Urban drainage, regulation and storage facility operation step-by-step decision analysis method based on risk assessment

Abstract

An urban drainage, regulation and storage facility operation step-by-step decision analysis method based on risk assessment. When information of each decision standard preference for urban drainage, regulation and storage facility operation is completely missing or is unclear, a method combining game theory with feasible weight space is used to aggregate urban drainage, regulation and storage facility operation weights; stochastic multi-criteria decision analysis algorithm and fuzzy optimization models are used to construct a stochastic multi-criteria decision analysis-fuzzy optimization model for the urban drainage, regulation and storage facility operation; an urban drainage, regulation and storage facility operation decision risk assessment model is constructed to quantitatively assess the risk of urban drainage, regulation and storage facility operation decision errors; and multi-stage multi-criteria decision analysis is used to determine step by step information of the weight of each standard of the urban drainage, regulation and storage facility operation, thereby achieving an optimal decision for the urban drainage, regulation and storage facility operation.

Description

A step-by-step decision analysis method for the operation of urban drainage storage facilities based on risk assessment Technical Field

[0001] The present invention belongs to the technical field of urban drainage storage and regulation facility operation, and in particular relates to a step-by-step decision analysis method for urban drainage storage and regulation facility operation based on risk assessment. Background Art

[0002] Most of my country's older urban areas utilize combined sewer systems. Due to limited underground space and significant renovation investments, complete rainwater and sewage separation remains unattainable. Instead, most cities implement end-of-line interception and storage facilities to control overflow pollution during the rainy season. New urban areas utilize separate sewer systems, and to prevent initial rainwater pollution from deteriorating water quality, most cities have already implemented initial rainwater interception and storage facilities. Drainage storage projects, due to their large size, complex pipe networks, frequent extreme rainfall events, unscientific control strategies, and lack of system coordination with power plants, networks, and rivers, have led to limited peak flow control effectiveness, poor control of overflow frequency and volume, and low operational efficiency. To address these issues, some cities have actively explored models to improve pollution interception efficiency and implement some high-efficiency treatment methods to address overflow pollution. Multi-criteria decision analysis methods, among other approaches, guide the operation of urban drainage storage and regulation facilities based on various monitoring data from these facilities. Currently, several multi-criteria decision analysis methods have been applied in the operation and management of urban drainage storage and regulation facilities. These methods can generally be divided into six categories: (1) utility function and multi-criteria evaluation value; (2) method evaluation of distance to the ideal point; (3) pairwise comparison; (4) fuzzy set analysis; (5) transcendental method; and (6) customized method. However, most existing multi-criteria decision analysis methods are limited to deterministic environments and do not consider the various uncertainties in the actual operation of urban drainage storage facilities. Uncertain data is not conducive to making quick decisions, but it is more in line with the actual situation.

[0003] The traditional multi-criteria decision analysis method follows the idea of ​​"single value and fixed ranking", which includes five steps: (1) selecting appropriate decision criteria; (2) using various monitoring data of urban drainage storage facilities to obtain various urban drainage storage facility operation alternatives and performance values; (3) determining the criteria and weights of various urban drainage storage facility operation alternatives based on decision preferences; (4) conducting a multi-criteria decision analysis process; (5) obtaining the final urban drainage storage facility operation plan. That is, the decision model takes the deterministic decision matrix and weight vector as input and generates a fixed ranking without considering the risk information related to the urban drainage storage facility operation decision. The operation of urban drainage storage facilities is a multi-stage decision process that is closely related to various complex factors such as society, economy, and environment, and has the characteristics of timeliness, irreversibility, and uncertainty. In the traditional decision process, decision makers must express accurate preferences in advance to ensure that the multi-criteria decision analysis model can operate, because the criterion weight is one of the most critical inputs of the multi-criteria decision analysis model. However, at the beginning of the multi-criteria decision analysis, there are still many situations where the decision support information is unknown. In reality, decision makers often face immense psychological pressure during multi-criteria decision-making analysis (MCDA). Preference information is the most critical and sensitive parameter directly influencing the model's output (i.e., the recommended drainage network cleaning solution). Clearly, traditional MCA methods are not the best choice for decision makers. This is because weighting criteria is one of the most difficult steps in MCA and is entirely determined by the decision maker.

[0004] In view of this, the present invention aims at the operation problem of urban drainage storage facilities and proposes a step-by-step decision analysis method for the operation of urban drainage storage facilities based on risk assessment.

[0005] Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a step-by-step decision analysis method for the operation of urban drainage and storage facilities based on risk assessment. Under the condition that the preference information of various decision criteria for the operation of urban drainage and storage facilities is completely missing or unclear, a multi-stage multi-criteria decision analysis is adopted to gradually determine the weight information of various decision criteria for the operation of urban drainage and storage facilities, thereby achieving the best decision for the operation of urban drainage and storage facilities.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0008] A step-by-step decision analysis method for the operation of urban drainage storage facilities based on risk assessment, the steps are:

[0009] 1. Treat the multi-criteria decision analysis of urban drainage storage and regulation facility operation as a multi-stage decision analysis problem, determine the key influencing factors of urban drainage storage and regulation facility operation scheduling, select appropriate urban drainage storage and regulation facility operation decision criteria, and obtain the urban drainage storage and regulation facility operation random decision matrix;

[0010] 2. A method for aggregating weights for decision-making criteria for the operation of urban drainage and storage facilities is proposed based on a combination of game theory and feasible rights space. This method addresses conflicts among multiple stakeholders in the decision-making process for the operation of urban drainage and storage facilities and estimates the uncertainty of the weights for each decision-making criterion for the operation of urban drainage and storage facilities.

[0011] 3. Combining a stochastic multi-criteria acceptability analysis algorithm with a fuzzy optimization model, a fuzzy optimization model for stochastic multi-criteria decision analysis of the operation of urban drainage storage facilities is constructed. The uncertainty of the decision criteria and their weights for urban drainage storage facilities is simulated and quantified, and several measurement descriptions of the robustness of urban drainage storage facility operation decisions are given.

[0012] 4. Construct a risk assessment model for the operation of urban drainage storage and regulation facilities, calculate the uncertainty level and risk of decision-making errors for each initial alternative operation plan, and quantitatively assess the risk of decision-making errors in the operation of urban drainage storage and regulation facilities;

[0013] 5. Make multi-stage decisions on the operation of urban drainage and storage facilities based on the step-by-step weight information method to ensure that each decision-making scheme for the operation of urban drainage and storage facilities is gradually solved within an acceptable decision-making risk range.

[0014] Furthermore, the step 1 is specifically as follows:

[0015] 1.1. Prepare a set of initial alternative operation schemes for urban drainage storage facilities A = {A i |i=1,2,…,m},A i represents the i-th alternative scheme for the operation of urban drainage storage facilities, and m represents the number of initial alternative schemes for the operation of urban drainage storage facilities;

[0016] 1.2. Determine the factors affecting the operation and scheduling of urban drainage storage facilities and select the appropriate decision-making standard set C = {C j |j=1,2,…,n}, in order to sort and screen the initial alternative operation scheme set of urban drainage storage facilities, C j represents the jth decision criterion for the operation of urban drainage storage facilities, and n represents the total number of decision criteria for the operation of urban drainage storage facilities;

[0017] 1.3. Select the parameters that have the greatest impact on the operation of urban drainage storage and regulation facilities as the decision-making criteria for the operation of urban drainage storage and regulation facilities. These criteria include: ① inlet flow; ② storage tank volume; ③ rainfall; ④ inlet water quality monitoring data; ⑤ storage tank outflow; ⑥ storage tank inlet pipe liquid level; ⑦ storage tank pump station size.

[0018] Furthermore, the step 2 is specifically as follows:

[0019] 2.1. To quantify the uncertainty of the decision-making criteria for the operation of urban drainage and storage facilities, this method uses the complementary judgment matrix method to quantify the uncertainty of each decision-making criterion. Based on the preferences of different decision-makers for the decision-making criteria for the operation of urban drainage and storage facilities, the quantitative decision-making criterion weights for each urban drainage and storage facility are obtained.

[0020] 2.2. Game theory is introduced into the stochastic multi-criteria decision analysis of urban drainage storage and regulation facilities. The weights of the conflicting decision criteria for the operation of urban drainage storage and regulation facilities are aggregated through Nash equilibrium to achieve preference compromise and conflict resolution, and the coordinated weights of the decision criteria for the operation of urban drainage storage and regulation facilities are obtained;

[0021] 2.3. Using the concept of feasible rights space, establish the feasible rights space for the decision-making standards of urban drainage and storage facilities operation, and quantify the uncertainty of each decision-making standard for the operation of urban drainage and storage facilities;

[0022] Furthermore, the step 3 is specifically as follows:

[0023] 3.1. When solving the multi-criteria decision-making problem for the operation of urban drainage and storage facilities, fuzzy functions are introduced and a fuzzy optimization model for urban drainage and storage facility operation decision-making is established. The fuzzy ideal distance and fuzzy anti-ideal distance are used to solve the multi-criteria decision-making problem for the operation of urban drainage and storage facilities.

[0024] 3.2. Based on the stochastic multi-criteria decision-making analysis model, a fuzzy optimization model for the operation decision-making of urban drainage and storage facilities is introduced. A stochastic multi-criteria decision-making analysis-fuzzy optimization model for the operation decision-making of urban drainage and storage facilities is established. The uncertainty measure of each initial alternative operation plan for urban drainage and storage facilities is obtained by solving this model. The advantages and disadvantages of each initial alternative operation plan for urban drainage and storage facilities are compared and evaluated.

[0025] Furthermore, the step 4 is specifically as follows:

[0026] 4.1. To further fully assess the uncertainty of the initial alternative operation plans for each urban drainage and storage facility, the risk of decision-making errors in the operation plans of urban drainage and storage facilities was calculated, and the uncertainty of the initial alternative operation plans for each urban drainage and storage facility was quantitatively assessed;

[0027] 4.2. After obtaining the ranking of the initial alternative operation plans for each city's drainage and storage facilities, calculate the uncertainty of each initial operation plan for the city's drainage and storage facilities based on the ranking results, and quantitatively evaluate the overall uncertainty of each initial alternative operation plan for the city's drainage and storage facilities.

[0028] Furthermore, the step 5 is specifically as follows:

[0029] The stepwise decision-making process for the operation of urban drainage and storage facilities begins with completely missing or unclear preference information and gradually obtains more accurate information as the process progresses. The basic idea is to iteratively run the stochastic multi-criteria decision-making fuzzy model for the operation of urban drainage and storage facilities after completing each round of information collection related to urban drainage and storage facility operation decisions, until sufficient preference information for the final decision is obtained within an acceptable risk range for decision errors. After each analysis of the stochastic multi-criteria decision-making fuzzy model for the operation of urban drainage and storage facilities, preference information is added by more accurately assessing the decision maker's preferences. If sufficient inaccurate information is available at an early stage of the stepwise decision-making process for the operation of urban drainage and storage facilities, the preference collection process can be significantly saved and the complex weighting process can be avoided.

[0030] 5.1. In the initial stage of operation of urban drainage storage and regulation facilities, due to the lack of weight information for multi-criteria decision-making analysis of urban drainage storage and regulation facilities operation, the missing weight information is expressed through the uniform distribution of the urban drainage storage and regulation facilities operation weight space.

[0031] In the initial stages of the stepwise decision-making process for urban drainage and storage facility operations, decision makers often find it difficult to express their preferences because the available decision-support information is very limited. Unlike traditional multi-criteria decision-making processes for urban drainage and storage facility operations, decision makers do not need to express any preferences in the first stage. Instead, the stochastic multi-criteria decision-making fuzzy model for urban drainage and storage facility operations is implemented using the entire weight space of urban drainage and storage facility operation decision criteria. The missing weight information is expressed through a uniform distribution across the weight space of urban drainage and storage facility operation decision criteria.

[0032] 5.2. Based on the statements of each decision maker's preference for each decision criterion for the operation of urban drainage storage and regulation facilities, the weight information of the step-by-step decision sequence for the operation of urban drainage storage and regulation facilities is obtained.

[0033] The weight information of the step-by-step decision sequence for the operation of urban drainage storage facilities is expressed in the form of linear constraints, such as w1>w2>…>w nThe weight information for the step-by-step decision-making sequence for the operation of urban drainage and storage facilities corresponds to the decision-maker's preference statement, i.e., criterion 1 is more important than criterion 2. Of course, there are also cases where the decision-maker cannot determine the appropriate criteria (w1?w2) or considers them equally important (w1=w2). The weight information for the step-by-step decision-making sequence for the operation of urban drainage and storage facilities can be represented as a triangular plane within the weight space of the decision-making criteria for the operation of urban drainage and storage facilities.

[0034] 5.3. The complementary matrix method is used to determine the quantitative weights of various decision-making criteria for the operation of urban drainage and storage facilities. The uncertainty of the weights is estimated through the probability distribution within the boundary of the feasible space for step-by-step decision-making on the operation of urban drainage and storage facilities under interval constraints. The weight interval can be expressed as a hexagonal plane within the entire feasible space for step-by-step decision-making on the operation of urban drainage and storage facilities.

[0035] 5.4. Utilize deterministic weight vectors to generate the final decision on the operation of urban drainage and storage facilities under an acceptable risk of decision error. If the step-by-step decision-making process for the operation of urban drainage and storage facilities is a single-decision-maker process, the complementary judgment matrix method is used to directly calculate and determine the weight vectors of each decision-making criterion for the operation of urban drainage and storage facilities. If the step-by-step decision-making process for the operation of urban drainage and storage facilities is a multiple-decision-maker process, the complementary judgment matrix method is used to calculate the weight vectors of each decision-making criterion for each decision-maker, and the weight aggregation method is used to obtain the coordination weight vectors of each decision-making criterion.

[0036] Furthermore, the step 2.1 is specifically as follows:

[0037] 2.1.1. Based on the empirical judgment of various decision criteria for the operation of urban drainage and storage facilities, a complementary judgment matrix for each decision criterion for the operation of urban drainage and storage facilities is constructed. Decision makers compare each pair of decision criteria for the operation of urban drainage and storage facilities to determine their relative importance.

[0038] 2.1.2. Considering that the complementary judgment matrix of the decision criteria for the operation of urban drainage storage and regulation facilities usually contains a certain degree of inconsistency, the least squares method is used to obtain the weight values ​​of the decision criteria for the operation of urban drainage storage and regulation facilities;

[0039] 2.1.3. Based on the complementary weights calculated in step 2.1.1 and the weights of each decision criterion determined in step 2.1.2, calculate the inconsistency error of the weights of each city's drainage and storage facility operation decision criterion and assess the inconsistency of the weights of each city's drainage and storage facility operation decision criterion. If the inconsistency error is small, the decision makers' empirical judgments are relatively accurate. Conversely, if the inconsistency error is large, the decision makers should reconsider their preference information for each decision criterion.

[0040] Furthermore, the step 2.2 is specifically as follows:

[0041] 2.2.1. Use the complementary judgment matrix method to determine the basic weight vectors of the decision criteria for the operation of urban drainage and storage facilities for each decision maker. Comprehensively consider the basic weight vectors of the decision criteria for the operation of urban drainage and storage facilities for each decision maker and use a linear combination method to obtain the basic weight vectors of the decision criteria for the operation of urban drainage and storage facilities;

[0042] 2.2.2. Based on Nash equilibrium, optimize the weight combination coefficients of the various decision-making criteria for the operation of urban drainage and storage facilities to achieve a compromise or consistency between the basic weight vectors of the decision-making criteria. Ultimately, a coordinated weight vector for the decision-making criteria for the operation of urban drainage and storage facilities is obtained, and the deviation between the basic weight vectors and the coordinated weight vector for the decision-making criteria for the operation of urban drainage and storage facilities is minimized.

[0043] 2.2.3. Use the linear programming method to solve the urban drainage storage facility operation decision model, obtain the optimal combination coefficient of the urban drainage storage facility operation decision, and calculate the urban drainage storage facility operation decision coordination weight vector.

[0044] Furthermore, the step 2.3 is specifically as follows:

[0045] 2.3.1. Construct the feasible space of decision-making standards for the operation of urban drainage and storage facilities, and expand the coordination weight vectors of various decision-making standards for the operation of urban drainage and storage facilities from a single point to certain subspaces in the weight space. The feasible space is the union of all possible weight vectors; 2.3.2. The feasible space of decision-making standards for urban drainage and storage facilities is regarded as a subspace in the plane, the center of which corresponds to the coordination weight vector of the operation of urban drainage and storage facilities. By applying interval constraints within the boundary of the feasible space, the probability distribution is used to measure the uncertainty of the weights of various decision-making standards for the operation of urban drainage and storage facilities.

[0046] Furthermore, the step 3.1 is specifically as follows:

[0047] 3.1.1. Define the triangular fuzzy function for the operation of urban drainage storage facilities and construct a fuzzy decision matrix for the operation of urban drainage storage facilities. Use the triangular fuzzy function to represent the performance preference values ​​of each alternative operation scheme for urban drainage storage facilities with respect to each decision criterion.

[0048] 3.1.2. Define the fuzzy anti-ideal weight distance and ideal weight distance for the operation of urban drainage storage facilities. Although ideal alternatives do not exist in real life, they provide a benchmark for evaluating alternatives.

[0049] 3.1.3. Fuzzy optimization is performed on the multi-criteria decision-making analysis for the operation of urban drainage storage and regulation facilities. Based on the decision-making criteria for the multi-criteria decision-making for the operation of urban drainage storage and regulation facilities, a global evaluation of the alternative plans for the operation of urban drainage storage and regulation facilities is performed to obtain a ranking of the alternative plans for the operation of urban drainage storage and regulation facilities.

[0050] Furthermore, the step 3.2 is specifically as follows:

[0051] 3.2.1. Targeting the multi-criteria decision-making analysis problem for the operation of urban drainage and storage facilities, a stochastic multi-criteria decision-making analysis-fuzzy optimization model for urban drainage and storage facility operation is established using stochastic multi-criteria decision-making methods and fuzzy optimization models. This optimization model combines the characteristics of the fuzzy optimization model and the stochastic multi-criteria decision-making analysis framework. To evaluate the performance of alternative operation plans for urban drainage and storage facilities based on the existing stochastic multi-criteria decision-making analysis framework, a real-valued utility function for the operation of urban drainage and storage facilities is defined.

[0052] 3.2.2. In order to better evaluate the initial alternative operation plans of urban drainage and storage facilities, based on the random multi-criteria decision-making analysis-fuzzy optimization model of urban drainage and storage facilities operation, the uncertainty measure of the multi-criteria decision-making analysis of urban drainage and storage facilities operation is calculated from four dimensions to provide a basis for the final decision-making of urban drainage and storage facilities operation. The uncertainty measure of the step-by-step decision-making of urban drainage and storage facilities operation mainly includes the following indicators: ① overall acceptability index (HAI), ② grade acceptability index (RAI), ③ confidence factor, and ④ center weight vector (CWV).

[0053] Furthermore, the step 4.1 is specifically as follows:

[0054] To examine and assess the uncertainty of initial alternative operational decisions for urban drainage and storage facilities, this method defines the risk of error in urban drainage and storage facility operational decisions. After using a multi-criteria decision analysis method to determine the highest-ranked alternative for urban drainage and storage facility operations, decision makers typically consider this alternative to be optimal. Obviously, assigning the highest rank to an alternative that is not actually the optimal choice will adversely affect the operation of the urban drainage and storage facility, deviating from the optimal decision for urban drainage and storage facility operations.

[0055] 4.1.1. Calculate the weighted probability that the highest rank is assigned to a non-optimal solution in the operation decision-making of urban drainage and storage facilities. This probability is defined as the risk of error in the operation decision-making of urban drainage and storage facilities. The formula for calculating the risk of error in the operation decision-making of urban drainage and storage facilities is:

[0056] Where, Represents the first-level acceptability index of the k-th alternative based on the overall acceptability index of the urban drainage storage and regulation facility operation decision.k It is the risk weight that distinguishes the role of each non-optimal solution in the total risk, defined as an incremental (m-1) dimensional vector

[0057] 4.1.2. Calculate the sum of the acceptability indices of all possible rankings of the urban drainage storage and regulation facility operation decision-making schemes except the final ranking:

[0058] Where g i is the initial alternative plan A for the operation decision of urban drainage storage facilities i A final rating based on its overall acceptability index.

[0059] Furthermore, the step 4.2 is specifically as follows:

[0060] 4.2.1. Calculate the overall acceptability index of each alternative scheme for the operation of urban drainage storage facilities. The overall acceptability index is expressed as The overall acceptability index is defined as the acceptability of each alternative scheme A for the operation of urban drainage storage facilities. i The ranking r gives the favorable ranking weights of alternatives with different valuations Obviously, the overall acceptability index assigns a certain ranking probability to each alternative. The overall acceptability index ranges from [0,1], where 0 indicates that the urban drainage storage and regulation facility operation alternative is absolutely impossible to be ranked in a certain ranking, and 1 indicates that the urban drainage storage and regulation facility operation alternative is always ranked in a certain ranking. During the multi-criteria decision-making analysis of urban drainage storage and regulation facility operation, the urban drainage storage and regulation facility operation alternative with the highest ranking and high overall acceptability index is generally considered the potential optimal option. Alternatives with poor rankings but high overall acceptability indices are directly deleted from the initial set of urban drainage storage and regulation facility operation alternatives.

[0061] 4.2.2. Calculate the acceptability index of the initial ranking of alternatives for urban drainage and storage facility operation decisions to measure the overall acceptability of each alternative for urban drainage and storage facility operation decisions. The acceptability index of the initial ranking of alternatives for urban drainage and storage facility operation decisions is obtained by weighting the overall acceptability index of all alternatives for urban drainage and storage facility operation decisions:

[0062] Where, α r It is used to show the role of the overall acceptability index of each specific urban drainage storage facility operation alternative in evaluating the alternatives. r Defined as a monotonically decreasing vector:

[0063] 4.2.3. Calculate the confidence factor of each alternative operation scheme of urban drainage storage and regulation facilities. The confidence factor of urban drainage storage and regulation facilities operation is a measure of the confidence factor of each alternative operation scheme of urban drainage storage and regulation facilities. i The expected center of gravity of the first-level weight space is favorable. The confidence factor for urban drainage and storage facility operation shows decision makers the association between different weights and specific decisions, thereby better helping them express their preferences. If the confidence factor for an alternative urban drainage and storage facility operation decision is very low, it means that even if this preference is selected for the multi-criteria decision-making process for urban drainage and storage facility operation, the probability of this alternative receiving the highest ranking is also low. If the confidence factor for an alternative urban drainage and storage facility operation decision is very high, it means that this alternative urban drainage and storage facility operation decision has the most appropriate and highest preference setting.

[0064] The present invention can achieve the following beneficial effects:

[0065] 1. By introducing a step-by-step decision analysis method, the present invention allows decision makers to adjust their decision preferences as information becomes clearer, thereby reducing errors caused by incomplete information in the early stages of decision-making, improving the accuracy and scientific nature of the final decision, and accelerating the decision-making process.

[0066] 2. The present invention, combined with risk assessment, can comprehensively consider the uncertainties in the operation of urban drainage and storage facilities, ensuring that the selected solution can maintain high performance under various possible scenarios, thereby enhancing the stability of the drainage system and its ability to cope with extreme events.

[0067] 3. Through fuzzy optimization model and random multi-criteria decision analysis, the present invention can more accurately evaluate the cost-effectiveness of each alternative plan, rationally allocate limited resources, avoid over-investment or waste of resources, and improve the efficiency of the use of financial funds.

[0068] 4. The present invention utilizes game theory and feasible rights space theory to resolve conflicts among multiple stakeholders, achieve a reasonable aggregation of decision-making criteria weights, promote the harmonious unification of the interests of multiple parties such as the government, operators, and the public, and improve the social acceptance of the decision.

[0069] 5. The present invention quantifies the risk of decision-making errors and the degree of uncertainty, enabling decision makers to intuitively understand the possible consequences of various plans, providing a quantitative basis for formulating risk prevention and control measures and emergency plans, and reducing potential environmental and social risks.

[0070] 6. The present invention fully considers the complexity of the operation of urban drainage and storage facilities, including the influence of multiple factors such as environment, economy, and society, improves the drainage system's adaptability to rapid urban development and climate change, and helps to build a sustainable urban water management system. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0072] FIG1 is a flow chart of a step-by-step decision-making method for operating urban drainage storage facilities according to the present invention;

[0073] FIG2 is a schematic diagram of the feasible space for step-by-step decision-making on the operation of urban drainage storage and regulation facilities according to the present invention;

[0074] FIG3 is a schematic diagram of gradually weighting information in the three-criteria decision analysis process of the present invention. DETAILED DESCRIPTION

[0075] The preferred scheme is shown in Figures 1 to 3. The step-by-step decision analysis method for the operation of urban drainage and storage facilities based on risk assessment adopts a step-by-step decision analysis method under the condition that the preference information of each decision criterion for the operation of urban drainage and storage facilities is completely missing or unclear, and determines the weight information of each decision criterion for the operation of urban drainage and storage facilities in stages, so as to achieve the best decision for urban drainage and storage facilities under the condition of minimum risk.

[0076] As shown in FIG1 , this embodiment discloses a step-by-step decision-making method for the operation of urban drainage storage facilities based on risk assessment, the method comprising the following steps:

[0077] 1. Treat the multi-criteria decision analysis of urban drainage storage and regulation facility operation as a multi-stage decision analysis problem, determine the key influencing factors of urban drainage storage and regulation facility operation scheduling, select appropriate urban drainage storage and regulation facility operation decision criteria, and obtain the urban drainage storage and regulation facility operation random decision matrix;

[0078] 1.1. For the urban drainage storage facility in the embodiment, 1000 initial alternative operation schemes of the urban drainage storage facility are randomly obtained. Prepare a set of initial alternative operation schemes of the urban drainage storage facility A = {A i |i=1,2,…,1000},A i represents the i-th alternative scheme for the operation of urban drainage storage facilities, and 1000 represents the number of initial alternative schemes for the operation of urban drainage storage facilities;

[0079] 1.2. Determine the factors affecting the operation and scheduling of urban drainage storage facilities and select the appropriate decision-making standard set C = {C j |j=1,2,…,n}, in order to sort and screen the initial alternative operation scheme set of urban drainage storage facilities, C j represents the jth decision criterion for the operation of urban drainage storage facilities, and n represents the total number of decision criteria for the operation of urban drainage storage facilities;

[0080] 1.3. Select the parameters that have the greatest impact on the operation of urban drainage storage and regulation facilities as the decision-making criteria for the operation of urban drainage storage and regulation facilities. These criteria include: ① inlet flow; ② storage tank volume; ③ rainfall; ④ inlet water quality monitoring data; ⑤ storage tank outflow; ⑥ storage tank inlet pipe liquid level; ⑦ storage tank pump station size.

[0081] 2. A method for aggregating weights of decision-making criteria for the operation of urban drainage and storage facilities based on a combination of game theory and feasible rights space is proposed to resolve the conflict problem among multiple stakeholders in the decision-making of the operation of urban drainage and storage facilities, and to estimate the uncertainty of the weights of various decision-making criteria for the operation of urban drainage and storage facilities.

[0082] 2.1. In order to quantify the uncertainty of the decision-making criteria for the operation of urban drainage and storage facilities, this method uses the complementary judgment matrix method to quantify the uncertainty of each decision-making criterion. The quantitative decision-making criterion weights of each urban drainage and storage facility are obtained based on the preferences of different decision makers for the decision-making criteria for the operation of each urban drainage and storage facility.

[0083] 2.1.1. Based on the empirical judgment of various decision criteria for the operation of urban drainage and storage facilities, a complementary judgment matrix for each decision criterion for the operation of urban drainage and storage facilities is constructed. Decision makers compare each pair of decision criteria for the operation of urban drainage and storage facilities to determine their relative importance.

[0084] Table 1 gives the verbal preference statements and their corresponding complementary comparison values. You can select the standard weights or directly give the complementary comparison values ​​a that meet the following conditions. ij and a ji To select: a ij +a ji =1

[0085] Where a ij represents the preference of urban drainage storage facility operation decision criterion i relative to urban drainage storage facility operation decision criterion j, a ji It represents the preference of urban drainage storage facility operation decision standard j over urban drainage storage facility operation decision standard i.

[0086] Table 1. Verbal preference statements for decision-making on the operation of urban drainage and storage facilities and their corresponding complementary comparison values.

[0087] The ratio of the complementary comparison values ​​corresponds to the weights:

[0088] will a ji =1-a ij Substituting into the above formula we get:

[0089] Among them, w iand w j They represent the weights of the decision criteria for the operation of the i-th and j-th urban drainage storage facilities, respectively. Based on the comparison values, a complementary judgment matrix can be constructed:

[0090] Where CJM represents the complementary judgment matrix of the multi-criteria decision analysis criteria for the operation of urban drainage and storage facilities. The main diagonal elements are equal to 0.5, because the importance of each criterion is equal. 2.1.2. Considering that the complementary judgment matrix of the decision criteria for the operation of urban drainage and storage facilities usually contains a certain degree of inconsistency, the least squares method is used to obtain the weight value of each decision criterion for the operation of urban drainage and storage facilities; according to get:

[0091] Taking into account the planning conditions of the weight values ​​of each decision-making criterion for the operation of urban drainage storage facilities to identify incompatible solutions, for solving the linear system, the weight values ​​of each decision-making criterion for the operation of urban drainage storage facilities can be obtained:

[0092] According to the above two equations, we can get a linear equation system, which can be further simplified to (n 2 -n) / 2 constraints and (n-1) variables: HW=b

[0093] Where W=[w1,w2,…,w n-1 ]. It is found that the linear system is overdetermined, and the least squares solution can be derived as: W=(HTH) -1 HTb

[0094] After solving W, according to Calculate the final weight w of each decision criterion for the operation of urban drainage storage facilities n .

[0095] 2.1.3. Based on the complementary weights calculated in step 2.1.1 and the weights of each decision criterion determined in step 2.1.2, calculate the inconsistency error of the weights of each city's drainage and storage facility operation decision criterion and assess the inconsistency of the weights of each city's drainage and storage facility operation decision criterion. If the inconsistency error is small, the decision makers' empirical judgments are relatively accurate. Conversely, if the inconsistency error is large, the decision makers should reconsider their preference information for each decision criterion.

[0096] 2.1.3. Based on the complementary weights calculated in step 2.1.1 and the weights of each decision criterion determined in step 2.1.2, calculate the inconsistency error of the weights of each city's drainage and storage facility operation decision criterion and assess the inconsistency of the weights of each city's drainage and storage facility operation decision criterion. If the inconsistency error is small, the decision makers' empirical judgments are relatively accurate. Conversely, if the inconsistency error is large, the decision makers should reconsider their preference information for each decision criterion.

[0097] The inconsistency error of the weights of various decision criteria for the operation of urban drainage storage facilities can be calculated as:

[0098] Where, e ij It represents the inconsistent error in the weights of various decision criteria for the operation of urban drainage storage facilities.

[0099] 2.2. Introducing game theory into the stochastic multi-criteria decision-making analysis of urban drainage storage and regulation facility operations, the weights of conflicting decision-making criteria for urban drainage storage and regulation facility operations are aggregated through Nash equilibrium to achieve preference compromise and conflict resolution.

[0100] 2.2.1. Use the complementary judgment matrix method to determine the basic weight vectors of the decision criteria for the operation of urban drainage and storage facilities for each decision maker. Comprehensively consider the basic weight vectors of the decision criteria for each decision maker and use a linear combination method to obtain the basic weight vectors for the operation of urban drainage and storage facilities;

[0101] The decision-making standard value of each city's drainage storage facility operation determined by the complementary judgment matrix method is defined as the basic weight vector Where L represents the number of decision makers involved in the operation decision-making of urban drainage storage facilities. The linear combination of the basic weight vectors for the operation decision-making of urban drainage storage facilities is:

[0102] 2.2.2. Based on Nash equilibrium, optimize the weight combination coefficients of the various decision-making criteria for the operation of urban drainage and storage facilities to achieve a compromise or consistency between the basic weight vectors of the decision-making criteria. Ultimately, a coordinated weight vector for the decision-making criteria for the operation of urban drainage and storage facilities is obtained, and the deviation between the basic weight vectors and the coordinated weight vector for the decision-making criteria for the operation of urban drainage and storage facilities is minimized.

[0103] Obtain the urban drainage storage facility operation decision coordination weight vector w * , and minimize each w k and w * Deviation between:

[0104] Where wk Represents the basic weight vector of each decision-making criterion for the operation of urban drainage storage facilities.

[0105] 2.2.3. Use the linear programming method to solve the urban drainage storage facility operation decision model, obtain the optimal combination coefficient of the urban drainage storage facility operation decision, and calculate the urban drainage storage facility operation decision coordination weight vector.

[0106] The optimal combination coefficient for urban drainage storage facility operation decision-making is expressed as The urban drainage storage facility operation decision coordination weight vector is calculated as follows:

[0107] 2.3 As shown in Figure 2, the concept of feasible rights space is used to quantify the uncertainty of each decision-making standard for the operation of urban drainage storage facilities;

[0108] 2.3.1. Construct a feasible weight space for decision-making criteria for the operation of urban drainage and storage facilities. Expand the coordination weight vectors of each decision-making criterion for the operation of urban drainage and storage facilities from a single point to certain subspaces in the weight space. The feasible weight space is the union of all possible weight vectors.

[0109] 2.3.2. The feasible space of decision-making criteria for the operation of urban drainage and storage facilities is regarded as a subspace in the plane, whose center corresponds to the coordination weight vector of the operation of urban drainage and storage facilities. By applying interval constraints within the boundary of the feasible space, the probability distribution is used to measure the uncertainty of the weights of each decision-making criterion for the operation of urban drainage and storage facilities.

[0110] The feasible space of multi-stage decision-making for the operation of urban drainage storage facilities can be expressed as:

[0111] In the formula, λ represents the uncertainty parameter for the weights of urban drainage and storage facility operation decisions. This parameter's value is related to the degree of conflict among the various criteria for urban drainage and storage facility operation decisions. If all decision-makers involved in urban drainage and storage facility operation decisions agree on a certain coordinated standard weight, λ is very small. Otherwise, a larger value is required to obtain a larger feasible weight space for multi-stage decision-making in urban drainage and storage facility operation. After resolving conflicts among decision-makers through aggregation, the feasible weight space for multi-stage decision-making in urban drainage and storage facility operation can reflect the uncertainty of the weights of various decision-making criteria without losing too much information.

[0112] 3. Combining a stochastic multi-criteria acceptability analysis algorithm with a fuzzy optimization model, a fuzzy optimization model for stochastic multi-criteria decision analysis of the operation of urban drainage and storage facilities is constructed. The uncertainty of the decision criteria and their weights for the operation of urban drainage and storage facilities is simulated and quantified, and several measurement descriptions of the robustness of the decision-making of the operation of urban drainage and storage facilities are given.

[0113] 3.1. Construct a fuzzy optimization model for the operation of urban drainage storage facilities, and use fuzzy anti-ideal distance and ideal distance to solve the multi-criteria decision-making problem of urban drainage storage facilities operation;

[0114] 3.1.1、Define the triangular fuzzy function of urban drainage storage and regulation facilities operation and construct the fuzzy decision matrix of urban drainage storage and regulation facilities operation. Use the triangular fuzzy function to express the performance preference value of each alternative scheme of urban drainage storage and regulation facilities operation for each decision criterion ... represents the performance preference value of each alternative scheme for urban drainage storage and regulation facilities operation for each decision criterion. Normalize to dimensionless value:

[0115] For the income standard

[0116] For cost standards

[0117] 3.1.2. Define the fuzzy anti-ideal weight distance and ideal weight distance for the operation of urban drainage storage facilities. Although ideal alternatives do not exist in real life, they provide a benchmark for evaluating alternatives.

[0118] The anti-ideal urban drainage storage facility operation plan and the ideal urban drainage storage facility operation plan are defined as: g=(g1, g2,…, g n )

[0119] Where g j =(1,1,1), Define the weighted anti-ideal and ideal options for the operation of urban drainage storage facilities: w g =(wg 1, wg 2, …,w gn )

[0120] Where, w j Indicates standard C j The weight of is a triangular fuzzy value in [0,1]. The fuzzy anti-ideal and ideal weighted distances are defined to measure the difference between the alternative operation schemes and the anti-ideal schemes of each city's drainage storage and regulation facilities.

[0121] Where, Indicates alternative operation plan A for urban drainage storage facilities i The weighted performance preference value vector of q=1 represents the Hemming distance, and q=2 represents the Euclidean distance.

[0122] 3.1.3. Fuzzy optimization is performed on the multi-criteria decision-making analysis for the operation of urban drainage and storage facilities. Based on the various decision-making criteria for the multi-criteria decision-making for the operation of urban drainage and storage facilities, a global evaluation is conducted on the alternative operation plans for urban drainage and storage facilities to obtain the ranking of the alternative operation plans for urban drainage and storage facilities.

[0123] Let u i Indicates that the operation of urban drainage storage facilities is based on all standards. i Global evaluation, in order to obtain u i The optimal value of , establish an objective function to minimize the sum of the squares of the weighted fuzzy ideal weight distance and its corresponding distance: min f (u i )=(u i ·dg i ) 2 +[(1-u i )·db i ] 2

[0124] Differentiating the above function yields:

[0125] Finally, we can get:

[0126] Where u i Alternative operation scheme A for urban drainage storage facilities based on the fuzzy concept of "optimal under all criteria" i According to the above definition, the membership degree u i The alternative is the most preferred alternative. In addition, by sorting the membership degrees corresponding to the alternatives for the operation of urban drainage storage facilities, the sorting order of the alternatives can be simply determined.

[0127] 3.2. Using stochastic multi-criteria decision analysis and fuzzy optimization models, establish a stochastic multi-criteria decision analysis-fuzzy optimization model for the operation of urban drainage and storage facilities. Calculate the uncertainty measures for each alternative operation plan for urban drainage and storage facilities and evaluate the alternative operation plans for each urban drainage and storage facility.

[0128] 3.2.1. Targeting the multi-criteria decision-making analysis problem for the operation of urban drainage and storage facilities, a stochastic multi-criteria decision-making analysis-fuzzy optimization model for urban drainage and storage facility operation is established using stochastic multi-criteria decision-making methods and fuzzy optimization models. This optimization model combines the characteristics of the fuzzy optimization model and the stochastic multi-criteria decision-making analysis framework. To evaluate the performance of alternative operation plans for urban drainage and storage facilities based on the existing stochastic multi-criteria decision-making analysis framework, a real-valued utility function for the operation of urban drainage and storage facilities is defined.

[0129] In order to evaluate the performance of the alternative operation schemes of urban drainage storage facilities based on the original stochastic multi-criteria decision analysis framework, the real-valued utility function s(·) of the operation of urban drainage storage facilities is defined as follows:

[0130] Where x i Alternative A for the operation of urban drainage storage facilities i The performance preference value vector for each decision criterion.

[0131] 3.2.2. In order to better evaluate the alternative operation plans of urban drainage and storage facilities, based on the random multi-criteria decision-making analysis-fuzzy optimization model of urban drainage and storage facilities operation, the uncertainty measure of the multi-criteria decision-making analysis of urban drainage and storage facilities operation is calculated from four dimensions to provide a basis for the final decision-making of urban drainage and storage facilities operation. The uncertainty measure of urban drainage and storage facilities operation mainly includes the following indicators: ① overall acceptability index (HAI), ② grade acceptability index (RAI), ③ confidence factor, and ④ center weight vector (CWV).

[0132] 4. Construct a risk assessment model for the operation of urban drainage and storage facilities, calculate the degree of uncertainty and the risk of decision-making errors for the operation alternatives of urban drainage and storage facilities, and quantitatively assess the risk of decision-making errors in the operation of urban drainage and storage facilities; 4.1. Calculate the risk of decision-making errors for the operation plans of urban drainage and storage facilities, and quantitatively assess the uncertainty of the operation alternatives of urban drainage and storage facilities;

[0133] To examine and assess the uncertainty of various urban drainage storage and regulation facility operation plans, this method defines the risk of operational errors in urban drainage storage and regulation facility operations. After using a multi-criteria decision analysis method to determine the highest-ranked plan for urban drainage storage and regulation facility operations, decision makers typically consider this plan to be optimal. Obviously, assigning the highest rank to a plan that is not actually the best option will adversely affect the operation of the urban drainage storage and regulation facility and deviate from the optimal sediment removal decision.

[0134] 4.1.1. Calculate the weighted probability that the highest rank is assigned to a non-optimal solution in the operation decision-making of urban drainage and storage facilities. This probability is defined as the risk of error in the operation decision-making of urban drainage and storage facilities. The formula for calculating the risk of error in the operation decision-making of urban drainage and storage facilities is:

[0135] Where, represents the first-level acceptability index of the k-th alternative based on the overall acceptability index. k It is the risk weight that distinguishes the role of each non-optimal solution in the total risk, defined as an incremental (m-1) dimensional vector

[0136] 4.1.2. Calculate the sum of the acceptability indices of all possible rankings of the urban drainage storage and regulation facility operation decision-making schemes except the final ranking:

[0137] Where g i The alternative schemes for the operation of urban drainage storage facilities are A i A final rating based on its overall acceptability index.

[0138] 4.2. Calculate the uncertainty of the operation plan of urban drainage storage and regulation facilities, and quantitatively evaluate the overall uncertainty of the ranking results of the alternative operation plans of urban drainage storage and regulation facilities.

[0139] 4.2.1. Calculate the overall acceptability index of each alternative scheme for the operation of urban drainage storage facilities. The overall acceptability index is expressed as The overall acceptability index is defined as the acceptability of each alternative scheme A for the operation of urban drainage storage facilities. i The ranking r gives the favorable ranking weights of alternatives with different valuations Obviously, the overall acceptability index assigns a certain ranking probability to each alternative. The overall acceptability index ranges from [0,1], where 0 indicates that the urban drainage storage and regulation facility operation alternative is absolutely impossible to be ranked in a certain ranking, and 1 indicates that the urban drainage storage and regulation facility operation alternative is always ranked in a certain ranking. During the multi-criteria decision-making analysis of urban drainage storage and regulation facility operation, the urban drainage storage and regulation facility operation alternative with the highest ranking and high overall acceptability index is generally considered the potential optimal option. Alternatives with poor rankings but high overall acceptability indices are directly deleted from the initial set of urban drainage storage and regulation facility operation alternatives.

[0140] and The calculation formulas are:

[0141] Where, is the most favorable rank weight, which means that any weight vector Granted the Urban Drainage Storage Facility Operation Alternative Plan A i Rank r; rank(·) is a ranking function that gives the order of the options.

[0142] 4.2.2. Calculate the acceptability index of the ranking of urban drainage and storage facilities operation to measure the overall acceptability of the alternative plans for the operation of urban drainage and storage facilities. The acceptability index of the ranking of urban drainage and storage facilities operation is obtained by weighting the overall acceptability index of all alternative plans for the operation of urban drainage and storage facilities:

[0143] Where, α r It is used to show the role of the overall acceptability index of each specific urban drainage storage facility operation alternative in evaluating the alternatives. r Defined as a monotonically decreasing vector:

[0144] 4.2.3. Calculate the confidence factor of each alternative operation scheme of urban drainage storage and regulation facilities. The confidence factor of urban drainage storage and regulation facilities operation is a measure of the confidence factor of each alternative operation scheme of urban drainage storage and regulation facilities. i The expected center of gravity of the favorable first-level weight space. The confidence factor of the operation of urban drainage and storage facilities shows decision makers the association between different weights and specific decisions, thereby better helping decision makers to express their preferences. If the confidence factor of an alternative plan for the operation of urban drainage and storage facilities is very low, it means that even if this preference is selected for the multi-criteria decision-making on the operation of urban drainage and storage facilities, the probability of this alternative plan obtaining the highest ranking is also very low. If the confidence factor of an alternative plan for the operation of urban drainage and storage facilities is very high, it means that this alternative plan for the operation of urban drainage and storage facilities has the most appropriate and highest preference setting;

[0145] In the form of multidimensional integrals in the favorable first-level weight and the standard weight distribution f x (ξ) we get:

[0146] Confidence factor (using ) represents the probability that an alternative becomes the most preferred option using its weighted solution. Determine whether the criteria weights are sufficiently accurate in distinguishing between candidate solutions. Expressed as a multidimensional integral over a standard weight distribution:

[0147] 5. As shown in Figure 3, a multi-stage decision-making process is performed on the operation of urban drainage storage facilities based on the step-by-step weight information method to ensure that the drainage network cleaning decision plan is gradually solved within an acceptable decision risk range.

[0148] The multi-stage decision-making process for the operation of urban drainage and storage facilities begins with completely missing or unclear preference information and gradually obtains more accurate information as the process progresses. The basic idea is to iteratively run the stochastic multi-criteria decision-making fuzzy model for the operation of urban drainage and storage facilities after completing each round of information collection related to urban drainage and storage facility operation decisions, until sufficient preference information for the final decision is obtained within an acceptable risk of decision error. After each analysis of the stochastic multi-criteria decision-making fuzzy model for the operation of urban drainage and storage facilities, preference information is added by more accurately evaluating the decision maker's preferences. If sufficient inaccurate information is available at the early stages of the multi-stage decision-making process for the operation of urban drainage and storage facilities, the preference collection process can be significantly saved and the complex weighting process can be avoided.

[0149] 5.1. When the weight information of the multi-criteria decision-making analysis of the operation of urban drainage and storage facilities is missing, the missing weight information is expressed by the uniform distribution of the weight space of the operation of urban drainage and storage facilities.

[0150] In the initial stages of the multi-stage decision-making process for urban drainage and storage facility operations, decision-makers often find it difficult to express their preferences because the available decision-support information is very limited. Unlike traditional urban drainage and storage facility operation decision-making processes, decision-makers do not need to express any preferences in the first stage. Instead, the stochastic multi-criteria decision-making fuzzy model for urban drainage and storage facility operations is run using the entire weight space. This missing weight information is expressed through a uniform distribution across the weight space.

[0151] 5.2. Based on the statements of each decision maker’s preference for various operation standards of urban drainage storage and regulation facilities, the weight information of the multi-stage decision sequence for the operation of urban drainage storage and regulation facilities is obtained.

[0152] The weight information of the multi-stage decision sequence of urban drainage storage facilities operation is expressed in the form of linear constraints, such as w1>w2>…>w n The weight information for the multi-stage decision-making sequence for the operation of urban drainage and storage facilities corresponds to the decision-maker's preference statement, that is, criterion 1 is more important than criterion 2. Of course, there are also cases where the decision-maker cannot judge certain criteria (w1?w2) or considers them equally important (w1=w2). The weight information for the multi-stage decision-making sequence for the operation of urban drainage and storage facilities can be represented as a triangular plane within the weight space of urban drainage and storage facility operation.

[0153] 5.3. The complementary matrix method is used to determine the quantitative weights of various operation standards for urban drainage and storage facilities. The uncertainty of the weights is estimated through the probability distribution within the boundary of the feasible space for multi-stage decision-making on the operation of urban drainage and storage facilities under interval constraints. The weight interval can be expressed as a hexagonal plane within the entire feasible space for multi-stage decision-making on the operation of urban drainage and storage facilities.

[0154] 5.4. Utilize deterministic weight vectors to generate the final decision on the operation of urban drainage and storage facilities under an acceptable risk of decision error. If the multi-stage decision-making process for the operation of urban drainage and storage facilities is a single-decision-maker process, the complementary judgment matrix method is used to directly calculate and determine the weight vectors for each criterion of the urban drainage and storage facility operation. If the multi-stage decision-making process for the operation of urban drainage and storage facilities is a multiple-decision-maker process, the complementary judgment matrix method is used to calculate the weight vectors for each criterion for each decision-maker, and the weight aggregation method is used to obtain the coordination weight vectors for each criterion.

[0155] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions set forth in the claims, including equivalent alternatives to the technical features of the technical solutions set forth in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A step-by-step decision-making analysis method for the operation of urban drainage storage facilities based on risk assessment, characterized in that: S1. Regard the multi-criteria decision-making analysis of the operation of urban drainage storage facilities as a multi-stage decision-making analysis problem, determine the key influencing factors for the operation and scheduling of urban drainage storage facilities, select appropriate decision-making criteria for the operation of urban drainage storage facilities, and obtain a stochastic decision matrix for the operation of urban drainage storage facilities; S2. Propose a method for aggregating the weights of decision-making criteria for the operation of urban drainage storage facilities based on the combination of game theory and the feasible weight space, solve the conflict problem among multiple stakeholders in the decision-making of the operation of urban drainage storage facilities, and estimate the uncertainty of the weights of each decision-making criterion for the operation of urban drainage storage facilities; S3. Combine the stochastic multi-criteria acceptability analysis algorithm and the fuzzy optimization model to construct a fuzzy optimization model for the stochastic multi-criteria decision-making analysis of the operation of urban drainage storage facilities, simulate and quantify the uncertainty of each decision-making criterion and its weight for the operation of urban drainage storage facilities, and give several measure descriptions of the robust decision-making for the operation of urban drainage storage facilities; S4. Construct a risk assessment model for the operation decision of urban drainage storage facilities, calculate the uncertainty degree and decision-making error risk of each initial alternative plan for the operation of urban drainage storage facilities, and quantitatively evaluate the risk of decision-making errors in the operation of urban drainage storage facilities; S5. Conduct multi-stage decision-making on the operation of urban drainage storage facilities based on the step-by-step weight information method to ensure that each decision-making plan for the operation of urban drainage storage facilities is gradually solved within an acceptable decision-making risk range.

2. The step-by-step decision-making analysis method for the operation of urban drainage and storage facilities based on risk assessment according to claim 1, characterized in that: The sub-steps of step S1 are: S1.

1. Prepare an initial set of alternative operation plans for urban drainage storage facilities: A = {A i | i = 1, 2, …, m}, Where A i represents the i-th alternative for the operation of urban drainage storage facilities, and m represents the number of initial alternative schemes for the operation of urban drainage storage facilities; S1.

2. Determine the influencing factors for the operation and scheduling of urban drainage storage facilities, and select an appropriate set of decision-making criteria for the operation plan of urban drainage storage facilities: C = {C j | j = 1, 2, …, n}, where C j represents the j-th decision criterion for the operation of urban drainage regulation facilities, and n represents the total number of decision criteria for the operation of urban drainage regulation facilities; the decision criterion set for the operation plan of urban drainage regulation facilities is used to sort and screen the initial alternative plan set for the operation of urban drainage regulation facilities; S1.

3. Select the parameter that has the greatest impact on the operation of urban drainage storage facilities as the decision-making criterion for the operation of urban drainage storage facilities. The decision-making criteria for the operation of urban drainage storage facilities include influent flow rate, storage tank volume, rainfall, influent water quality monitoring data, storage tank effluent flow rate, storage tank inlet pipe liquid level, and storage tank pump station size.

3. According to the step-by-step decision-making analysis method for the operation of urban drainage storage facilities based on risk assessment described in claim 1, characterized in that: the sub-steps of step S2 are: S2.

1. Quantify the uncertainty of each decision-making criterion using the complementary judgment matrix method, and obtain the quantitative decision-making criterion weights for each urban drainage storage facility according to the preferences of different decision-makers for each decision-making criterion for the operation of urban drainage storage facilities; used to quantify the uncertainty of the decision-making criteria for the operation of urban drainage storage facilities; S2.

2. Introduce game theory into the stochastic multi-criteria decision-making analysis of urban drainage storage facilities, and aggregate the weights of each conflicting decision-making criterion for the operation of urban drainage storage facilities through Nash equilibrium to achieve preference compromise and conflict resolution, and obtain the coordinated weights of the decision-making criteria for the operation of urban drainage storage facilities; S2.

3. Adopt the method of feasible weight space to establish a feasible weight space for the decision-making criteria for the operation of urban drainage storage facilities, and quantify the uncertainty of each decision-making criterion for the operation of urban drainage storage facilities.

4. The step-by-step decision-making analysis method for the operation of urban drainage storage facilities based on risk assessment according to claim 3, characterized in that: The sub-steps of step S2.1 are: S2.1.

1. Construct a complementary judgment matrix for each decision-making criterion of the urban drainage regulation facility operation; compare each pair of decision-making criteria for the urban drainage regulation facility operation to determine their relative importance; S2.1.

2. Considering that the complementary judgment matrix for each decision-making criterion of the urban drainage regulation facility operation usually contains a certain degree of inconsistency, use the least squares method to obtain the weight values of each decision-making criterion for the urban drainage regulation facility operation; S2.1.

3. According to the complementary weight values calculated in step S2.1.1 and the weight values of each decision-making criterion determined in step S2.1.2, calculate the inconsistency error of the weight values of each decision-making criterion for the urban drainage regulation facility operation, and evaluate the inconsistency of the weight values of each decision-making criterion for the urban drainage regulation facility operation; If the inconsistency error of the weight values of each decision-making criterion for the urban drainage regulation facility operation is small, it means that the empirical judgment of each decision maker is relatively accurate; on the contrary, if the inconsistency error of the weight values of each decision-making criterion for the urban drainage regulation facility operation is large, each decision maker should reconsider the preference information of each decision-making criterion.

5. The step-by-step decision-making analysis method for the operation of urban drainage storage facilities based on risk assessment according to claim 3, characterized in that: The sub-steps of step S2.2 are as follows: S2.2.

1. Use the complementary judgment matrix method to determine the basic weight vectors of each decision-making criterion for the urban drainage regulation facility operation of each decision maker. Considering the basic weight vectors of each decision-making criterion of each decision maker comprehensively, use the linear combination method to obtain the basic weight vector of the decision-making criterion for the urban drainage regulation facility operation; S2.2.

2. According to the Nash equilibrium, optimize the weight combination coefficients of each decision-making criterion for the urban drainage regulation facility operation to make the basic weight vectors of each decision-making criterion compromise or consistent. Finally, obtain the coordinated weight vector of the decision-making criterion for the urban drainage regulation facility operation, and minimize the deviation between the basic weight vectors of each decision-making criterion for the urban drainage regulation facility operation and the coordinated weight vector; S2.2.

3. Use the linear programming method to solve the decision-making model for the urban drainage regulation facility operation, obtain the optimal combination coefficient of the decision-making for the urban drainage regulation facility operation, and calculate the coordinated weight vector of the decision-making for the urban drainage regulation facility operation.

6. The method for gradually making decisions on the operation of urban drainage storage facilities based on risk assessment according to claim 3, wherein: The sub-steps of step S2.3 are as follows: S2.3.

1. Construct a feasible weight space for the decision-making criterion of the urban drainage regulation facility operation, expand the coordinated weight vector of each decision-making criterion for the urban drainage regulation facility operation from a single point to a subspace in the weight space, and the feasible weight space is the union of all possible weight vectors; S2.3.

2. Regard the feasible weight space of the decision-making criterion of the urban drainage regulation facility as a subspace in the plane, and its center corresponds to the coordinated weight vector of the urban drainage regulation facility operation. By applying interval constraints within the boundary of the feasible weight space, use probability distribution to measure the uncertainty of the weight of each decision-making criterion for the urban drainage regulation facility operation.

7. The step-by-step decision-making analysis method for the operation of urban drainage storage facilities based on risk assessment according to claim 1, characterized in that: The sub-steps of step S3 are as follows: S3.

1. When solving the multi-criterion decision-making problem of the urban drainage regulation facility operation, introduce a fuzzy function and establish a fuzzy optimization model for the decision-making of the urban drainage regulation facility operation, and use the fuzzy ideal distance and the fuzzy anti-ideal distance to solve the multi-criterion decision-making problem of the urban drainage regulation facility operation respectively; S3.

2. Introduce the fuzzy optimization model for the operation decision of urban drainage and storage facilities based on the random multi-criteria decision analysis model, establish the random multi-criteria decision analysis - fuzzy optimization model for the operation decision of urban drainage and storage facilities, solve the model to obtain the uncertainty measure of each initial alternative plan for the operation of urban drainage and storage facilities, and compare and evaluate the advantages and disadvantages of each initial alternative plan for the operation of urban drainage and storage facilities.

8. The step-by-step decision-making analysis method for the operation of urban drainage storage facilities based on risk assessment according to claim 7, characterized in that: The sub-steps of step S3.1 are as follows: S3.1.

1. Define the triangular fuzzy function for the operation of urban drainage and storage facilities and construct the fuzzy decision matrix for the operation of urban drainage and storage facilities. Use the triangular fuzzy function to represent the performance preference values of each alternative plan for the operation of urban drainage and storage facilities for each decision criterion. S3.1.

2. Define the fuzzy anti-ideal weight distance and ideal weight distance for the operation of urban drainage and storage facilities. S3.1.

3. Conduct fuzzy optimization for the multi-criteria decision analysis of the operation of urban drainage and storage facilities, and conduct a global evaluation of the alternative plans for urban drainage and storage facilities according to each decision criterion of the multi-criteria decision analysis of the operation of urban drainage and storage facilities to obtain the ranking of each alternative plan for the operation of urban drainage and storage facilities.

9. The step-by-step decision-making analysis method for the operation of urban drainage and storage facilities based on risk assessment according to claim 7, characterized in that: The sub-steps of step S3.2 are as follows: S3.2.

1. For the multi-criteria decision analysis problem of the operation of urban drainage and storage facilities, establish the random multi-criteria decision analysis - fuzzy optimization model for the operation of urban drainage and storage facilities by using the random multi-criteria decision analysis method and the fuzzy optimization model. S3.2.

2. In order to better evaluate each initial alternative plan for the operation of urban drainage and storage facilities, based on the random multi-criteria decision analysis - fuzzy optimization model for the operation of urban drainage and storage facilities, calculate the uncertainty measure of the multi-criteria decision analysis for the operation of urban drainage and storage facilities from four dimensions, providing a basis for the final decision of the operation of urban drainage and storage facilities. The uncertainty measure of the gradual decision of the operation of urban drainage and storage facilities mainly includes the following indicators: ① overall acceptability index, ② grade acceptability index, ③ confidence factor, ④ central weight vector. The sub-steps of step S4 are as follows:

10. The step-by-step decision-making analysis method for the operation of urban drainage storage facilities based on risk assessment according to claim 1, characterized in that: S4.

1. Calculate the decision-making error risk of the operation plan of urban drainage and storage facilities, and quantitatively evaluate the uncertainty of each initial alternative plan for the operation of urban drainage and storage facilities; used to fully evaluate the uncertainty of each initial alternative plan for the operation of urban drainage and storage facilities. S4.

2. After obtaining the ranking of each initial alternative plan for the operation of urban drainage and storage facilities, calculate the uncertainty degree of each initial plan for the operation of urban drainage and storage facilities according to the ranking results of each initial alternative plan for the operation of urban drainage and storage facilities, and quantitatively evaluate the overall uncertainty of each initial alternative plan for the operation of urban drainage and storage facilities. The sub-steps of step S4.1 are as follows:

11. The step-by-step decision-making analysis method for the operation of urban drainage regulation facilities based on risk assessment according to claim 10, characterized in that: The sub-steps of step S4.2 are as follows: S4.1.

1. Calculate the weighted probability that the operation decision of urban drainage regulation facilities assigns the highest rank to non-optimal schemes, and define it as the risk of operation decision error of urban drainage regulation facilities. The calculation formula for the risk of operation decision error of urban drainage regulation facilities is as follows: In the formula, denotes the first - level acceptability index of the k - th alternative for the overall acceptability index of the operation decision - making of urban drainage regulation facilities; β k is the risk weight that differentiates the role of each non - optimal alternative in the total risk, defined as an incremental (m - 1) - dimensional vector S4.1.

2. Calculate the sum of the grade acceptability indices obtained for all possible rankings except the final ranking for each scheme of the operation decision of urban drainage regulation facilities: where, g i is the final grade of each initial alternative A i for the operation decision-making of urban drainage regulation facilities according to its overall acceptability index.

12. The step-by-step decision-making analysis method for the operation of urban drainage storage facilities based on risk assessment according to claim 11, characterized in that: volume; 4.2.

1. Calculate the overall acceptability index for each alternative operation of urban drainage and storage facilities. The overall acceptability index is represented by Indicates that the overall acceptability index is defined as the favorable level weight of alternative solutions with different valuations given by the ranking r of each alternative solution A for the operation of urban drainage regulation facilities i of the ranking r for alternative solutions with different valuations The overall acceptability index assigns a certain probability of ranking to each alternative plan. The value range of the overall acceptability index is [0, 1]. 0 indicates that the alternative plan for the operation of this urban drainage and storage facility is absolutely impossible to be in a certain ranking, and 1 indicates that the alternative plan for the operation of this urban drainage and storage facility is always in a certain ranking. ​ In the process of multi-criteria decision-making analysis for the operation of urban drainage regulation facilities, the operation alternative of urban drainage regulation facilities with the highest ranking and a high overall acceptability index is usually regarded as the potential optimal solution. For the alternative with a poor ranking but a high overall acceptability index, it is directly deleted from the initial alternative set of the operation of urban drainage regulation facilities; 4.2.

2. Calculate the acceptability index for ranking the initial alternative solutions for the operation decision of urban drainage regulation facilities, which is used to measure the overall acceptability of each alternative solution for the operation decision of urban drainage regulation facilities; the acceptability index for ranking the initial alternative solutions for the operation decision of urban drainage regulation facilities is obtained by weighting the overall acceptability indices of all alternative solutions for the operation of urban drainage regulation facilities: where α r is used to show the role of the overall acceptability index of each specific urban drainage storage facility operation alternative in evaluating each alternative; α r is defined as a monotonically decreasing vector: 4.2.

3. Calculate the confidence factors of each alternative for the operation of urban drainage and storage facilities; the confidence factor for the operation of urban drainage and storage facilities is a measure of the expected centroid of the favorable first-level weight space for each alternative A of the operation of urban drainage and storage facilities i ; the confidence factor for the operation of urban drainage and storage facilities shows the decision maker the association between different weights and a specific decision, thus better helping the decision maker to express their preferences. If the confidence factor of an operation decision alternative for urban drainage regulation facilities is very low, it indicates that even if this preference is used for multi-criteria decision-making on the operation of urban drainage regulation facilities, the probability of this alternative obtaining the highest ranking is very low; If the confidence factor of an operation alternative for urban drainage regulation facilities is very high, it indicates that this operation alternative for urban drainage regulation facilities has the most appropriate and highest preference setting.

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