm flood resilience, and the city under this level will face great flood risk and the subsequent recovery process will be very slow. Level 2 indicates that the level of storm flood resilience of a city is relatively poor. Cities under this level are still facing great flood risk, and uncontrollable accident consequences may occur when the rainstorm comes. Level 3 indicates that the city’s flood resilience level is in a good stage. Any city under this level has a certain resistance capacity and can be controlled in a relatively quick time once it is attacked by the flood. Level 4 indicates that the city has the highest degree of flood resilience, and a city under this level can make corresponding prediction measures in advance by virtue of its strong resistance and adaptability to avoid large losses.

Due to the limited space , only the fuzzy description of each third – level indicator under the second – level indicator is display . For the fuzzy description of the remain third – level indicator . See the

Supplementary Material

.

(1) Fuzzy description of resistance indicator grade

The proportion of population over 60 years old and under 18 years old C

₁

value standard: the proportion of population over 60 years old and under 18 years old in the total population of the city. The fuzzy description of C

₁

is shown in

Table 5

.

(2) Fuzzy description of recovery indicator grade

Per capita GDP C

₇

value standard: measure the GDP ranking obtained by the National Bureau of Statistics to judge the level of the city’s per capita GDP. The fuzzy description of C

₇

is shown in

Table 6

.

(3) Fuzzy description of adaptability indicator grade

Per capita public green area C

₁₂

value standard : the average area of public green space occupy by each resident in the city . The fuzzy description of C

₁₂

is shown in

table 7

.

( 4 ) secondary indicator evaluation grade value

The evaluation index grades of resistance are shown in

Table 8

.

The evaluation index grade of recovery are show in

table 9

.

The evaluation index grades of adaptability are shown in

Table 10

.

4.2.2 . Standard for Resilience Grade of Urban Stormwater

According to the grade fuzzy description of resilience index, the initial evaluation matrix A_K was constructed.

Set the resistance evaluation matrix as

A₁

,

$A_1=\left[\begin{array}{cccccc}1& 1& 1& 1& 1& 1\\ 2& 2& 2& 2& 2& 2\\ 3& 3& 3& 3& 3& 3\\ 4& 4& 4& 4& 4& 4\end{array}\right]$

The distance s

₁⁺

, S

₁⁻

, and closeness degree e

_i⁺

between the resistance indicator class value and the positive and negative ideal solution were calculated, as

Table 11

show .

set the recovery evaluation matrix as

A₂

,

$A_2=\left[\begin{array}{ccccc}1& 1& 1& 1& 1\\ 2& 2& 2& 2& 2\\ 3& 3& 3& 3& 3\\ 4& 4& 4& 4& 4\end{array}\right]$

The distance s

₁⁺

, S

₁⁻

, and closeness degree e

_i⁺

between the recovery indicator class value and the positive and negative ideal solution were calculated, as

Table 12

show .

Set the adaptability evaluation matrix as

A₃

,

$A_3=\left[\begin{array}{ccccccc}1& 1& 1& 1& 1& 1& 1\\ 2& 2& 2& 2& 2& 2& 2\\ 3& 3& 3& 3& 3& 3& 3\\ 4& 4& 4& 4& 4& 4& 4\end{array}\right]$

The distance s

₁⁺

, S

₁⁻

, and closeness degree e

_i⁺

between the adaptability indicator class value and the positive and negative ideal solution were calculated, as

Table 13

show .

To sum up, the urban stormwater resilience grade standard is shown in

Table 14

.

According to

Table 14

, the grading standard of urban stormwater resilience can be obtain as follow :

Level 1: 0 ≤ E_i⁺ < 0.3896

Level 2: 0.3896 ≤ E_i⁺ < 0.7194

Level 3: 0.7194 ≤ E_i⁺ < 1

level 4 : E_i⁺ = 1

In the first level, the resilience of urban stormwater is at the least ideal state. Once in the first level, the system will be faced with huge flood risk or the disaster resistance and recovery ability of the system is very poor, which will cause extremely serious consequences. Level 2 refers to the situation in which the resilience of urban stormwater is relatively poor. The system in level 2 is still facing great flood risk and will cause uncontrollable accident consequences once the rainstorm occurs. Level 3 refers to the situation in which the resilience of urban stormwater is relatively good. The system in level 3 is capable of resisting floods to a certain extent, and it can be controlled within a certain period of time once the rainstorm occurs. Level 4 is the ideal condition of urban stormwater resilience. The system in level 4 can predict and avoid or respond to the flood in time, so that it will not cause great losses. The system has a strong learning ability and can draw experience from the flood disaster suffered by the system, which makes the resilience level of the system higher and higher.