Multi-stage decision analysis method for drainage network cleaning based on step-by-step weight information

Abstract

A multi-stage decision analysis method for drainage network cleaning based on step-by-step weight information is proposed. Under the condition that the preference information of each decision standard for drainage network sediment cleaning is completely missing or unclear, the weights of drainage network sediment cleaning 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 drainage network sediment cleaning. A drainage network sediment cleaning decision risk assessment model is constructed to quantitatively assess the risk of drainage network sediment cleaning decision errors. Multi-stage multi-criteria decision analysis is used to gradually determine the weight information of each standard for drainage network sediment cleaning, thereby achieving the best decision for drainage network sediment cleaning.

Description

Technical Field

[0001] The invention belongs to the technical field of urban drainage pipe network silt cleaning, and in particular relates to a multi-stage decision analysis method for drainage pipe network cleaning based on step-by-step weight information. Background Art

[0002] According to the strategies used in urban drainage network maintenance, the overall maintenance work can be divided into two categories: passive and active. Compared with passive strategies, active strategies are more economical because the active strategy system takes into account the condition of the drainage network and adopts corresponding operation and maintenance functions to prevent failures. Active strategies require a large amount of monitoring data to predict the condition of the drainage network system, which is usually obtained from closed-circuit television, flow monitoring and inspection wells. However, it is time-consuming and laborious to conduct a comprehensive inspection of the drainage network system during its normal use, and usually only a part of it can be inspected due to budget constraints. Therefore, a drainage network system operation status prediction model is developed and used as a subset of the active method, using part of the drainage network monitoring data to evaluate the operation status of the drainage network. The use of a drainage network operation status prediction model can help drainage companies set inspection priorities.

[0003] At present, the most commonly used drainage network operation status prediction models are divided into two categories, namely statistical methods (deterministic and probabilistic) and artificial intelligence methods. For example, some methods use logistic regression models to predict pipeline conditions and take into account factors such as pipe age, pipe diameter, pipe material and average coverage depth. Through historical inspection records, the model can determine the pipes that need priority maintenance in the future. Similar methods have been widely used. For example, by considering factors such as bending materials, street types and pipe depth, the prediction model obtains the pipe network structure and operation degradation curve to represent the relationship between the operating rating and the age of the pipe. Geographic information systems and fuzzy reasoning systems are used to develop drainage network risk assessment models, which take into account economic, social and environmental factors and can rank the priority of drainage network maintenance. In addition, linear regression and neural networks are also used to construct drainage network operation status prediction models to determine the faulty drainage network pipes.

[0004] The operation and maintenance functions of drainage networks can be further subdivided into inspection, cleaning, blockage removal, chemical dosing, rodent control, and structural repair. The operation and maintenance of drainage networks can be evaluated based on their response to blockage-related failures, so that more proactive maintenance measures can be taken. At present, some methods predict the operation status of drainage networks through blockage events. For example, statistical methods are used to analyze blockage data and predict blockage of drainage networks. The empirical formula for the accumulation of blockage in drainage networks over time is obtained through polynomial regression. Various statistical methods have been widely used in the prediction and management of drainage network blockage. The Poisson process model is used to use pipeline slope, diameter, length, and customer complaint data to achieve active management of drainage network blockage. Similarly, data-driven methods have also been applied to drainage network functional failures. By constructing a random failure prediction model for drainage networks, pipelines with a higher probability of blockage failure are identified and compared and evaluated.

[0005] The multi-criteria decision analysis method evaluates the cleaning sequence and cleaning plan of each pipe in the drainage network based on various monitoring data of the drainage network. At present, some multi-criteria decision analysis methods have been applied in the operation and maintenance of drainage networks. These methods can generally be divided into six categories: (1) utility function and multi-criteria evaluation value; (2) method evaluation of the distance to 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 the drainage network. Uncertain data is not conducive to making quick decisions, but it is more in line with the actual situation.

[0006] 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 the drainage network to obtain various drainage network cleaning alternatives and performance values; (3) Determine the criteria and weights of various cleaning schemes according to the decision preference; (4) Conduct the multi-criteria decision analysis process; (5) Obtain the final drainage network cleaning scheme. 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 drainage network cleaning decision. Drainage network cleaning is a multi-stage decision process, which 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-making process, decision makers must express accurate preferences in advance to ensure that the multi-criteria decision analysis model can run, 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 criteria is one of the most difficult steps in multi-criteria decision analysis, which is completely determined by the decision maker.

[0007] In view of this, the present invention proposes a multi-stage decision analysis method for cleaning of urban drainage pipe networks based on step-by-step weight information for cleaning of silt in urban drainage pipe networks. Summary of the invention

[0008] The technical problem to be solved by the present invention is to provide a multi-stage decision analysis method for drainage network cleaning based on step-by-step weight information. Under the condition that the preference information of each decision standard for drainage network silt cleaning is completely missing or unclear, a multi-stage multi-criteria decision analysis is adopted to gradually determine the weight information of each standard for drainage network silt cleaning, thereby achieving the best decision for drainage network silt cleaning.

[0009] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0010] A multi-stage decision analysis method for drainage network cleaning based on step-by-step weight information, the steps are:

[0011] 1. Treat the multi-criteria decision analysis of drainage network sediment cleaning as a multi-stage decision analysis problem, determine the drainage network blockage parameters, select appropriate drainage network sediment cleaning decision criteria, and obtain the drainage network sediment cleaning random decision matrix;

[0012] 2. A method for weight aggregation of drainage network sediment removal based on game theory and feasible rights space is proposed to solve the conflict problem among multiple stakeholders in drainage network sediment removal, and estimate the uncertainty of the weight of each decision-making criterion for drainage network sediment removal;

[0013] 3. Combining the random multi-criteria acceptability analysis algorithm and the fuzzy optimization model, a random multi-criteria decision analysis fuzzy optimization model for drainage network sediment cleaning is constructed, the uncertainty of the drainage network sediment cleaning decision criteria and their weights is simulated and quantified, and several measurement descriptions of the robustness decision of drainage network sediment cleaning are given;

[0014] 4. Construct a risk assessment model for drainage network sediment removal decision-making, calculate the uncertainty degree and decision-making error risk of each drainage network sediment removal alternative plan, and quantitatively assess the risk of decision-making error in drainage network sediment removal;

[0015] 5. Make multi-stage decisions on the cleaning of silt in the drainage network based on the step-by-step weight information method to ensure that the decision-making plan for cleaning the drainage network is gradually solved within an acceptable decision-making risk range.

[0016] Further, the step 1 is specifically as follows:

[0017] 1.1. Prepare a set of initial alternative solutions for cleaning the sewer network sediment A = {A i |i=1,2,…,m},A i represents the ith alternative for clearing sediment in the drainage network, and m represents the number of initial alternatives for clearing sediment in the drainage network;

[0018] 1.2. Determine the blockage parameters of the drainage network, select appropriate decision criteria for clearing the silt in the drainage network, and obtain the decision criteria set C = {C j |j=1,2,…,n}, so as to sort and screen the initial alternative solution set for drainage network sediment removal, C j represents the jth decision criterion for clearing sediment in the drainage network, and n represents the total number of decision criteria for clearing sediment in the drainage network;

[0019] 1.3. The parameters with the greatest impact on the blockage of the drainage network are selected as the decision criteria for clearing sediment from the drainage network. These criteria include: ① slope; ② age; ③ material; ④ diameter; ⑤ upstream manhole conditions; ⑥ branch and connection density of each pipe; ⑦ road type; ⑧ tree density along the pipeline; ⑨ pipeline depth; and ⑩ the density of restaurants and car washes along the pipeline.

[0020] Furthermore, the step 2 is specifically as follows:

[0021] 2.1. In order to quantify the uncertainty of the decision-making criteria for the drainage network sediment removal plan, this method uses the complementary judgment matrix method to quantify the uncertainty of each decision-making criterion, and converts the preference information of each decision maker for each decision-making criterion into the quantitative weight of each decision-making criterion;

[0022] 2.2. Introduce game theory into the random multi-criteria decision analysis of drainage network sediment removal, and aggregate the weights of various conflicting decision criteria of drainage network sediment removal through Nash equilibrium to achieve preference compromise and conflict resolution;

[0023] 2.3. Use the concept of feasible rights space to quantify the uncertainty of each decision-making criterion for clearing sediment in the drainage network;

[0024] Furthermore, the step 3 is specifically as follows:

[0025] 3.1. Construct a fuzzy optimization model for clearing sediment in the drainage network, and use fuzzy anti-ideal distance and ideal distance to solve the multi-criteria decision-making problem of clearing sediment in the drainage network;

[0026] 3.2. Using the random multi-criteria decision analysis method and fuzzy optimization model, a random multi-criteria decision analysis-fuzzy optimization model for drainage network sediment cleaning is established, the uncertainty measure of each drainage network sediment cleaning alternative is calculated, and each drainage network sediment cleaning alternative is evaluated;

[0027] Furthermore, the step 4 is specifically as follows:

[0028] 4.1. Calculate the risk of decision-making errors in the drainage network sediment removal plan and quantitatively evaluate the uncertainty of the drainage network sediment removal alternatives;

[0029] 4.2. Calculate the uncertainty of the drainage network sediment removal plan and quantitatively evaluate the overall uncertainty of the ranking results of the drainage network sediment removal alternative plans.

[0030] Furthermore, the step 5 is specifically as follows:

[0031] The multi-stage decision-making process for drainage network sediment removal starts with completely missing or unclear preference information, and gradually obtains more accurate information as the drainage network sediment removal decision-making process develops. The basic idea is to iteratively run the random multi-criteria decision-making fuzzy model for drainage network sediment removal after completing each round of drainage network sediment removal decision-related information collection until sufficient final decision preference information is obtained within an acceptable risk range of decision error. After each analysis of the random multi-criteria decision-making fuzzy model for drainage network sediment removal, 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 drainage network sediment removal, the preference collection process can be significantly saved and the complex weighting process can be avoided.

[0032] 5.1. When the weight information of the multi-criteria decision-making analysis for drainage network sediment cleaning is missing, the missing weight information is expressed by the uniform distribution of the drainage network sediment cleaning weight space.

[0033] In the initial stage of the multi-stage decision-making process for drainage network sediment removal, 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 drainage network sediment removal, decision makers do not need to express any preference information in the first stage. Instead, the entire weight space is used to run the random multi-criteria decision-making fuzzy model for drainage network sediment removal, and the missing weight information is expressed through the uniform distribution of the drainage network sediment removal weight space.

[0034] 5.2. Based on the statements of each decision maker’s preference for each standard for drainage network sediment cleaning, the weight information of the multi-stage decision sequence for drainage network sediment cleaning is obtained.

[0035] The weight information of the multi-stage decision sequence for the drainage network sediment cleaning is expressed in the form of linear constraints, such as w1>w2>…>wn. The weight information of the multi-stage decision sequence for the drainage network sediment cleaning 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 some criteria (w1?w2) or thinks they are equally important (w1=w2). The weight information of the multi-stage decision sequence for the drainage network sediment cleaning can be expressed as a triangular plane in the drainage network sediment cleaning weight space.

[0036] 5.3. The complementary matrix method is used to determine the quantitative weights of each standard for drainage network sediment cleaning. The uncertainty of the weight is estimated through the probability distribution within the boundary of the feasible weight space of the multi-stage decision-making for drainage network sediment cleaning under interval constraints. The weight interval can be expressed as a hexagonal plane within the entire feasible weight space of the multi-stage decision-making for drainage network sediment cleaning.

[0037] 5.4. Use deterministic weight vectors to generate the final decision on drainage network sediment cleaning under an acceptable risk of decision error. If the multi-stage decision on drainage network sediment cleaning is a single decision-maker decision process, the complementary judgment matrix method is used to directly calculate and determine the weight vectors of each standard of drainage network sediment cleaning; if the multi-stage decision on drainage network sediment cleaning is a multi-decision-maker decision process, 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.

[0038] Furthermore, the step 2.1 is specifically as follows:

[0039] 2.1.1. Based on the experience of the decision criteria for drainage network sediment cleaning, a complementary judgment matrix for the decision criteria for drainage network sediment cleaning is constructed. The decision maker compares each pair of drainage network sediment cleaning criteria to determine their relative importance;

[0040] 2.1.2. Considering that the complementary judgment matrix of the decision criteria for clearing sediment in the drainage network usually contains a certain degree of inconsistency, the least squares method is used to obtain the weight value of each decision criterion for clearing sediment in the drainage network;

[0041] 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 each drainage network sediment cleaning decision criterion is calculated, and the inconsistency of the weight values ​​of each drainage network sediment cleaning decision criterion is evaluated. If the inconsistency error of the weight values ​​of each drainage network sediment cleaning decision criterion is small, the experience judgment of each decision maker is more accurate; on the contrary, if the inconsistency error of the weight values ​​of each drainage network sediment cleaning decision criterion is large, each decision maker should reconsider the preference information of each decision criterion.

[0042] Furthermore, the step 2.2 is specifically as follows:

[0043] 2.2.1. The complementary judgment matrix method is used to determine the basic weight vectors of the decision criteria for clearing the drainage network sediment for each decision maker. The basic weight vectors of the decision criteria for clearing the drainage network sediment for each decision maker are comprehensively considered and the basic weight vectors of the decision criteria for clearing the drainage network sediment are obtained by linear combination;

[0044] 2.2.2. According to Nash equilibrium, the weight combination coefficients of the criteria for clearing sediment from the drainage network are optimized to make the basic weight vectors of the criteria compromise or consistent, and finally obtain the coordinated weight vector of the criteria for clearing sediment from the drainage network, and minimize the deviation between the basic weight vectors of the criteria for clearing sediment from the drainage network and the coordinated weight vector;

[0045] 2.2.3. The linear programming method is used to solve the drainage network sediment cleaning decision model, obtain the optimal combination coefficient of the drainage network sediment cleaning decision, and calculate the drainage network sediment cleaning decision coordination weight vector.

[0046] Furthermore, the step 2.3 is specifically as follows:

[0047] 2.3.1. Construct feasible weight space of decision-making criteria for drainage network sediment cleaning, and expand the coordination weight vectors of various decision-making criteria for drainage network sediment cleaning from a single point to certain subspaces in the weight space. The feasible weight space is the union of all possible weight vectors;

[0048] 2.3.2. The feasible weight space of decision-making criteria for drainage network sediment cleaning is regarded as a subspace in the plane, whose center corresponds to the coordination weight vector of drainage network sediment cleaning. By applying interval constraints within the boundary of the feasible weight space, the probability distribution is used to measure the uncertainty of the weights of each decision-making criterion for drainage network sediment cleaning.

[0049] Furthermore, the step 3.1 is specifically as follows:

[0050] 3.1.1. Define the triangular fuzzy function of drainage network sediment cleaning and construct the fuzzy decision matrix of drainage network sediment cleaning. Use the triangular fuzzy function to represent the performance preference value of each alternative scheme for drainage network sediment cleaning for each decision criterion;

[0051] 3.1.2. Define the fuzzy anti-ideal weight distance and ideal weight distance for drainage network sediment removal. Although there is no ideal alternative in real life, it provides a benchmark for evaluating alternatives.

[0052] 3.1.3. Fuzzy optimization is performed on the multi-criteria decision analysis for drainage network sediment cleaning, and a global evaluation is performed on the alternative plans for drainage network sediment cleaning based on the various decision criteria for the multi-criteria decision-making for drainage network sediment cleaning, and the ranking of the alternative plans for drainage network sediment cleaning is obtained.

[0053] Furthermore, the step 3.2 is specifically as follows:

[0054] 3.2.1. Aiming at the multi-criteria decision analysis problem of drainage network sediment cleaning, a random multi-criteria decision analysis-fuzzy optimization model for drainage network sediment cleaning 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 each drainage network sediment cleaning alternative based on the original random multi-criteria decision analysis framework, a real-valued utility function for drainage network sediment cleaning is defined;

[0055] 3.2.2. In order to better evaluate the alternative plans for drainage network sediment cleaning, the uncertainty measure of drainage network sediment cleaning multi-criteria decision analysis is calculated from four dimensions based on the random multi-criteria decision analysis-fuzzy optimization model of drainage network sediment cleaning, which provides a basis for the final decision of drainage network sediment cleaning. The uncertainty measure of drainage network sediment cleaning mainly includes the following indicators: ① overall acceptability index (HAI), ② grade acceptability index (RAI), ③ confidence factor, and ④ central weight vector (CWV).

[0056] Furthermore, the step 4.1 is specifically as follows:

[0057] In order to test and evaluate the uncertainty of each drainage network sediment cleaning scheme, this method defines the risk of wrong decision-making for drainage network sediment cleaning. After obtaining the highest ranking scheme for drainage network sediment cleaning 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 drainage network sediment cleaning and deviate from the optimal sediment cleaning decision.

[0058] 4.1.1. Calculate the weighted probability that the drainage network sediment cleaning decision assigns the highest rank to the non-optimal solution, and define it as the drainage network sediment cleaning decision error risk. The drainage network sediment cleaning decision error risk calculation formula is:

[0059]

[0060] In the formula, Represents the first-level acceptability index of the k-th alternative based on HAI. β k 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

[0061] 4.1.2. Calculate the sum of the grade acceptability index of each drainage network sediment removal decision plan for all possible rankings except the final ranking:

[0062]

[0063] In the formula, g i Alternative solutions for clearing sediment from drainage networks A i The final grade is based on its overall acceptability index.

[0064] Furthermore, the step 4.2 is specifically as follows:

[0065] 4.2.1. Calculate the overall acceptability index of each alternative solution for drainage network sediment removal. The overall acceptability index is expressed as The overall acceptability index is defined as the acceptability of each alternative A for cleaning the sewer network sediment. i The ranking r gives the favorable rank weights of the 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 drainage network sediment cleaning alternative is absolutely impossible to be in a certain ranking, and 1 means that the drainage network sediment cleaning alternative is always in a certain ranking. In the process of multi-criteria decision analysis of drainage network sediment cleaning, the drainage network sediment cleaning alternative with the highest ranking and 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 set of drainage network sediment cleaning alternatives.

[0066] 4.2.2. Calculate the acceptability index of the drainage network sediment cleaning ranking to measure the overall acceptability of the drainage network sediment cleaning alternatives. The drainage network sediment cleaning ranking acceptability index is obtained by weighting the overall acceptability index of all drainage network sediment cleaning alternatives:

[0067]

[0068] In the formula, α r The overall acceptability index used to show the role of each specific sewer network sediment removal alternative in evaluating the alternatives. r Defined as a monotonically decreasing vector:

[0069]

[0070] 4.2.3. Calculate the confidence factor of each alternative solution for drainage network sediment removal. The confidence factor of drainage network sediment removal is a measure of the confidence factor of each alternative solution for drainage network sediment removal. i The expected center of gravity of the first-level weight space is favorable. The confidence factor of drainage network sediment cleaning 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 drainage network sediment cleaning alternative is very low, it means that even if this preference is selected for drainage network sediment cleaning multi-criteria decision-making, the probability of this alternative obtaining the highest ranking is also low. If the confidence factor of a drainage network sediment cleaning alternative is very high, it means that the drainage network sediment cleaning alternative has the most appropriate and highest preference setting.

[0071] The present invention can achieve the following beneficial effects:

[0072] 1. Through the gradual weight information method, this method allows decision makers to start the decision-making process in the early stage when the information is incomplete or unclear. As the information is gradually collected and the environment changes, the decision weights are continuously adjusted and optimized, which enhances the adaptability and flexibility of the decision and makes the decision process closer to the actual operation and maintenance needs.

[0073] 2. Combining game theory and feasible rights space theory, it effectively solves the preference conflicts among multiple stakeholders and ensures the rationality of decision-making criteria weights. Fuzzy optimization model and random multi-criteria decision analysis further improve the ability to deal with decision uncertainty, reduce the risk of decision errors, and improve the accuracy and reliability of decisions.

[0074] 3. By constructing a risk assessment model for drainage network sediment removal decisions, the risk of decision-making errors and the degree of uncertainty of each plan are quantified, enabling decision makers to intuitively understand potential risks, providing a scientific basis for formulating risk management strategies, and facilitating efficient resource allocation and risk control.

[0075] 4. The dynamic adjustment mechanism based on multi-stage decision-making can optimize the priority and resource allocation of cleaning operations according to real-time monitoring data and continuously updated decision preferences, avoiding unnecessary maintenance operations, saving costs and improving the efficiency of maintenance work. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0077] Figure 1 This is a multi-stage decision analysis flow chart for cleaning silt in the drainage network of the present invention;

[0078] Figure 2 It is a schematic diagram of the feasible rights space for multi-stage decision-making of cleaning sediment in the drainage network of the present invention;

[0079] Figure 3 It is a schematic diagram of gradually weighting information in the three-criteria decision analysis process of the present invention. DETAILED DESCRIPTION

[0080] The preferred solution is Figures 1 to 3 As shown in the figure, a multi-stage decision analysis method for drainage network cleaning based on step-by-step weight information is proposed. When the preference information of each decision criterion for drainage network sediment cleaning is completely missing or unclear, a multi-stage multi-criteria decision analysis is adopted to gradually determine the weight information of each criterion for drainage network sediment cleaning, thereby achieving the best decision for drainage network sediment cleaning.

[0081] like Figure 1 As shown, this embodiment discloses a multi-stage decision analysis method for cleaning a drainage network based on step-by-step weight information, the method comprising the following steps:

[0082] 1. Treat the multi-criteria decision analysis of drainage network sediment cleaning as a multi-stage decision analysis problem, determine the drainage network blockage parameters, select appropriate drainage network sediment cleaning decision criteria, and obtain the drainage network sediment cleaning random decision matrix;

[0083] For the drainage network in the embodiment, 1000 drainage network sediment cleaning solutions are randomly obtained. A set of initial alternative solutions for drainage network sediment cleaning is prepared A = {A i |i=1,2,…,1000},A i represents the ith alternative for clearing sediment in the drainage network, and 1000 represents the number of initial alternatives for clearing sediment in the drainage network;

[0084] Determine the drainage network blockage parameters, select appropriate drainage network sediment cleaning decision criteria, and obtain the drainage network sediment cleaning solution decision criteria set C = {C j |j=1,2,…,10}, in order to sort and screen the initial alternative solution set for drainage network sediment removal, C j represents the jth decision criterion for clearing sediment in the drainage network, and 10 represents the total number of decision criteria for clearing sediment in the drainage network;

[0085] The parameters that have the greatest impact on the blockage of the drainage network were selected as the decision criteria for clearing sediment from the drainage network, including: ① slope; ② age; ③ material; ④ diameter; ⑤ upstream manhole conditions; ⑥ branch and connection density of each pipe; ⑦ road type; ⑧ tree density along the pipeline; ⑨ pipeline depth; and ⑩ the density of restaurants and car washes along the pipeline.

[0086] 2. A method for weight aggregation of drainage network sediment removal based on game theory and feasible rights space is proposed to solve the conflict problem among multiple stakeholders in drainage network sediment removal, and estimate the uncertainty of the weight of each decision-making criterion for drainage network sediment removal;

[0087] 2.1. In order to quantify the uncertainty of the decision-making criteria for the drainage network sediment removal plan, this method uses the complementary judgment matrix method to quantify the uncertainty of each decision-making criterion, and converts the preference information of each decision maker for each decision-making criterion into the quantitative weight of each decision-making criterion;

[0088] 2.1.1. Based on the experience of the decision criteria for drainage network sediment cleaning, a complementary judgment matrix of the decision criteria for drainage network sediment cleaning is constructed. The decision maker compares each pair of drainage network sediment cleaning criteria to determine their relative importance.

[0089] Table 1 gives the verbal preference statements and their corresponding complementary comparison values. Standard weights can be selected or complementary comparison values ​​a can be directly given to satisfy the following conditions. ij and a ji To choose:

[0090] a ij +a ji =1

[0091] In the formula, a ij represents the preference of drainage network sediment cleaning decision criterion i relative to drainage network sediment cleaning decision criterion j, a ji It represents the preference of drainage network sediment cleaning decision criterion j over drainage network sediment cleaning decision criterion i.

[0092] Table 1 Verbal preference statements for decision-making on drainage network sediment removal and their corresponding complementary comparison values

[0093] Verbal Preference Statement <![CDATA[a ij ]]> <![CDATA[a ji ]]> i is definitely more important than j 0.9 0.1 i is much more important than j 0.8 0.2 i is slightly more important than j 0.7 0.3 i is more important than j 0.6 0.4 i and j are equally important 0.5 0.5

[0094] The ratio of the complementary comparison values ​​corresponds to the weights:

[0095]

[0096] A ji =1-a ij Substituting into the above formula, we get:

[0097]

[0098] Among them, w i and w j They represent the weights of the decision criteria for clearing sediment in the i-th and j-th drainage network, respectively. A complementary judgment matrix can be constructed based on the comparison values:

[0099]

[0100] In the formula, CJM represents the complementary judgment matrix of the multi-criteria decision analysis for the drainage network sediment removal. The main diagonal elements are equal to 0.5 because the importance of each criterion is equal.

[0101] 2.1.2. Considering that the complementary judgment matrix of the decision criteria for drainage network sediment cleaning usually contains a certain degree of inconsistency, the least squares method is used to obtain the weight value of each decision criterion for drainage network sediment cleaning; get:

[0102]

[0103] Considering the planning conditions of the weight values ​​of each decision criterion for clearing sediment in the drainage network, the incompatible solutions are identified. For solving the linear system, the weight values ​​of each decision criterion for clearing sediment in the drainage network can be obtained:

[0104]

[0105] 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:

[0106] HW=b

[0107] 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:

[0108] W=(HTH) -1 HkDJ

[0109] After solving W, according to Calculate the final weight w of each decision criterion for drainage network sediment removal n .

[0110] 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 each drainage network sediment cleaning decision criterion is calculated, and the inconsistency of the weight values ​​of each drainage network sediment cleaning decision criterion is evaluated. If the inconsistency error of the weight values ​​of each drainage network sediment cleaning decision criterion is small, the experience judgment of each decision maker is more accurate; on the contrary, if the inconsistency error of the weight values ​​of each drainage network sediment cleaning decision criterion is large, each decision maker should reconsider the preference information of each decision criterion.

[0111] The inconsistency error of the weights of each decision criterion for drainage network sediment removal can be calculated as:

[0112]

[0113] In the formula, e ij It represents the inconsistent error of the weights of various decision criteria for clearing sediment in the drainage network.

[0114] 2.2. Introduce game theory into the random multi-criteria decision analysis of drainage network sediment removal, and aggregate the weights of various conflicting decision criteria of drainage network sediment removal through Nash equilibrium to achieve preference compromise and conflict resolution;

[0115] 2.2.1. The complementary judgment matrix method is used to determine the basic weight vectors of the decision criteria for clearing the drainage network sediment for each decision maker. The basic weight vectors of the decision criteria for clearing the drainage network sediment for each decision maker are comprehensively considered and the basic weight vectors of the decision criteria for clearing the drainage network sediment are obtained by linear combination;

[0116] The decision standard value of sediment removal in each drainage network 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 decision-making process of clearing sediment in the drainage network. The linear combination of the basic weight vectors for the decision-making process of clearing sediment in the drainage network is:

[0117]

[0118] 2.2.2. According to Nash equilibrium, the weight combination coefficients of the criteria for clearing sediment from the drainage network are optimized to make the basic weight vectors of the criteria compromise or consistent, and finally obtain the coordinated weight vector of the criteria for clearing sediment from the drainage network, and minimize the deviation between the basic weight vectors of the criteria for clearing sediment from the drainage network and the coordinated weight vector;

[0119] Get the drainage network sediment cleaning decision coordination weight vector w * , and minimize each w k and w * Deviation between:

[0120]

[0121] In the formula, w k Represents the basic weight vector of each decision-making criterion for clearing sediment in the drainage network.

[0122] 2.2.3. The linear programming method is used to solve the drainage network sediment cleaning decision model, obtain the optimal combination coefficient of the drainage network sediment cleaning decision, and calculate the drainage network sediment cleaning decision coordination weight vector.

[0123] The optimal combination coefficient for drainage network sediment removal decision is expressed as The coordination weight vector of the drainage network sediment removal decision is calculated:

[0124]

[0125] 2.3, such as Figure 2 As shown in the figure, the concept of feasible rights space is used to quantify the uncertainty of each decision-making criterion for clearing sediment in the drainage network;

[0126] 2.3.1. Construct feasible weight space of decision-making criteria for drainage network sediment cleaning, and expand the coordination weight vectors of various decision-making criteria for drainage network sediment cleaning from a single point to certain subspaces in the weight space. The feasible weight space is the union of all possible weight vectors;

[0127] 2.3.2. The feasible weight space of decision-making criteria for drainage network sediment cleaning is regarded as a subspace in the plane, whose center corresponds to the coordination weight vector of drainage network sediment cleaning. By applying interval constraints within the boundary of the feasible weight space, the probability distribution is used to measure the uncertainty of the weights of each decision-making criterion for drainage network sediment cleaning.

[0128] The multi-stage decision-making feasible space for drainage network sediment removal can be expressed as:

[0129]

[0130] In the formula, λ represents the parameter of the uncertainty of the weight value of the drainage network sediment cleaning decision, and the parameter value is related to the degree of conflict between the various criteria of the drainage network sediment cleaning decision. If all decision makers involved in the drainage network sediment cleaning decision agree on a certain coordinated standard weight, then λ is a very small value; otherwise, it is necessary to give λ a larger value to obtain a larger multi-stage decision-making feasible weight space for drainage network sediment cleaning. After resolving the conflicts of various decision makers through aggregation, the multi-stage decision-making feasible weight space for drainage network sediment cleaning can reflect the uncertainty of the weights of various decision criteria without losing too much information.

[0131] 3. Combining the random multi-criteria acceptability analysis algorithm and the fuzzy optimization model, a random multi-criteria decision analysis fuzzy optimization model for drainage network sediment cleaning is constructed, the uncertainty of the drainage network sediment cleaning decision criteria and their weights is simulated and quantified, and several measurement descriptions of the robustness decision of drainage network sediment cleaning are given;

[0132] 3.1. Construct a fuzzy optimization model for clearing sediment in the drainage network, and use fuzzy anti-ideal distance and ideal distance to solve the multi-criteria decision-making problem of clearing sediment in the drainage network;

[0133] 3.1.1. Define the triangular fuzzy function of drainage network sediment cleaning and construct the fuzzy decision matrix of drainage network sediment cleaning. Use the triangular fuzzy function to represent the performance preference value of each alternative scheme for drainage network sediment cleaning for each decision criterion;

[0134] Using triangular fuzzy function represents the performance preference value of each alternative scheme for drainage network sediment cleaning for each decision criterion. Normalize to dimensionless value:

[0135] For the income standard

[0136] For cost standards

[0137] 3.1.2. Define the fuzzy anti-ideal weight distance and ideal weight distance for drainage network sediment removal. Although there is no ideal alternative in real life, it provides a benchmark for evaluating alternatives.

[0138] The anti-ideal drainage network sediment cleaning scheme and the ideal drainage network sediment cleaning scheme are defined as:

[0139] g=(g1,g2,…,g n )

[0140]

[0141] In the formula, g j =(1,1,1), Define weighted anti-ideal and ideal options for sewer network sediment removal:

[0142] w g =(w g1 ,w g2 ,…,w gn )

[0143]

[0144] In the formula, w j Indicates standard C j The weight is a triangular fuzzy value in [0,1]. Define the fuzzy anti-ideal and ideal weight distances to measure the difference between the alternative solutions and the anti-ideal solutions for the silt removal of each drainage network;

[0145]

[0146]

[0147] In the formula, Indicates alternative solution A for clearing sediment from drainage network i The weighted performance preference value vector of q=1 represents the Hemming distance, and q=2 represents the Euclidean distance.

[0148] 3.1.3. Fuzzy optimization is performed on the multi-criteria decision analysis for drainage network sediment cleaning, and a global evaluation is performed on the alternative plans for drainage network sediment cleaning based on the various decision criteria for the multi-criteria decision-making for drainage network sediment cleaning, and the ranking of the alternative plans for drainage network sediment cleaning is obtained.

[0149] Let u iIndicates alternative A for clearing silt from sewer networks according to all criteria i The global evaluation of 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:

[0150] min f(u i )=(u i ·dg i ) 2 +[(1-u i )·db i ] 2

[0151] Differentiating the above function yields:

[0152]

[0153] Finally, we can get:

[0154]

[0155] In the formula, u i Alternative solution A for clearing sediment from the drainage network based on the fuzzy concept of "optimal under all criteria" i According to the above definition, the member with the maximum membership u i The alternative is the most preferred alternative. In addition, by sorting the membership degrees corresponding to the alternatives for clearing sediment in the drainage network, the sorting order of the alternatives can be simply determined.

[0156] 3.2. Using the random multi-criteria decision analysis method and fuzzy optimization model, a random multi-criteria decision analysis-fuzzy optimization model for drainage network sediment cleaning is established, the uncertainty measure of each drainage network sediment cleaning alternative is calculated, and each drainage network sediment cleaning alternative is evaluated;

[0157] 3.2.1. Aiming at the multi-criteria decision analysis problem of drainage network sediment cleaning, a random multi-criteria decision analysis-fuzzy optimization model for drainage network sediment cleaning 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 each drainage network sediment cleaning alternative based on the original random multi-criteria decision analysis framework, a real-valued utility function for drainage network sediment cleaning is defined;

[0158] In order to evaluate the performance of the alternatives for drainage network sediment removal based on the original stochastic multi-criteria decision analysis framework, the real-valued utility function s(·) for drainage network sediment removal is defined as:

[0159]

[0160] In the formula, x i Alternative A for clearing sediment from sewer networks i A vector of performance preference values ​​for each decision criterion.

[0161] 3.2.2. In order to better evaluate the alternative plans for drainage network sediment cleaning, the uncertainty measure of drainage network sediment cleaning multi-criteria decision analysis is calculated from four dimensions based on the random multi-criteria decision analysis-fuzzy optimization model of drainage network sediment cleaning, which provides a basis for the final decision of drainage network sediment cleaning. The uncertainty measure of drainage network sediment cleaning mainly includes the following indicators: ① overall acceptability index (HAI), ② grade acceptability index (RAI), ③ confidence factor, and ④ central weight vector (CWV).

[0162] 4. Construct a risk assessment model for drainage network sediment removal decision-making, calculate the uncertainty degree and decision-making error risk of each drainage network sediment removal alternative plan, and quantitatively assess the risk of decision-making error in drainage network sediment removal;

[0163] 4.1. Calculate the risk of decision-making errors in the drainage network sediment removal plan and quantitatively evaluate the uncertainty of the drainage network sediment removal alternatives;

[0164] In order to test and evaluate the uncertainty of each drainage network sediment cleaning scheme, this method defines the risk of wrong decision-making for drainage network sediment cleaning. After obtaining the highest ranking scheme for drainage network sediment cleaning 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 drainage network sediment cleaning and deviate from the optimal sediment cleaning decision.

[0165] 4.1.1. Calculate the weighted probability that the drainage network sediment cleaning decision assigns the highest rank to the non-optimal solution, and define it as the drainage network sediment cleaning decision error risk. The drainage network sediment cleaning decision error risk calculation formula is:

[0166]

[0167] In the formula, represents the first-level acceptability index of the k-th alternative based on the overall acceptability index. k 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

[0168] 4.1.2. Calculate the sum of the grade acceptability index of each drainage network sediment removal decision plan for all possible rankings except the final ranking:

[0169]

[0170] In the formula, g i Alternative solutions for clearing sediment from drainage networks A i The final grade is based on its overall acceptability index.

[0171] 4.2. Calculate the uncertainty of the drainage network sediment removal plan and quantitatively evaluate the overall uncertainty of the ranking results of the drainage network sediment removal alternative plans.

[0172] 4.2.1. Calculate the overall acceptability index of each alternative solution for drainage network sediment removal. The overall acceptability index is expressed as The overall acceptability index is defined as the acceptability of each alternative A for cleaning the sewer network sediment. i The ranking r gives the favorable rank weights of the 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 drainage network sediment cleaning alternative is absolutely impossible to be in a certain ranking, and 1 means that the drainage network sediment cleaning alternative is always in a certain ranking. In the process of multi-criteria decision analysis of drainage network sediment cleaning, the drainage network sediment cleaning alternative with the highest ranking and 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 set of drainage network sediment cleaning alternatives.

[0173] and The calculation formulas are:

[0174]

[0175] In the formula, is the most favorable rank weight, which means that any weight vector Alternative A for the removal of sediment from the sewer network was granted i Rank r; rank(·) is a ranking function that gives the ordering of the options.

[0176] 4.2.2. Calculate the acceptability index of the drainage network sediment cleaning ranking to measure the overall acceptability of the drainage network sediment cleaning alternatives. The drainage network sediment cleaning ranking acceptability index is obtained by weighting the overall acceptability index of all drainage network sediment cleaning alternatives:

[0177]

[0178] In the formula, α r The overall acceptability index used to show the role of each specific sewer network sediment removal alternative in evaluating the alternatives. r Defined as a monotonically decreasing vector:

[0179]

[0180] 4.2.3. Calculate the confidence factor of each alternative solution for drainage network sediment removal. The confidence factor of drainage network sediment removal is a measure of the confidence factor of each alternative solution for drainage network sediment removal. i The expected center of gravity of the favorable first-level weight space. The confidence factor of drainage network sediment cleaning 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 drainage network sediment cleaning alternative is very low, it means that even if this preference is selected for drainage network sediment cleaning multi-criteria decision-making, the probability of this alternative obtaining the highest ranking is also very low. If the confidence factor of a drainage network sediment cleaning alternative is very high, it means that the drainage network sediment cleaning alternative has the most appropriate and highest preference setting;

[0181] In the form of multidimensional integrals, the first-level weights are favorable and standard PV distribution f x (ξ) we get:

[0182]

[0183] Confidence factor (using ) represents the probability of an alternative becoming the most preferred option using its CWV. Determine whether the standard PV is accurate enough in distinguishing candidate solutions. Expressed as a multidimensional integral over the standard PV distribution:

[0184]

[0185] 5. If Figure 3 As shown, a multi-stage decision is made on the cleaning of silt in the drainage network based on the stepwise weight information method to ensure that the decision plan for cleaning the drainage network is gradually solved within an acceptable decision risk range.

[0186] The multi-stage decision-making process for drainage network sediment removal starts with completely missing or unclear preference information, and gradually obtains more accurate information as the drainage network sediment removal decision-making process develops. The basic idea is to iteratively run the random multi-criteria decision-making fuzzy model for drainage network sediment removal after completing each round of drainage network sediment removal decision-related information collection until sufficient final decision preference information is obtained within an acceptable risk range of decision error. After each analysis of the random multi-criteria decision-making fuzzy model for drainage network sediment removal, 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 drainage network sediment removal, 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 for drainage network sediment cleaning is missing, the missing weight information is expressed by the uniform distribution of the drainage network sediment cleaning weight space.

[0188] In the initial stage of the multi-stage decision-making process for drainage network sediment removal, 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 drainage network sediment removal, decision makers do not need to express any preference information in the first stage. Instead, the entire weight space is used to run the random multi-criteria decision-making fuzzy model for drainage network sediment removal, and the missing weight information is expressed through the uniform distribution of the drainage network sediment removal weight space.

[0189] 5.2. Based on the statements of each decision maker’s preference for each standard for drainage network sediment cleaning, the weight information of the multi-stage decision sequence for drainage network sediment cleaning is obtained.

[0190] The weight information of multi-stage decision sequence for drainage network sediment removal is expressed in the form of linear constraints, such as w1>w2>…>w n The weight information of the multi-stage decision sequence for the drainage network sediment cleaning 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 some criteria (w1?w2) or considers them equally important (w1=w2). The weight information of the multi-stage decision sequence for the drainage network sediment cleaning can be expressed as a triangular plane in the drainage network sediment cleaning weight space.

[0191] 5.3. The complementary matrix method is used to determine the quantitative weights of each standard for drainage network sediment cleaning. The uncertainty of the weight is estimated through the probability distribution within the boundary of the feasible weight space of the multi-stage decision-making for drainage network sediment cleaning under interval constraints. The weight interval can be expressed as a hexagonal plane within the entire feasible weight space of the multi-stage decision-making for drainage network sediment cleaning.

[0192] 5.4. Use deterministic weight vectors to generate the final decision on drainage network sediment cleaning under an acceptable risk of decision error. If the multi-stage decision on drainage network sediment cleaning is a single decision-maker decision process, the complementary judgment matrix method is used to directly calculate and determine the weight vectors of each standard of drainage network sediment cleaning; if the multi-stage decision on drainage network sediment cleaning is a multi-decision-maker decision process, 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 multi-stage decision analysis method for drainage network cleaning based on step-by-step weight information, characterized by the following steps: S1. Treat the multi-criteria decision analysis of drainage network sediment cleaning as a multi-stage decision analysis problem, determine the drainage network blockage parameters, select appropriate drainage network sediment cleaning decision criteria, and obtain the drainage network sediment cleaning random decision matrix; S2. A method for weight aggregation of drainage network sediment removal based on game theory and feasible rights space is proposed to solve the conflict problem among multiple stakeholders in drainage network sediment removal, and to estimate the uncertainty of the weight of each decision-making criterion for drainage network sediment removal; S3. Combining the random multi-criteria acceptability analysis algorithm and the fuzzy optimization model, a random multi-criteria decision analysis fuzzy optimization model for drainage network sediment cleaning is constructed, the uncertainty of the drainage network sediment cleaning decision criteria and their weights is simulated and quantified, and several measurement descriptions of the robustness decision of drainage network sediment cleaning are given; S4. Construct a risk assessment model for drainage network sediment removal decision-making, calculate the uncertainty degree and decision-making error risk of each drainage network sediment removal alternative plan, and quantitatively assess the risk of decision-making error in drainage network sediment removal; S5 makes multi-stage decisions on the cleaning of silt in the drainage network based on the step-by-step weight information method, ensuring that the decision-making scheme for cleaning the drainage network is gradually solved within an acceptable decision risk range; The S1 sub-steps are: S1.1 Prepare an initial set of alternatives for clearing sediment from the sewer network , Indicates the first alternatives, represents the number of initial alternatives for clearing sediment from the sewer network; S1.2 Determine the drainage network blockage parameters, select appropriate drainage network sediment cleaning decision criteria, and obtain the drainage network sediment cleaning plan decision criteria set , in order to sort and screen the initial set of alternative solutions for clearing sediment in the drainage network, Indicates the first decision criteria, It represents the total number of decision criteria for clearing sediment in the drainage network; S1.3 Select the parameters that have the greatest impact on the blockage of the drainage network as the decision criteria for clearing sediment from the drainage network. The criteria include slope, age, material, diameter, upstream manhole conditions, branch and connection density of each pipeline, road type, tree density along the pipeline, pipeline depth, and density of restaurants and car washes along the pipeline; S2 is specifically: S2.

1. In order to quantify the uncertainty of the decision-making criteria for the drainage network sediment removal plan, the complementary judgment matrix method is used to quantify the uncertainty of each decision-making criterion, and the preference information of each decision-maker for the drainage network sediment removal plan on each decision-making criterion is converted into a quantitative weight of each decision-making criterion; S2.2, introduce game theory into the random multi-criteria decision analysis of drainage network sediment removal, and aggregate the weights of conflicting decision criteria of drainage network sediment removal through Nash equilibrium, so as to achieve preference compromise and conflict resolution; S2.

3. Use the concept of feasible rights space to quantify the uncertainty of each decision-making criterion for clearing sediment from the drainage network; The S3 sub-steps are: S3.

1. Construct a fuzzy optimization model for clearing sediment in the drainage network, and use fuzzy anti-ideal distance and ideal distance to solve the multi-criteria decision-making problem of clearing sediment in the drainage network; S3.

2. Using the random multi-criteria decision analysis method and the fuzzy optimization model, a random multi-criteria decision analysis-fuzzy optimization model for drainage network sediment cleaning is established, the uncertainty measure of each drainage network sediment cleaning alternative is calculated, and each drainage network sediment cleaning alternative is evaluated; S3.1 specifically: S3.1.

1. Define the triangular fuzzy function for drainage network sediment cleaning and construct the fuzzy decision matrix for drainage network sediment cleaning. Use the triangular fuzzy function to represent the performance preference value of each alternative scheme for drainage network sediment cleaning for each decision criterion; S3.1.2, define the fuzzy anti-ideal weight distance and ideal weight distance for clearing sediment in the drainage network; S3.1.

3. Perform fuzzy optimization on the multi-criteria decision analysis for drainage network sediment cleaning, and perform a global evaluation on the drainage network sediment cleaning alternatives according to the various decision criteria for the multi-criteria decision analysis for drainage network sediment cleaning, and obtain the ranking of the drainage network sediment cleaning alternatives; The sub-steps of S3.2 are: S3.2.

1. Aiming at the multi-criteria decision analysis problem of drainage network sediment cleaning, a random multi-criteria decision analysis-fuzzy optimization model for drainage network sediment cleaning is established by using the random multi-criteria decision analysis method and the fuzzy optimization model. The 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 each drainage network sediment cleaning alternative on the basis of the original random multi-criteria decision analysis framework, a real-valued utility function for drainage network sediment cleaning is defined. S3.2.

2. In order to better evaluate the alternative plans for drainage network sediment cleaning, the uncertainty measure of drainage network sediment cleaning multi-criteria decision analysis is calculated from four dimensions based on the random multi-criteria decision analysis-fuzzy optimization model of drainage network sediment cleaning, which provides a basis for the final decision of drainage network sediment cleaning. The uncertainty measure of drainage network sediment cleaning mainly includes the following indicators: ① overall acceptability index, ② grade acceptability index, ③ confidence factor, ④ center weight vector; The S4 sub-steps are: S4.

1. Calculate the risk of decision-making errors in the drainage network sediment removal plan and quantitatively evaluate the uncertainty of the drainage network sediment removal alternatives; S4.

2. Calculate the uncertainty of the drainage network sediment removal plan and quantitatively evaluate the overall uncertainty of the ranking results of the drainage network sediment removal alternative plans; The sub-steps of S4.1 are: In order to test and evaluate the uncertainty of each drainage network sediment cleaning scheme, the risk of drainage network sediment cleaning decision error was defined; after using the multi-criteria decision analysis method to obtain the highest ranking scheme for drainage network sediment cleaning, the decision maker believed that this scheme was the optimal scheme; obviously, assigning the first rank to a scheme that is not actually the best choice will have an adverse effect on the drainage network sediment cleaning and deviate from the optimal sediment cleaning decision; therefore, the adopted scheme is: S4.1.

1. Calculate the weighted probability that the drainage network sediment cleaning decision will assign the highest rank to the non-optimal solution, and define it as the drainage network sediment cleaning decision error risk. The drainage network sediment cleaning decision error risk calculation formula is: ； In the formula, represents the first-level acceptability index of the k-th alternative based on HAI; 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 drainage network sediment removal decision plan for all possible rankings except the final ranking: ； In the formula, It is an alternative solution for cleaning sediment in drainage pipe network Final rating based on its overall acceptability index; The S5 sub-steps are: The multi-stage decision-making process for drainage network sediment cleaning starts with completely missing or unclear preference information, and gradually obtains more accurate information as the drainage network sediment cleaning decision-making process develops; the basic idea is to iteratively run the drainage network sediment cleaning random multi-criteria decision-making fuzzy model after completing each round of drainage network sediment cleaning decision-making related information collection, until sufficient final decision preference information is obtained within an acceptable decision error risk range; After each analysis of the random multi-criteria decision-making fuzzy model for drainage network sediment removal, preference information is added by more accurately evaluating the decision maker's preferences; the multi-stage decision-making process for drainage network sediment removal can significantly save the preference collection process and avoid complex weighting processes if there is enough inaccurate information to make decisions in the early stages; the operation is as follows: S5.

1. When the weight information of the multi-criteria decision-making analysis for drainage network sediment removal is missing, the missing weight information is expressed by the uniform distribution of the drainage network sediment removal weight space; In the initial stage of the multi-stage decision-making process for drainage network sediment removal, 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 drainage network sediment removal, decision makers do not need to express any preference information in the first stage. Instead, the entire weight space is used to run the random multi-criteria decision-making fuzzy model for drainage network sediment removal, and the missing weight information is expressed through the uniform distribution of the drainage network sediment removal weight space. S5.2, based on the statements of the preferences of the decision makers for the various standards for clearing the silt in the drainage network, the weight information of the multi-stage decision sequence for clearing the silt in the drainage network is obtained; The multi-stage decision sequence weight information for drainage network sediment removal is expressed in the form of linear constraints, namely ; The multi-stage decision-making order weight information for drainage network sediment removal corresponds to the decision maker's preference statement, that is, criterion 1 is more important than criterion 2; because there are some criteria that decision makers cannot judge ( ) or considered equally important ( ) situation; The multi-stage decision sequence weight information of drainage network sediment cleaning can be expressed as a triangular plane in the drainage network sediment cleaning weight space; S5.

3. The complementary matrix method is used to determine the quantitative weights of the various criteria for drainage network sediment cleaning. The uncertainty of the weights is estimated through the probability distribution within the boundary of the feasible weight space of the multi-stage decision-making for drainage network sediment cleaning under interval constraints. The weight interval can be expressed as a hexagonal plane within the entire feasible weight space of the multi-stage decision-making for drainage network sediment cleaning; S5.

4. Use deterministic weight vectors to generate the final decision on drainage network sediment cleaning under an acceptable risk of decision-making errors; if the multi-stage decision on drainage network sediment cleaning is a single decision-maker decision-making process, then use the complementary judgment matrix method to directly calculate and determine the weight vectors of each standard for drainage network sediment cleaning; if the multi-stage decision on drainage network sediment cleaning is a multiple decision-maker decision-making process, then use the complementary judgment matrix method to calculate the weight vector of each standard for each decision-maker, and use the weight aggregation method to obtain the coordination weight vector of each standard.

2. The multi-stage decision analysis method for drainage network cleaning based on step-by-step weight information according to claim 1 is characterized by: S2.1 specifically: S2.1.

1. Based on the experience of the decision criteria for clearing sediment in the drainage network, a complementary judgment matrix of the decision criteria for clearing sediment in the drainage network is constructed; the decision maker compares each pair of the criteria for clearing sediment in the drainage network to determine their relative importance; S2.1.

2. Considering that the complementary judgment matrix of the decision criteria for clearing sediment in the drainage network usually contains a certain degree of inconsistency, the least squares method is used to obtain the weight value of each decision criterion for clearing sediment in the drainage network; 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 each drainage network sediment cleaning decision criterion, and evaluate the inconsistency of the weight values ​​of each drainage network sediment cleaning decision criterion; if the inconsistency error of the weight values ​​of each drainage network sediment cleaning decision criterion is small, the experience judgment of each decision maker is more accurate; conversely, if the inconsistency error of the weight values ​​of each drainage network sediment cleaning decision criterion is large, each decision maker should reconsider the preference information of each decision criterion.

3. The multi-stage decision analysis method for drainage network cleaning based on step-by-step weight information according to claim 2 is characterized by: 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 clearing sediment in the drainage network of each decision maker, comprehensively consider the basic weight vectors of the decision criteria of each decision maker, and use the linear combination method to obtain the basic weight vectors of the decision criteria for clearing sediment in the drainage network; S2.2.

2. According to Nash equilibrium, the weight combination coefficients of the criteria for clearing sediment from the drainage network are optimized to make the basic weight vectors of the criteria compromise or consistent, and finally obtain the coordinated weight vector of the criteria for clearing sediment from the drainage network, and minimize the deviation between the basic weight vectors of the criteria for clearing sediment from the drainage network and the coordinated weight vector; S2.2.

3. The linear programming method is used to solve the drainage network sediment cleaning decision model, the optimal combination coefficient of the drainage network sediment cleaning decision is obtained, and the drainage network sediment cleaning decision coordination weight vector is calculated.

4. The multi-stage decision analysis method for drainage network cleaning based on step-by-step weight information according to claim 1 is characterized by: S2.3 specifically: S2.3.

1. Construct feasible weight space of decision-making criteria for drainage network sediment cleaning, and expand the coordination weight vectors of various decision-making criteria for drainage network sediment cleaning from a single point to certain subspaces in the weight space. The feasible weight space is the union of all possible weight vectors; S2.3.

2. The feasible weight space of decision criteria for drainage network sediment cleaning is regarded as a subspace in the plane, the center of which corresponds to the coordination weight vector of drainage network sediment cleaning. By applying interval constraints within the boundary of the feasible weight space, the probability distribution is used to measure the uncertainty of the weights of each decision criterion for drainage network sediment cleaning.

5. The multi-stage decision analysis method for drainage network cleaning based on step-by-step weight information according to claim 1 is characterized by: The sub-steps of S4.2 are: S4.2.

1. Calculate the overall acceptability index of each alternative solution for drainage network sediment removal. The overall acceptability index is expressed as The overall acceptability index is defined as the Sorting Favorable rank weightings given to alternatives with different valuations volume; Obviously, the overall acceptability index assigns a certain ranking probability to each alternative, and the value range of the overall acceptability index is [0,1], 0 means that the drainage network sediment cleaning alternative is absolutely impossible to be in a certain ranking, and 1 means that the drainage network sediment cleaning alternative is always in a certain ranking; in the process of multi-criteria decision analysis of drainage network sediment cleaning, the drainage network sediment cleaning alternative with the highest ranking and high overall acceptability index is usually regarded as the potential optimal solution, and the alternative with a poor ranking but a high overall acceptability index is directly deleted from the initial alternative set of drainage network sediment cleaning; S4.2.

2. Calculate the acceptability index of the drainage network sediment cleaning ranking to measure the overall acceptability of the drainage network sediment cleaning alternatives; the drainage network sediment cleaning ranking acceptability index is obtained by weighting the overall acceptability index of all drainage network sediment cleaning alternatives: ； In the formula, An overall acceptability index to show the role of each specific sewer network sediment removal alternative in evaluating the alternatives; Defined as a monotonically decreasing vector: ； S4.2.

3. Calculate the confidence factor of each alternative solution for drainage network sediment removal. The confidence factor of drainage network sediment removal is a measure of the confidence factor of each alternative solution for drainage network sediment removal. The expected center of gravity of the first-level weight space is favorable; the confidence factor of the drainage network sediment removal shows the 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 drainage network sediment cleaning alternative is very low, it means that even if this preference is selected for drainage network sediment cleaning multi-criteria decision-making, the probability of this alternative getting the highest ranking is also very low; If the confidence factor for a drainage network sediment removal alternative is high, it means that the drainage network sediment removal alternative has the most appropriate and highest preference setting.

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