Step-by-step decision analysis method for operation of urban drainage storage facilities based on risk assessment

Abstract

A step-by-step decision analysis method for the operation of urban drainage and storage facilities based on risk assessment is proposed. 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, the weights of the operation of urban drainage and storage facilities are aggregated by combining game theory and feasible weight space. A random multi-criteria decision analysis algorithm and fuzzy optimization model are used to construct a random multi-criteria decision analysis fuzzy optimization model for the operation of urban drainage and storage facilities. A risk assessment model for the operation of urban drainage and storage facilities is constructed to quantitatively assess the risk of decision-making errors in the operation of urban drainage and storage facilities. Multi-stage multi-criteria decision analysis is used to gradually determine the weight information of various standards for the operation of urban drainage and storage facilities, thereby achieving the best decision for the operation of urban drainage and storage facilities.

Description

Technical Field

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

[0002] Most of the old urban areas in my country are combined sewer systems. Due to the limitations of underground space and huge investment in transformation, it is still impossible to achieve complete rainwater and sewage diversion transformation at the current stage. Most cities have set up terminal interception and storage facilities at the end to control the overflow pollution problem in the rainy season; the construction of new urban areas adopts a diversion drainage system. In order to prevent the initial rain pollution from deteriorating the water quality, most cities have set up initial rain interception and storage facilities. Due to the large size of the city, complex pipe network, frequent extreme rainfall weather, unscientific control strategy, and failure to achieve system coordination with the plant network river, the drainage storage project has problems such as low peak control effect, poor control of overflow times and overflow volume, and low operation efficiency. In response to these problems, some cities in China have begun to actively explore the establishment of relevant models to improve the efficiency of pollution interception and adopt some high-efficiency treatment methods to deal with overflow pollution. Among them, the multi-criteria decision analysis method guides the operation of urban drainage storage facilities based on various monitoring data of urban drainage storage facilities. At present, some multi-criteria decision analysis methods have been applied in the operation and management of urban drainage storage facilities. These methods can generally be divided into six categories: (1) utility function and multi-criteria evaluation value; (2) method evaluation to the distance of the ideal point; (3) pairwise comparison; (4) fuzzy set analysis; (5) transcendence method; (6) customized method. However, most of the 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) Select appropriate decision criteria; (2) Use various monitoring data of urban drainage storage facilities to obtain various urban drainage storage facility operation alternatives and performance values; (3) Determine the criteria and weights of various urban drainage storage facility operation alternatives according to decision preferences; (4) Conduct multi-criteria decision analysis process; (5) Obtain 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, which is closely related to a variety of complex factors such as society, economy, and environment, and has the characteristics of timeliness, irreversibility, and uncertainty. In the traditional decision-making 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 fact, decision makers usually face great psychological pressure in the process of multi-criteria decision analysis. Preference information is the most critical and sensitive parameter that directly affects the model output (i.e. the recommended drainage network cleaning solution). Obviously, the traditional multi-criteria decision analysis method is not the best choice for decision makers. This is because the weighted criterion is one of the most difficult steps in multi-criteria decision analysis, which is completely determined by the decision maker.

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

[0005] 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 and 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.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A step-by-step decision analysis method for the operation of urban drainage storage facilities based on risk assessment, the steps are:

[0008] The multi-criteria decision analysis of the operation of urban drainage and storage facilities is regarded as a multi-stage decision analysis problem, the key influencing factors of the operation and scheduling of urban drainage and storage facilities are determined, the appropriate decision criteria for the operation of urban drainage and storage facilities are selected, and the random decision matrix for the operation of urban drainage and storage facilities is obtained; 2. A weight aggregation method for the decision criteria for the operation of urban drainage and storage facilities based on the combination of game theory and feasible space is proposed to solve the conflict problem among multiple stakeholders in the decision-making of the operation of urban drainage and storage facilities, and the uncertainty of the weights of each decision criterion for the operation of urban drainage and storage facilities is estimated;

[0009] 3. Combining the random multi-criteria acceptability analysis algorithm and the fuzzy optimization model, a fuzzy optimization model for random multi-criteria decision analysis of urban drainage and storage facilities is constructed. The uncertainty of the decision criteria and their weights of urban drainage and storage facilities is simulated and quantified, and several measurement descriptions of the robustness decision of urban drainage and storage facilities are given;

[0010] 4. Construct a risk assessment model for the operation decision of urban drainage and storage facilities, calculate the uncertainty degree and decision-making error risk of each initial alternative plan for the operation of urban drainage and storage facilities, and quantitatively assess the risk of decision-making errors in the operation of urban drainage and storage facilities;

[0011] 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.

[0012] Further, the step 1 is specifically as follows:

[0013] 1.1 Prepare a set of initial alternative scenarios for the operation of urban drainage storage facilities , Indicates the operation of urban drainage storage facilities alternatives, It represents the number of initial alternatives for the operation of urban drainage storage facilities;

[0014] 1.2. Determine the factors affecting the operation and dispatch of urban drainage storage facilities and select the appropriate decision-making standard set for the operation plan of urban drainage storage facilities. , in order to sort and screen the initial alternative operation scheme set for urban drainage storage facilities, Indicates the operation of urban drainage storage facilities decision criteria, It represents the total number of decision criteria for the operation of urban drainage storage facilities;

[0015] 1.3. Select the parameters that have the greatest impact on the operation of urban drainage storage facilities as the decision-making criteria for the operation of urban drainage storage facilities. These criteria include: ① inlet flow; ② storage tank volume; ③ rainfall; ④ inlet water quality monitoring data; ⑤ storage tank outflow flow; ⑥ storage tank inlet pipe liquid level; ⑦ storage tank pump station size.

[0016] Furthermore, the step 2 is specifically as follows:

[0017] 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, and obtains the weight of the quantitative decision-making criteria for each urban drainage and storage facility based on the preferences of different decision makers for the decision-making criteria for the operation of each urban drainage and storage facility;

[0018] 2.2. Introduce game theory into the random multi-criteria decision analysis of urban drainage storage facilities, aggregate the weights of the conflicting decision criteria for the operation of urban drainage storage facilities through Nash equilibrium, so as to achieve preference compromise and conflict resolution, and obtain the coordination weights of the decision criteria for the operation of urban drainage storage facilities;

[0019] 2.3. Adopt the concept of feasible rights space, establish the feasible rights space of the decision-making standards for the operation of urban drainage and storage facilities, and quantify the uncertainty of each decision-making standard for the operation of urban drainage and storage facilities;

[0020] Furthermore, the step 3 is specifically as follows:

[0021] 3.1. When solving the multi-criteria decision-making problem of urban drainage and storage facilities operation, fuzzy functions are introduced and a fuzzy optimization model for urban drainage and storage facilities operation decision-making is established. Fuzzy ideal distance and fuzzy anti-ideal distance are used to solve the multi-criteria decision-making problem of urban drainage and storage facilities operation;

[0022] 3.2. Based on the random multi-criteria decision analysis model, a fuzzy optimization model for the operation decision of urban drainage and storage facilities is introduced, and a random multi-criteria decision analysis-fuzzy optimization model for the operation decision of urban drainage and storage facilities is established. The uncertainty measure of each initial alternative scheme for the operation of urban drainage and storage facilities is obtained by solving the model, and the advantages and disadvantages of each initial alternative scheme for the operation of urban drainage and storage facilities are compared and evaluated;

[0023] Furthermore, the step 4 is specifically as follows:

[0024] 4.1. In order to further fully evaluate the uncertainty of the initial alternative operation plans of each city's drainage and storage facilities, the risk of decision-making errors in the operation plans of urban drainage and storage facilities is calculated, and the uncertainty of the initial alternative operation plans of each city's drainage and storage facilities is quantitatively evaluated;

[0025] 4.2. After obtaining the ranking of each initial alternative operation scheme for each city's drainage and regulation and storage facilities, the uncertainty of each initial operation scheme for urban drainage and regulation and storage facilities is calculated based on the ranking results of the initial alternative operation scheme for each city's drainage and regulation and storage facilities, and the overall uncertainty of each initial alternative operation scheme for urban drainage and regulation and storage facilities is quantitatively evaluated.

[0026] Furthermore, the step 5 is specifically as follows:

[0027] The step-by-step decision-making process for the operation of urban drainage and storage facilities starts with completely missing or unclear preference information, and gradually obtains more accurate information as the decision-making process for the operation of urban drainage and storage facilities develops. The basic idea is to iteratively run the random multi-criteria decision-making fuzzy model for the operation of urban drainage and storage facilities after completing each round of information collection related to the operation of urban drainage and storage facilities, until sufficient final decision preference information is obtained within an acceptable risk range of decision errors. After each analysis of the random 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 there is enough inaccurate information to make decisions in the early stages of the step-by-step 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.

[0028] 5.1. In the initial stage of operation of urban drainage and storage facilities, due to the lack of weight information for multi-criteria decision-making analysis of urban drainage and storage facilities operation, the missing weight information is expressed by the uniform distribution of the weight space of urban drainage and storage facilities operation.

[0029] In the initial stage of the step-by-step decision-making process for the operation of urban drainage and storage facilities, it is usually difficult for decision makers to express their preferences because the decision support information available at this stage is very limited. Unlike the traditional multi-criteria decision-making process for the operation of urban drainage and storage facilities, decision makers do not need to express any preference information in the first stage. Instead, the entire urban drainage and storage facility operation decision-making standard weight space is used to operate the urban drainage and storage facility operation random multi-criteria decision-making fuzzy model, and the missing weight information is expressed through the uniform distribution of the urban drainage and storage facility operation decision-making standard weight space.

[0030] 5.2. Based on the statements of the preferences of each decision maker on the decision criteria for the operation of urban drainage and storage facilities, the weight information of the step-by-step decision sequence for the operation of urban drainage and storage facilities is obtained.

[0031] 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, e.g. The weight information of the step-by-step decision sequence for the operation of urban drainage storage facilities corresponds to the decision maker's preference statement, that is, standard 1 is more important than standard 2. Of course, there are also cases where the decision maker cannot judge some standards ( ) or considered equally important ( The step-by-step decision order weight information of the operation of urban drainage and storage facilities can be expressed as a triangular plane in the weight space of the decision criteria for the operation of urban drainage and storage facilities.

[0032] 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.

[0033] 5.4. Use deterministic weight vectors to generate the final decision on the operation of urban drainage and storage facilities under an acceptable risk of decision-making errors. If the step-by-step decision-making process of the operation of urban drainage and storage facilities is a decision-making process of a single decision-maker, 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 of the operation of urban drainage and storage facilities is a decision-making process of multiple decision-makers, the complementary judgment matrix method is used to calculate the weight vectors of each decision-maker's decision criteria, and the weight aggregation method is used to obtain the coordination weight vectors of each decision criterion.

[0034] Furthermore, the step 2.1 is specifically as follows:

[0035] 2.1.1. Based on the experience of various decision-making criteria for the operation of urban drainage and storage facilities, a complementary judgment matrix for the decision-making criteria for the operation of urban drainage and storage facilities is constructed. The decision-maker compares each pair of decision-making criteria for the operation of urban drainage and storage facilities to determine their relative importance;

[0036] 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 values ​​of the decision criteria for the operation of urban drainage and storage facilities;

[0037] 2.1.3. According to the complementary weight values ​​calculated in step 2.1.1 and the weight values ​​of each decision criterion determined in step 2.1.2, the inconsistency error of the weight values ​​of the operation decision criterion of drainage and storage facilities in each city is calculated, and the inconsistency of the weight values ​​of the operation decision criterion of drainage and storage facilities in each city is evaluated. If the inconsistency error of the weight values ​​of the operation decision criterion of drainage and storage facilities in each city is small, the experience judgment of each decision maker is more accurate; on the contrary, if the inconsistency error of the weight values ​​of the operation decision criterion of drainage and storage facilities in each city is large, each decision maker should reconsider the preference information of each decision criterion.

[0038] Furthermore, the step 2.2 is specifically as follows:

[0039] 2.2.1. The complementary judgment matrix method is used to determine the basic weight vectors of the decision criteria for the operation of urban drainage and storage facilities of each decision maker. The basic weight vectors of the decision criteria for the operation of urban drainage and storage facilities are obtained by comprehensively considering the basic weight vectors of the decision criteria for each decision maker and by using a linear combination method;

[0040] 2.2.2. According to Nash equilibrium, the weight combination coefficients of various decision-making criteria for the operation of urban drainage and storage facilities are optimized to make the basic weight vectors of various decision-making criteria compromise or consistent, and finally obtain the coordinated weight vector of the decision-making criteria for the operation of urban drainage and storage facilities, and minimize the deviation between the basic weight vectors of various decision-making criteria for the operation of urban drainage and storage facilities and the coordinated weight vector;

[0041] 2.2.3. The linear programming method is used to solve the operation decision model of urban drainage and storage facilities, the optimal combination coefficient of the operation decision of urban drainage and storage facilities is obtained, and the coordination weight vector of the operation decision of urban drainage and storage facilities is calculated.

[0042] Furthermore, the step 2.3 is specifically as follows:

[0043] 2.3.1. Construct the feasible weight space of the decision-making standards for the operation of urban drainage and storage facilities, and expand the coordination weight vectors of the 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 weight space is the union of all possible weight vectors;

[0044] 2.3.2. The feasible space of decision-making criteria for 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.

[0045] Furthermore, the step 3.1 is specifically as follows:

[0046] 3.1.1. Define the triangular fuzzy function of the operation of urban drainage storage facilities and construct the fuzzy decision matrix of the operation of urban drainage storage facilities. Use the triangular fuzzy function to represent the performance preference value of each alternative scheme for the operation of urban drainage storage facilities for each decision criterion;

[0047] 3.1.2. Define the fuzzy anti-ideal weight distance and ideal weight distance of urban drainage storage facilities operation. Although there is no ideal alternative in real life, it provides a benchmark for evaluating alternatives.

[0048] 3.1.3. Fuzzy optimization is performed on the multi-criteria decision-making analysis of the operation of urban drainage and storage facilities, and a global evaluation is performed on the alternative plans for the operation of urban drainage and storage facilities based on the various decision-making criteria of the multi-criteria decision-making of the operation of urban drainage and storage facilities to obtain the ranking of the alternative plans for the operation of urban drainage and storage facilities.

[0049] Furthermore, the step 3.2 is specifically as follows:

[0050] 3.2.1. Aiming at the multi-criteria decision analysis problem of urban drainage and storage facilities operation, a random multi-criteria decision analysis-fuzzy optimization model for urban drainage and storage facilities operation is established by using the random multi-criteria decision analysis method and the fuzzy optimization model. This optimization model combines the characteristics of the fuzzy optimization model and the random multi-criteria decision analysis framework. In order to evaluate the performance of the alternative operation schemes of urban drainage and storage facilities based on the original random multi-criteria decision analysis framework, the real-valued utility function of urban drainage and storage facilities operation is defined;

[0051] 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 analysis-fuzzy optimization model of urban drainage and storage facilities operation, the uncertainty measure of multi-criteria decision analysis of urban drainage and storage facilities operation is calculated from four dimensions to provide a basis for the final decision of urban drainage and storage facilities operation. The step-by-step decision 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 central weight vector (CWV).

[0052] Furthermore, the step 4.1 is specifically as follows:

[0053] In order to test and evaluate the uncertainty of the initial alternatives for the operation decision of each urban drainage storage facility, this method defines the risk of error in the operation decision of urban drainage storage facilities. After obtaining the highest ranking scheme for the operation of urban drainage storage facilities using the multi-criteria decision analysis method, decision makers usually consider this scheme to be the optimal scheme. Obviously, assigning the first rank to a scheme that is not actually the best choice will have an adverse impact on the operation of urban drainage storage facilities and deviate from the optimal decision for the operation of urban drainage storage facilities.

[0054] 4.1.1. Calculate the weighted probability that the highest rank is assigned to the non-optimal solution in the operation decision of urban drainage and storage facilities, and define it as the risk of error in the operation decision of urban drainage and storage facilities. The calculation formula for the risk of error in the operation decision of urban drainage and storage facilities is:

[0055]

[0056] In the formula, The first index represents the overall acceptability index of the operation decision of urban drainage storage facilities. The first-level acceptability index of the alternative options. 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 index of each decision-making scheme for the operation of urban drainage and storage facilities for all possible rankings except the final ranking:

[0058]

[0059] In the formula, The initial alternatives for the operation decision of urban drainage storage facilities The final grade is based on its overall acceptability index.

[0060] Furthermore, the step 4.2 is specifically as follows:

[0061] 4.2.1. Calculate the overall acceptability index of each alternative operation scheme for urban drainage storage facilities. The overall acceptability index is expressed as The overall acceptability index is defined as the acceptability of the alternatives for the operation of urban drainage storage facilities. Sorting Favorable rank weightings given to alternatives with different valuations Obviously, the overall acceptability index assigns a certain ranking probability to each alternative. The value range of the overall acceptability index is [0,1], where 0 means that the alternative operation of the urban drainage and storage facilities will never be in a certain ranking, and 1 means that the alternative operation of the urban drainage and storage facilities will always be in a certain ranking. In the process of multi-criteria decision-making analysis of the operation of urban drainage and storage facilities, the alternative operation of urban drainage and storage facilities with the highest ranking and high overall acceptability index is usually regarded as the potential optimal solution. For the alternatives with poor ranking but high overall acceptability index, they are directly deleted from the initial set of alternatives for the operation of urban drainage and storage facilities.

[0062] 4.2.2. Calculate the acceptability index of the initial alternatives for the operation decision of urban drainage and storage facilities to measure the overall acceptability of the alternatives for the operation decision of urban drainage and storage facilities. The acceptability index of the initial alternatives for the operation decision of urban drainage and storage facilities is obtained by weighting the overall acceptability index of all alternatives for the operation of urban drainage and storage facilities:

[0063]

[0064] In the formula, The overall acceptability index used to show the role of each specific urban drainage storage facility operation alternative in evaluating the alternatives. Defined as a monotonically decreasing vector:

[0065]

[0066] 4.2.3. Calculate the confidence factor of each alternative operation scheme of urban drainage regulation and storage facilities. The confidence factor of urban drainage regulation and storage facility operation is a measure of the confidence factor of each alternative operation scheme of urban drainage regulation and storage facilities. 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 a decision alternative for the operation of urban drainage and storage facilities is very low, it means that even if this preference is selected for multi-criteria decision-making on the operation of urban drainage and storage facilities, the probability of this alternative obtaining the highest ranking is also very low. If the confidence factor of a decision alternative for the operation of urban drainage and storage facilities is very high, it means that the decision alternative for the operation of urban drainage and storage facilities has the most appropriate and highest preference setting.

[0067] The present invention can achieve the following beneficial effects:

[0068] 1. The present invention introduces a step-by-step decision analysis method, allowing 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 speeding up the decision-making process.

[0069] 2. The present invention combines risk assessment to comprehensively consider the uncertainties in the operation of urban drainage and storage facilities, ensuring that the selected solution can maintain high performance in a variety of possible scenarios, thereby enhancing the stability of the drainage system and its ability to cope with extreme events.

[0070] 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.

[0071] 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 criterion 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 decisions.

[0072] 5. The present invention quantifies the risk of decision-making errors and the degree of uncertainty, so that decision makers can intuitively understand the possible consequences of various plans, provide a quantitative basis for the formulation of risk prevention and control measures and emergency plans, and reduce potential environmental and social risks.

[0073] 6. The present invention fully considers the complexity of the operation of urban drainage and storage facilities, including the impact of multiple factors such as environment, economy, and society, improves the ability of the drainage system to adapt to rapid urban development and climate change, and helps to build a sustainable urban water management system. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0075] Figure 1 It is a flow chart of the step-by-step decision-making method for the operation of urban drainage regulation and storage facilities of the present invention;

[0076] Figure 2 It is a schematic diagram of the feasible space for step-by-step decision-making of the operation of the urban drainage regulation and storage facilities of the present invention;

[0077] Figure 3 It is a schematic diagram of gradually weighting information in the three-criteria decision analysis process of the present invention. DETAILED DESCRIPTION

[0078] The preferred solution is Figures 1 to 3 As shown in the figure, a step-by-step decision analysis method for the operation of urban drainage and storage facilities based on risk assessment is used. When the preference information of various decision criteria for the operation of urban drainage and storage facilities is completely missing or unclear, a step-by-step decision analysis method is adopted to determine the weight information of various decision criteria 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.

[0079] like Figure 1 As shown, this embodiment discloses a step-by-step decision-making method for the operation of urban drainage storage facilities based on risk assessment, and the method includes the following steps:

[0080] 1. Treat the multi-criteria decision analysis of urban drainage storage and regulation facilities operation as a multi-stage decision analysis problem, determine the key influencing factors of urban drainage storage and regulation facilities operation and dispatch, select appropriate decision criteria for urban drainage storage and regulation facilities operation, and obtain the random decision matrix of urban drainage storage and regulation facilities operation;

[0081] 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. A set of initial alternative operation schemes of the urban drainage storage facility is prepared. , Indicates the operation of urban drainage storage facilities alternatives, It represents the number of initial alternatives for the operation of urban drainage storage facilities;

[0082] 1.2. Determine the factors affecting the operation and dispatch of urban drainage storage facilities and select the appropriate decision-making standard set for the operation plan of urban drainage storage facilities. , in order to sort and screen the initial alternative operation scheme set for urban drainage storage facilities, Indicates the operation of urban drainage storage facilities decision criteria, It represents the total number of decision criteria for the operation of urban drainage storage facilities;

[0083] 1.3. Select the parameters that have the greatest impact on the operation of urban drainage storage facilities as the decision-making criteria for the operation of urban drainage storage facilities. These criteria include: ① inlet flow; ② storage tank volume; ③ rainfall; ④ inlet water quality monitoring data; ⑤ storage tank outflow flow; ⑥ storage tank inlet pipe liquid level; ⑦ storage tank pump station size.

[0084] 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 solve the conflict problem among multiple stakeholders in the operation decision-making 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.

[0085] 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, and obtains the weights of the quantitative decision-making criteria for each urban drainage and storage facility based on the preferences of different decision makers for the decision-making criteria for the operation of each urban drainage and storage facility.

[0086] 2.1.1. Based on the experience of various decision-making criteria for the operation of urban drainage and storage facilities, a complementary judgment matrix for the decision-making criteria for the operation of urban drainage and storage facilities is constructed. The decision-maker compares each pair of decision-making criteria for the operation of urban drainage and storage facilities to determine their relative importance;

[0087] Table 1 gives the verbal preference statements and their corresponding complementary comparison values. Standard weights can be selected or complementary comparison values ​​that meet the following conditions can be directly given. and To choose:

[0088]

[0089] In the formula, Indicates the decision-making criteria for the operation of urban drainage storage facilities Relative to the decision-making criteria for the operation of urban drainage storage facilities Preferences, It represents the decision-making criteria for the operation of urban drainage storage facilities Relative to the decision-making criteria for the operation of urban drainage storage facilities preferences.

[0090] Table 1 Verbal preference statements for decision-making on the operation of urban drainage and storage facilities and their corresponding complementary comparison values

[0091]

[0092] The ratio of the complementary comparison values ​​corresponds to the weights:

[0093]

[0094] Will Substituting into the above formula, we get:

[0095]

[0096] in, and Respectively represent and The weight of the decision-making criteria for the operation of urban drainage and storage facilities. A complementary judgment matrix can be constructed based on the comparison value:

[0097]

[0098] In the formula, 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

[0099] 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 values ​​of the decision criteria for the operation of urban drainage and storage facilities; get:

[0100]

[0101] Taking into account the planning conditions of the weight values ​​of various decision criteria for the operation of urban drainage and storage facilities to identify incompatible solutions, for solving the linear system, the weight values ​​of various decision criteria for the operation of urban drainage and storage facilities can be obtained:

[0102]

[0103] According to the above two equations, we can get a linear equation system, which can be further simplified into constraints and variables:

[0104]

[0105] In the formula, It is found that the linear system is overdetermined, and the least squares solution can be derived as:

[0106]

[0107] In solving Afterwards, according to Calculate the final weight of each decision-making standard for the operation of urban drainage storage facilities .

[0108] 2.1.3. According to the complementary weight values ​​calculated in step 2.1.1 and the weight values ​​of each decision criterion determined in step 2.1.2, the inconsistency error of the weight values ​​of the operation decision criterion of drainage and storage facilities in each city is calculated, and the inconsistency of the weight values ​​of the operation decision criterion of drainage and storage facilities in each city is evaluated. If the inconsistency error of the weight values ​​of the operation decision criterion of drainage and storage facilities in each city is small, the experience judgment of each decision maker is more accurate; on the contrary, if the inconsistency error of the weight values ​​of the operation decision criterion of drainage and storage facilities in each city is large, each decision maker should reconsider the preference information of each decision criterion.

[0109] 2.1.3. According to the complementary weight values ​​calculated in step 2.1.1 and the weight values ​​of each decision criterion determined in step 2.1.2, the inconsistency error of the weight values ​​of the operation decision criterion of drainage and storage facilities in each city is calculated, and the inconsistency of the weight values ​​of the operation decision criterion of drainage and storage facilities in each city is evaluated. If the inconsistency error of the weight values ​​of the operation decision criterion of drainage and storage facilities in each city is small, the experience judgment of each decision maker is more accurate; on the contrary, if the inconsistency error of the weight values ​​of the operation decision criterion of drainage and storage facilities in each city is large, each decision maker should reconsider the preference information of each decision criterion.

[0110] The inconsistency error of the weights of various decision criteria for the operation of urban drainage storage facilities can be calculated as:

[0111]

[0112] In the formula, It represents the inconsistent error of the weights of various decision criteria for the operation of urban drainage and storage facilities.

[0113] 2.2. Introduce game theory into the random multi-criteria decision analysis of urban drainage and storage facility operation, and aggregate the weights of various conflicting decision criteria of urban drainage and storage facility operation through Nash equilibrium, so as to achieve preference compromise and conflict resolution;

[0114] 2.2.1. The complementary judgment matrix method is used to determine the basic weight vectors of the decision criteria for the operation of urban drainage and storage facilities of each decision maker. The basic weight vectors of the decision criteria of each decision maker are comprehensively considered and the basic weight vectors of the decision criteria for the operation of urban drainage and storage facilities are obtained by linear combination;

[0115] 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 of urban drainage storage facilities. The linear combination of the basic weight vectors for the operation decision of urban drainage storage facilities is:

[0116]

[0117] 2.2.2. According to Nash equilibrium, the weight combination coefficients of various decision-making criteria for the operation of urban drainage and storage facilities are optimized to make the basic weight vectors of various decision-making criteria compromise or consistent, and finally obtain the coordinated weight vector of the decision-making criteria for the operation of urban drainage and storage facilities, and minimize the deviation between the basic weight vectors of various decision-making criteria for the operation of urban drainage and storage facilities and the coordinated weight vector;

[0118] Obtain the coordination weight vector of urban drainage storage facility operation decision , and minimize each and Deviation between:

[0119]

[0120] In the formula, Represents the basic weight vector of various decision criteria for the operation of urban drainage and storage facilities.

[0121] 2.2.3. The linear programming method is used to solve the operation decision model of urban drainage and storage facilities, the optimal combination coefficient of the operation decision of urban drainage and storage facilities is obtained, and the coordination weight vector of the operation decision of urban drainage and storage facilities is calculated.

[0122] The optimal combination coefficient for the operation decision of urban drainage storage facilities is expressed as , the urban drainage storage facility operation decision coordination weight vector is calculated:

[0123]

[0124] 2.3, such as Figure 2 As shown in the figure, the concept of feasible rights space is used to quantify the uncertainty of various decision-making criteria for the operation of urban drainage and storage facilities;

[0125] 2.3.1. Construct the feasible weight space of the decision-making standards for the operation of urban drainage and storage facilities, and expand the coordination weight vectors of the 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 weight space is the union of all possible weight vectors;

[0126] 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, 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 each decision-making criterion for the operation of urban drainage and storage facilities.

[0127] The feasible space of multi-stage decision-making for the operation of urban drainage storage facilities can be expressed as:

[0128]

[0129] In the formula, The parameter representing the uncertainty of the weight value of the urban drainage storage facility operation decision is related to the degree of conflict between the various standards for the urban drainage storage facility operation decision. If all decision makers involved in the urban drainage storage facility operation decision agree on a certain coordinated standard weight, then is a very small value; otherwise, it is necessary to give A larger value is obtained, thus obtaining a larger feasible space for multi-stage decision-making in the operation of urban drainage and storage facilities. After resolving the conflicts among decision makers through aggregation, the feasible space for multi-stage decision-making in the operation of urban drainage and storage facilities can reflect the uncertainty of the weights of each decision criterion without losing too much information.

[0130] 3. Combining the random multi-criteria acceptability analysis algorithm and the fuzzy optimization model, a fuzzy optimization model for random multi-criteria decision analysis of urban drainage and storage facilities operation is constructed, the uncertainty of the decision criteria and their weights of urban drainage and storage facilities operation is simulated and quantified, and several measurement descriptions of the robustness decision of urban drainage and storage facilities operation are given;

[0131] 3.1. Construct a fuzzy optimization model for the operation of urban drainage and storage facilities, and use fuzzy anti-ideal distance and ideal distance to solve the multi-criteria decision-making problem of the operation of urban drainage and storage facilities;

[0132] 3.1.1. Define the triangular fuzzy function of the operation of urban drainage storage facilities and construct the fuzzy decision matrix of the operation of urban drainage storage facilities. Use the triangular fuzzy function to represent the performance preference value of each alternative scheme for the operation of urban drainage storage facilities for each decision criterion;

[0133] Using triangular fuzzy function 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:

[0134] For the income standard

[0135] For cost standards

[0136] 3.1.2. Define the fuzzy anti-ideal weight distance and ideal weight distance of urban drainage storage facilities operation. Although there is no ideal alternative in real life, it provides a benchmark for evaluating alternatives.

[0137] The anti-ideal urban drainage storage facility operation plan and the ideal urban drainage storage facility operation plan are defined as:

[0138]

[0139]

[0140] In the formula, , . Define the weighted anti-ideal and ideal options for the operation of urban drainage storage facilities:

[0141]

[0142]

[0143] In the formula, ; . Indication Standard The weight of is a triangular fuzzy value in [0,1]. Define the fuzzy anti-ideal and ideal weight distances to measure the difference between the alternative operation schemes and the anti-ideal schemes of drainage storage facilities in each city;

[0144]

[0145]

[0146] In the formula, Represents alternative operation schemes for urban drainage storage facilities The weighted performance preference value vector of ; represents the Hemming distance, represents the Euclidean distance.

[0147] 3.1.3. Fuzzy optimization is performed on the multi-criteria decision-making analysis of the operation of urban drainage and storage facilities, and a global evaluation is performed on the alternative operation plans of urban drainage and storage facilities based on the various decision-making criteria of the multi-criteria decision-making of the operation of urban drainage and storage facilities to obtain the ranking of the alternative operation plans of urban drainage and storage facilities.

[0148] set up Indicates alternatives for the operation of urban drainage storage facilities according to all standards In order to obtain the global evaluation of 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:

[0149]

[0150] Differentiating the above function yields:

[0151]

[0152] Finally, we can get:

[0153]

[0154] In the formula, Alternative operation schemes for urban drainage storage facilities based on the fuzzy concept of "optimal under all criteria" According to the above definition, the one with the maximum membership The alternative is the most preferred alternative. In addition, by sorting the membership degrees corresponding to the alternatives for the operation of urban drainage and storage facilities, the sorting order of the alternatives can be simply determined.

[0155] 3.2. Using the random multi-criteria decision analysis method and fuzzy optimization model, establish the random multi-criteria decision analysis-fuzzy optimization model for the operation of urban drainage and storage facilities, calculate the uncertainty measure of the alternative operation schemes of each urban drainage and storage facility, and evaluate the alternative operation schemes of each urban drainage and storage facility;

[0156] 3.2.1. Aiming at the multi-criteria decision analysis problem of urban drainage and storage facilities operation, a random multi-criteria decision analysis-fuzzy optimization model for urban drainage and storage facilities operation is established by using the random multi-criteria decision analysis method and the fuzzy optimization model. This optimization model combines the characteristics of the fuzzy optimization model and the random multi-criteria decision analysis framework. In order to evaluate the performance of the alternative operation schemes of urban drainage and storage facilities based on the original random multi-criteria decision analysis framework, the real-valued utility function of urban drainage and storage facilities operation is defined;

[0157] In order to evaluate the performance of alternative operation schemes of urban drainage storage facilities based on the original stochastic multi-criteria decision analysis framework, a real-valued utility function of urban drainage storage facilities operation is defined. :

[0158]

[0159] In the formula, Alternative solutions for the operation of urban drainage storage facilities A vector of performance preference values ​​for each decision criterion.

[0160] 3.2.2. In order to better evaluate the alternative operation plans of urban drainage and storage facilities, the uncertainty measure of the multi-criteria decision-making analysis of the operation of urban drainage and storage facilities is calculated from four dimensions on the basis of the random multi-criteria decision-making analysis-fuzzy optimization model of the operation of urban drainage and storage facilities, which provides a basis for the final decision-making of the operation of urban drainage and storage facilities. The uncertainty measure of the operation of urban drainage and storage facilities mainly includes the following indicators: ① overall acceptability index (HAI), ② grade acceptability index (RAI), ③ confidence factor, and ④ central weight vector (CWV).

[0161] 4. Construct a risk assessment model for the operation decision of urban drainage and storage facilities, calculate the uncertainty degree and decision-making error risk of 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;

[0162] 4.1. Calculate the risk of decision-making errors in the operation plan of urban drainage and storage facilities, and quantitatively evaluate the uncertainty of alternative operation plans of urban drainage and storage facilities;

[0163] In order to test and evaluate the uncertainty of the operation schemes of urban drainage and storage facilities, this method defines the risk of wrong decision-making in the operation of urban drainage and storage facilities. After obtaining the highest-ranked scheme for the operation of urban drainage and storage facilities using the multi-criteria decision analysis method, decision makers usually consider this scheme to be the optimal scheme. Obviously, assigning the first rank to a scheme that is not actually the best choice will have an adverse impact on the operation of urban drainage and storage facilities and deviate from the optimal sediment removal decision.

[0164] 4.1.1. Calculate the weighted probability that the highest rank is assigned to the non-optimal solution in the operation decision of urban drainage and storage facilities, and define it as the risk of error in the operation decision of urban drainage and storage facilities. The calculation formula for the risk of error in the operation decision of urban drainage and storage facilities is:

[0165]

[0166] In the formula, Indicates the first The first-level acceptability index of the alternative options. 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 .

[0167] 4.1.2. Calculate the sum of the acceptability index of each decision-making scheme for the operation of urban drainage and storage facilities for all possible rankings except the final ranking:

[0168]

[0169] In the formula, It is an alternative plan for the operation of urban drainage storage facilities The final grade is based on its overall acceptability index.

[0170] 4.2. Calculate the uncertainty of the operation plan of urban drainage and storage facilities, and quantitatively evaluate the overall uncertainty of the ranking results of alternative operation plans of urban drainage and storage facilities.

[0171] 4.2.1. Calculate the overall acceptability index of each alternative operation scheme for urban drainage storage facilities. The overall acceptability index is expressed as The overall acceptability index is defined as the acceptability of the alternatives for the operation of urban drainage storage facilities. Sorting Favorable rank weightings given to alternatives with different valuations Obviously, the overall acceptability index assigns a certain ranking probability to each alternative. The value range of the overall acceptability index is [0,1], where 0 means that the alternative operation of the urban drainage and storage facilities will never be in a certain ranking, and 1 means that the alternative operation of the urban drainage and storage facilities will always be in a certain ranking. In the process of multi-criteria decision-making analysis of the operation of urban drainage and storage facilities, the alternative operation of urban drainage and storage facilities with the highest ranking and high overall acceptability index is usually regarded as the potential optimal solution. For the alternatives with poor ranking but high overall acceptability index, they are directly deleted from the initial set of alternatives for the operation of urban drainage and storage facilities.

[0172] and The calculation formulas are:

[0173]

[0174]

[0175] In the formula, is the most favorable rank weight, which means that any weight vector Granting alternative operation plan for urban drainage storage facilities rank ; is a ranking function that gives the ranking of the options.

[0176] 4.2.2. Calculate the acceptability index of the operation ranking of urban drainage and storage facilities to measure the overall acceptability of the alternative schemes for the operation of urban drainage and storage facilities. The acceptability index of the operation ranking of urban drainage and storage facilities is obtained by weighting the overall acceptability index of all alternative schemes for the operation of urban drainage and storage facilities:

[0177]

[0178] In the formula, The overall acceptability index used to show the role of each specific urban drainage storage facility operation alternative in evaluating the alternatives. Defined as a monotonically decreasing vector:

[0179]

[0180] 4.2.3. Calculate the confidence factor of each alternative operation scheme of urban drainage regulation and storage facilities. The confidence factor of urban drainage regulation and storage facility operation is a measure of the confidence factor of each alternative operation scheme of urban drainage regulation and storage facilities. 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 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 the alternative plan for the operation of urban drainage and storage facilities has the most appropriate and highest preference setting;

[0181] In the form of multidimensional integrals, the first-level weights are favorable and standard weight distribution Get:

[0182]

[0183] Confidence factor (using ) represents the probability of an alternative solution becoming the most preferred solution using its weighted solution. Determine whether the criteria weights are accurate enough in distinguishing between candidate solutions. Expressed as a multidimensional integral over a standard weight distribution:

[0184]

[0185] 5. If Figure 3 As shown, multi-stage decision-making is carried out on the operation of urban drainage and 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.

[0186] The multi-stage decision-making process for the operation of urban drainage and storage facilities starts with completely missing or unclear preference information, and gradually obtains more accurate information as the decision-making process for the operation of urban drainage and storage facilities develops. The basic idea is to iteratively run the random multi-criteria decision-making fuzzy model for the operation of urban drainage and storage facilities after completing each round of information collection related to the operation of urban drainage and storage facilities, until sufficient final decision preference information is obtained within an acceptable risk range of decision errors. After each analysis of the random 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 there is enough inaccurate information to make decisions in 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.

[0187] 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.

[0188] In the initial stage of the multi-stage decision-making process for the operation of urban drainage and storage facilities, it is usually difficult for decision makers to express their preferences because the decision support information available at this stage is very limited. Unlike the traditional decision-making process for the operation of urban drainage and storage facilities, decision makers do not need to express any preference information in the first stage. Instead, the entire weight space is used to operate the random multi-criteria decision-making fuzzy model for the operation of urban drainage and storage facilities, and the missing weight information is expressed through the uniform distribution of the weight space of the operation of urban drainage and storage facilities.

[0189] 5.2. Based on the statements of decision makers on the preferences for various operation standards of urban drainage and storage facilities, the weight information of the multi-stage decision-making sequence for the operation of urban drainage and storage facilities is obtained.

[0190] The weight information of multi-stage decision sequence for the operation of urban drainage storage facilities is expressed in the form of linear constraints, e.g. The weight information of the multi-stage decision sequence for the operation of urban drainage storage facilities corresponds to the preference statement of the decision maker, that is, criterion 1 is more important than criterion 2. Of course, there are also cases where the decision maker cannot judge some criteria ( ) or considered equally important ( The weight information of multi-stage decision sequence of urban drainage storage and regulation facility operation can be expressed as a triangular plane in the weight space of urban drainage storage and regulation facility operation.

[0191] 5.3. The complementary matrix method is used to determine the quantitative weights of various operating 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.

[0192] 5.4. Use deterministic weight vectors to generate the final decision on the operation of urban drainage and storage facilities under an acceptable risk of decision-making errors. If the multi-stage decision-making process of the operation of urban drainage and storage facilities is a decision-making process of a single decision-maker, the complementary judgment matrix method is used to directly calculate and determine the weight vectors of each standard of the operation of urban drainage and storage facilities; if the multi-stage decision-making process of the operation of urban drainage and storage facilities is a decision-making process of multiple decision-makers, the complementary judgment matrix method is used to calculate the weight vectors of each standard of each decision-maker, and the weight aggregation method is used to obtain the coordination weight vectors of each standard.

[0193] The above embodiments are only preferred technical solutions of the present invention and should not be regarded as limiting the present invention. The protection scope of the present invention shall be the technical solutions recorded in the claims, including equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A step-by-step decision analysis method for the operation of urban drainage and storage facilities based on risk assessment, characterized by: S1. Consider the multi-criteria decision analysis of urban drainage storage and regulation facilities operation as a multi-stage decision analysis problem, determine the key influencing factors of urban drainage storage and regulation facilities operation and dispatch, select appropriate decision criteria for urban drainage storage and regulation facilities operation, and obtain the random decision matrix for urban drainage storage and regulation facilities operation; S2. A method for aggregating weights of decision criteria for the operation of urban drainage and storage facilities based on game theory and feasible rights space is proposed to solve the conflict problem among multiple stakeholders in the operation of urban drainage and storage facilities, and to estimate the uncertainty of the weights of various decision criteria for the operation of urban drainage and storage facilities; S3. Combining the random multi-criteria acceptability analysis algorithm and the fuzzy optimization model, a random multi-criteria decision analysis fuzzy optimization model for the operation of urban drainage and storage facilities is constructed, the uncertainty of each decision criterion and its weight of urban drainage and storage facilities is simulated and quantified, and several measurement descriptions of the robustness decision of the operation of urban drainage and storage facilities are given; S4. Construct a risk assessment model for the operation decision of urban drainage and storage facilities, calculate the uncertainty degree and decision-making error risk of each initial alternative plan for the operation of urban drainage and storage facilities, and quantitatively assess the risk of decision-making errors in the operation of urban drainage and storage facilities; S5. 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 risk range; The sub-steps of S1 are: S1.

1. Prepare a set of initial alternative operation scenarios for urban drainage storage facilities: , In the formula, Indicates the operation of urban drainage storage facilities alternatives, It represents the number of initial alternatives for the operation of urban drainage storage facilities; S1.

2. Determine the factors affecting the operation and scheduling of urban drainage storage facilities, and select the appropriate decision-making standard set for the operation plan of urban drainage storage facilities: ， In the formula, Indicates the operation of urban drainage storage facilities decision criteria, It represents the total number of decision criteria for the operation of urban drainage and storage facilities; the decision criteria set for the operation scheme of urban drainage and storage facilities is used to sort and screen the initial alternative scheme set for the operation of urban drainage and storage facilities; S1.

3. Select the parameters that have the greatest impact on the operation of urban drainage storage facilities as the decision-making criteria for the operation of urban drainage storage facilities. The decision-making criteria for the operation of urban drainage storage facilities include inflow flow, storage tank volume, rainfall, inflow water quality monitoring data, storage tank outflow flow, storage tank inlet pipe liquid level and storage tank pump station size; S2.

1. The complementary judgment matrix method is used to quantify the uncertainty of each decision-making standard, and the weights of the quantitative decision-making standards of each urban drainage and storage facility are obtained according to the preferences of different decision makers for the operation decision-making standards of each urban drainage and storage facility; it is used to quantify the uncertainty of the operation decision-making standards of urban drainage and storage facilities; S2.2, introduce game theory into the random multi-criteria decision analysis of urban drainage storage facilities, aggregate the weights of the conflicting decision criteria of urban drainage storage facilities operation through Nash equilibrium, so as to achieve preference compromise and conflict resolution, and obtain the coordination weights of the decision criteria of urban drainage storage facilities operation; S2.

3. Use the method of feasible rights space to establish the feasible rights space of the decision-making standards for the operation of urban drainage and storage facilities, and quantify the uncertainty of each decision-making standard for the operation of urban drainage and storage facilities; The sub-steps of S3 are: S3.

1. When solving the multi-criteria decision-making problem of urban drainage and storage facilities operation, fuzzy functions are introduced and a fuzzy optimization model for urban drainage and storage facilities operation decision-making is established. Fuzzy ideal distance and fuzzy anti-ideal distance are used to solve the multi-criteria decision-making problem of urban drainage and storage facilities operation; S3.

2. Based on the random multi-criteria decision analysis model, a fuzzy optimization model for the operation decision of urban drainage and storage facilities is introduced to establish a random multi-criteria decision analysis-fuzzy optimization model for the operation decision of urban drainage and storage facilities. The uncertainty measure of each initial alternative scheme for the operation of urban drainage and storage facilities is obtained by solving the model, and the advantages and disadvantages of each initial alternative scheme for the operation of urban drainage and storage facilities are compared and evaluated. The sub-steps of S3.1 are: 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 scheme 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. Perform fuzzy optimization on the multi-criteria decision-making analysis of the operation of urban drainage and storage facilities, and conduct a global evaluation of the alternative plans for the operation of urban drainage and storage facilities based on the various decision-making criteria for the multi-criteria decision-making of the operation of urban drainage and storage facilities, and obtain the ranking of the alternative plans for the operation of urban drainage and storage facilities; The sub-steps of S3.2 are: S3.2.

1. Aiming at the multi-criteria decision analysis problem of urban drainage and storage facilities operation, a random multi-criteria decision analysis method and fuzzy optimization model are used to establish a random multi-criteria decision analysis-fuzzy optimization model for urban drainage and storage facilities operation; S3.2.

2. In order to better evaluate the initial alternative plans for the operation of urban drainage and storage facilities, the uncertainty measure of the multi-criteria decision analysis of the operation of urban drainage and storage facilities is calculated from four dimensions based on the random multi-criteria decision analysis-fuzzy optimization model of the operation of urban drainage and storage facilities, which provides a basis for the final decision of the operation of urban drainage and storage facilities. The uncertainty measure of the step-by-step 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 center weight vector; The sub-steps of S4 are: S4.

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

2. After obtaining the ranking of each initial alternative scheme for the operation of drainage and storage facilities in each city, calculate the uncertainty of each initial scheme for the operation of drainage and storage facilities in each city according to the ranking results of the initial alternative scheme for the operation of drainage and storage facilities in each city, and conduct a quantitative assessment of the overall uncertainty of each initial alternative scheme for the operation of drainage and storage facilities in each city; The sub-steps of S4.1 are: S4.1.

1. Calculate the weighted probability that the highest rank is assigned to the non-optimal solution in the operation decision of urban drainage and storage facilities, and define it as the risk of error in the operation decision of urban drainage and storage facilities. The calculation formula for the risk of error in the operation decision of urban drainage and storage facilities is: ； In the formula, The first index represents the overall acceptability index of the operation decision of urban drainage storage facilities. The first level acceptability index of the alternatives; 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 ; S4.1.

2. Calculate the sum of the acceptability index of each decision-making scheme for the operation of urban drainage and storage facilities for all possible rankings except the final ranking: ； In the formula, The initial alternatives for the operation decision of urban drainage storage facilities Final rating based on its overall acceptability index; The sub-steps of S4.2 are: 4.2.

1. Calculate the overall acceptability index of each alternative operation scheme for urban drainage storage facilities. The overall acceptability index is expressed as The overall acceptability index is defined as the acceptability of the alternatives for the operation of urban drainage storage facilities. Sorting Favorable rank weightings given to alternatives with different valuations Volume; The overall acceptability index assigns a probability of a certain ranking to each alternative. The value range of the overall acceptability index is [0,1], where 0 means that the alternative operation of the urban drainage and storage facilities is absolutely impossible to be in a certain ranking, and 1 means that the alternative operation of the urban drainage and storage facilities is always in a certain ranking; In the process of multi-criteria decision-making analysis of urban drainage storage facility operation, the alternative scheme of urban drainage storage facility operation with the highest ranking and high overall acceptability index is usually regarded as the potential optimal scheme, and the alternative scheme with poor ranking but high overall acceptability index is directly deleted from the initial alternative scheme set of urban drainage storage facility operation; 4.2.

2. Calculate the acceptability index of the initial alternatives for the operation decision of urban drainage and storage facilities to measure the overall acceptability of the alternatives for the operation decision of urban drainage and storage facilities; the acceptability index of the initial alternatives for the operation decision of urban drainage and storage facilities is obtained by weighting the overall acceptability index of all alternatives for the operation of urban drainage and storage facilities: ； In the formula, The overall acceptability index used to show the role of each specific urban drainage storage facility operation alternative in evaluating the alternatives; Defined as a monotonically decreasing vector: ； 4.2.

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

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

1. Construct a complementary judgment matrix for the decision criteria for the operation of urban drainage and storage facilities; compare each pair of decision criteria for the operation of urban drainage and storage facilities to determine their relative importance; S2.1.

2. Considering that the complementary judgment matrix of various 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; S2.1.

3. Based on the complementary weight values ​​calculated in S2.1.1 and the weight values ​​of each decision criterion determined in S2.1.2, calculate the inconsistency error of the weight values ​​of the decision criterion for the operation of drainage and storage facilities in each city, and evaluate the inconsistency of the weight values ​​of the decision criterion for the operation of drainage and storage facilities in each city; If the inconsistency of the weight values ​​of the decision-making standards for the operation of drainage and storage facilities in various cities has a small error, the experience judgment of each decision maker is more accurate; conversely, if the inconsistency of the weight values ​​of the decision-making standards for the operation of drainage and storage facilities in various cities has a large error, each decision maker should reconsider the preference information of each decision criterion.

3. The step-by-step decision analysis method for the operation of urban drainage and storage facilities based on risk assessment according to claim 1 is characterized in that: The sub-steps of S2.2 are: S2.2.

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, and use the linear combination method to obtain the basic weight vectors of the decision criteria for the operation of urban drainage and storage facilities; S2.2.

2. According to Nash equilibrium, the weight combination coefficients of various criteria for the operation decision of urban drainage and storage facilities are optimized to make the basic weight vectors of various decision criteria compromise or consistent, and finally obtain the coordinated weight vector of the operation decision criteria of urban drainage and storage facilities, and minimize the deviation between the basic weight vectors of various decision criteria for the operation of urban drainage and storage facilities and the coordinated weight vector; S2.2.

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

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

1. Construct the feasible weight space of the decision-making standards for the operation of urban drainage and storage facilities, and expand the coordination weight vectors of the decision-making standards for the operation of urban drainage and storage facilities from a single point to a subspace in the weight space. The feasible weight space is the union of all possible weight vectors; S2.3.

2. The feasible space of decision-making criteria 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 each decision-making criterion for the operation of urban drainage and storage facilities.

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