Improved Variable Weight AHP-Fuzzy Comprehensive Evaluation Method for Analyzing Dam Safety Status

Abstract

The present invention relates to an improved variable weight method for analyzing the safety status of a dam. AHP The fuzzy comprehensive evaluation method includes the following steps: constructing a reservoir safety evaluation hierarchical model; obtaining basic reservoir operation data and previous safety appraisal results; determining the reservoir safety level and scoring range; constructing a comment set for evaluating the safety of secondary evaluation parameters; calculating the variable weights and fuzzy membership matrix of each secondary evaluation parameter; calculating the fuzzy comprehensive evaluation matrix of each primary evaluation parameter and the final layer, and obtaining the corresponding fuzzy comprehensive score to obtain the final safety evaluation conclusion. The present invention provides an improved method for selecting the equalization coefficient, which can effectively reduce the traditional variable weight vector based on the state variable weight vector and the equalization function. AHP The subjectivity and blindness in the selection of the equilibrium coefficient affect the objectivity and authenticity of the evaluation results, which can better expose the current safety hazards of the reservoir and provide a certain reference basis for the formulation of subsequent reservoir hazard removal and reinforcement plans and the implementation of work.

Description

Technical Field

[0001] The present invention relates to a method for dam safety evaluation, in particular to an improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing the safety status of dams. Background Art

[0002] Reservoirs are crucial for economic and social development and people's livelihood security, and play an important supporting role in flood control, water supply, power generation, ecology, etc. China is a major country in the development and utilization of water resources. There are more than 98,000 existing reservoir dams, with a total storage capacity of 898.3 billion cubic meters. Small and medium-sized reservoirs account for about 95%, and earth-rock dams account for about 92%. The vast majority of reservoirs were built in the 1950s to 1970s. Restricted by factors such as construction technology, personnel quality, and economic level at that time, during the operation process of more than fifty years, some reservoirs have shown varying degrees of diseases and risks, facing a certain risk of dam break. Therefore, carrying out regular safety evaluations and appraisals of old and dangerous reservoirs to timely and early discover potential safety hazards existing in the current situation of reservoir dams has important practical significance for ensuring the safe operation of reservoirs and maintaining social long-term stability.

[0003] At present, safety evaluation methods for reservoir dams, such as the structural safety factor method, the fuzzy comprehensive evaluation method, and the analytic hierarchy process (AHP), have been applied by many scholars to practical engineering and achieved good results. The analytic hierarchy process (AHP) is a systematic analysis and decision-making method for complex problems that combines qualitative and quantitative approaches. However, since it is constructed on a fixed weight system of factors, it may lead to the failure of the composite ranking method for a few specific solutions that reflect the interaction mechanism among system elements. Compared with AHP, the variable weights AHP has been a relatively novel and rapidly developing systematic safety evaluation method in recent years. It emphasizes the variable weights idea that "the factor weights should change with the state values". Moreover, from the perspective of the complexity of the internal mechanism of the system, it can be seen that the variable weights AHP uses the variable weights idea to improve the fixed weight system of factors and the corresponding composite ranking method of traditional AHP, which can avoid the failure problem of the fixed weights AHP method model. Thus, it can better reflect the essential characteristics of complex systems such as nonlinearity, emergence, and dynamics, and can effectively improve the scientificity of the AHP evaluation and decision-making scheme. Therefore, it is more suitable for the requirements of reservoir safety evaluation for complex index systems and multiple evaluation subjects. At present, the variable weights theory has been applied to multiple research fields, such as the patent "Method for determining the weight adjustment parameter in the variable weights vulnerability evaluation method for water inrush from coal seam floor" (CN103761448B) by Wu Qiang et al. from China University of Mining and Technology (Beijing), the patent "A method for early warning of landscape water quality based on variable weights combination" (CN104155423B) by Zhao Jiabin et al. from Tianjin University, the patent "Method for flood control storage capacity allocation of reservoir groups based on maximizing the remaining flood control storage capacity with variable weights" (CN107180318B) by Kang Ling et al. from Huazhong University of Science and Technology, and the patent "Method for evaluating the health status of satellites based on variable weights hierarchical scoring" (CN103218515B) by Zhou Jun et al. from Northwestern Polytechnical University.

[0004] Some experts and scholars have given penalty-type, incentive-type, and mixed variable weights axiomatic systems, as well as multi-objective decision-making methods based on concepts such as state variable weights vectors and equilibrium functions. This method has a simple calculation process and strong engineering applicability and has currently been applied to the field of dam-break risk evaluation methods for tailings ponds. For the traditional variable weights AHP based on state variable weights vectors and equilibrium functions, the key to reasonably determining the variable weights of each secondary evaluation quantity within the initial layer lies in the scientific selection of the equilibrium coefficient. However, referring to the application of existing traditional variable weights AHP in the dam-break risk evaluation of tailings ponds, it can be found that the assignment of the equilibrium coefficient of the secondary evaluation quantity by decision-makers based on engineering experience has certain subjectivity and blindness. The following two methods for determining the equilibrium coefficient value will have an adverse impact on the objectivity and authenticity of the evaluation results of the safety status of reservoir dams:

[0005] (1) One method is to independently assign values ​​to the balance coefficients of each secondary evaluation quantity according to the subjective will of the decision maker. This may result in the weight of the secondary evaluation quantity with a relatively small state value, that is, a relatively poor safety condition, belonging to the same primary evaluation quantity being further reduced after the weighting process, while the weight of the secondary evaluation quantity with a relatively large state value, that is, a relatively good safety condition, is increased after the weighting process, thereby covering up the current condition and danger of the reservoir. The safety score of the primary evaluation quantity will be unreasonably increased, which will affect the objectivity and authenticity of the reservoir safety evaluation results, and the determination of the focus of the subsequent risk elimination and reinforcement project construction will also be affected to a certain extent;

[0006] (2) Another method is for decision makers to assign the same balance coefficient to each secondary parameter based on engineering experience. Although this method can avoid the above-mentioned "state imbalance" problem, it fails to consider the mutual influence between the constant weights of each secondary parameter under the same primary parameter and the state values. The variable weight range of the secondary parameter with relatively poor state value may be small, which is not enough to reflect the current safety hazards of the reservoir in the final evaluation results of the safety status of the reservoir dam, and there is a certain degree of blindness. Summary of the invention

[0007] The purpose of the present invention is to provide an improved method for determining the value of the balance coefficient in order to overcome the defects of the above-mentioned prior art. By introducing the method into the traditional variable weight AHP based on the state variable weight vector and the balance function and combining it with the fuzzy comprehensive evaluation method, an improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing the safety status of the dam is constructed for the field of reservoir dam safety evaluation methods. It can avoid the problem of "state imbalance" between the secondary evaluation quantities belonging to the same primary evaluation quantity that may be caused by the independent assignment of the balance coefficient of each secondary evaluation quantity by the traditional variable weight AHP; at the same time, the method considers the mutual influence between the constant weights and the state values ​​of the secondary evaluation quantities belonging to the same primary evaluation quantity in the process of weighting the constant weights of each secondary evaluation quantity, effectively reducing the blindness brought by the traditional variable weight AHP assigning the same balance coefficient to each secondary evaluation quantity in actual engineering applications, and can more effectively highlight the impact of the current safety hazards of the reservoir on the evaluation results, appropriately improve the degree of fit between the evaluation results and the actual safety status of the reservoir operation, and provide a certain reference basis for the formulation of subsequent reservoir risk elimination and reinforcement plans and the orderly development of work.

[0008] The purpose of the present invention can be achieved by the following technical solutions:

[0009] An improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing dam safety status includes the following steps:

[0010] Step 1: Construct a hierarchical structure model for the evaluation of the dam safety status, including the final layer A, the intermediate layer B, and the initial layer C. The final layer A is the overall goal of the reservoir dam safety status evaluation; the intermediate layer B contains multiple first-level evaluation factors that may affect the fuzzy comprehensive score of the final layer A. Assume that there are n first-level evaluation factors in the intermediate layer B, and the i-th first-level evaluation factor is denoted as B i , where i = 1, 2, …, n; each first-level evaluation factor B i contains multiple second-level evaluation factors that may affect its fuzzy comprehensive score. Assume that there are m i second-level evaluation factors under B i , and the j-th second-level evaluation factor is denoted as C ij , where j = 1, 2, …, m i , and all the second-level evaluation factors C ij together constitute the initial layer C;

[0011] Step 2: Obtain basic data such as the project overview of the target reservoir dam through on-site investigation, and separately obtain the reservoir operation monitoring data, the results of previous dam safety appraisals, and the current operation safety status within a relatively long period related to each second-level evaluation factor C ij in the initial layer C;

[0012] Step 3: Divide the safety level of the target reservoir dam into five levels from A to E, and take the conclusion obtained after the detailed induction, digestion, analysis, demonstration, and summary of the historical project overview and current operation conditions and other basic data of the reservoir dam by the safety appraisal expert group this time as the basic basis, and thereby determine the scoring interval corresponding to each safety level of the target reservoir dam, and on this basis, determine the evaluation initial layer C within the second-level evaluation factor C ij safety status comment set and the scoring interval corresponding to each comment;

[0013] Step 4: Calculate the variable weight w ij of each second-level evaluation factor C ij in the initial layer C;

[0014] Step 5: Calculate the fuzzy membership matrix of each second-level evaluation factor C ij in the initial layer C;

[0015] Step 6: First, through multi-level evaluation factor fuzzy comprehensive operation, respectively obtain the fuzzy comprehensive evaluation matrix of each first-level evaluation factor B i in the intermediate layer B and the final layer A. Secondly, according to the safety level and the scoring interval corresponding to each safety level determined in Step 3 for evaluating the safety status of the target reservoir dam, select the corresponding grade parameter vector V. Finally, respectively multiply the n fuzzy comprehensive evaluation matrices W Biand the fuzzy comprehensive evaluation matrix W of the final layer A A Performing matrix multiplication with V can obtain each first-level evaluation vector B within the connection layer B i The fuzzy comprehensive score F Bi and the fuzzy comprehensive score F of the final layer A, which is the overall goal of evaluating the safety status of the reservoir dam A .

[0016] As a further optimized solution, step 3 includes the following steps:

[0017] Step 301: Determine the safety level of the target reservoir dam:

[0018] To accurately describe the current safety status of the target reservoir dam, the safety level of the reservoir dam to be evaluated is divided into five levels from A to E. Based on the basic conclusions obtained after the detailed induction, digestion, analysis, demonstration, and summary of the basic data such as the project overview and operation conditions of the reservoir dam by the safety appraisal expert group this time, the scoring intervals corresponding to each safety level and the reservoir operation status and countermeasures are determined, as shown in Table 1.

[0019] Table 1 Classification of Dam Safety Evaluation Levels

[0020]

[0021] Step 302: Determine the comment set for evaluating the safety status of the secondary evaluation quantities:

[0022] According to the safety level of the target reservoir dam to be evaluated and the scoring intervals corresponding to each safety level, the secondary evaluation quantities C within the initial layer C that match them are determined ij The comment set for the safety status and the scoring intervals corresponding to each comment. Based on this and step 301, the comment set for evaluating the safety degree of each secondary evaluation quantity C ij The set expression is φ = {safe, relatively safe, generally safe, relatively dangerous, dangerous}, where the scoring intervals corresponding to each comment match the scoring intervals corresponding to the safety levels for evaluating the safety status of the reservoir dam in Table 1.

[0023] As a further optimized solution, step 4 is specifically as follows:

[0024] Step 401: According to the hierarchical structure model for evaluating the safety status of the target reservoir dam constructed in step 1, invite reservoir management personnel, on-site technical investigation personnel, and members of the safety appraisal expert group this time to combine the nine-scale method based on the data sorted and summarized in step 2 to evaluate the importance of each first-level evaluation quantity B within the connection layer B i and each secondary evaluation quantity C within the initial layer C ij to construct the "connection layer B - final layer A" judgment matrix MB-A and the judgment matrix of "initial layer C - connection layer B" Use the "root method" or the "sum method" to calculate the constant weight w of each first - level evaluation factor B within the connection layer B i and the constant weight w of each second - level evaluation factor C within the initial layer i 0 where i = 1, 2, …, n, j = 1, 2, …, m ij and the constant weight w of each second - level evaluation factor C within the initial layer ij 0 where n is the total number of first - level evaluation factors B within the connection layer B i and m i is the number of second - level evaluation factors C i contained in the first - level evaluation factor B i ; ij

[0025] Step 402: Prepare η questionnaires, distribute them to reservoir management personnel, on - site technical investigation personnel, and members of the safety appraisal expert group for this time, and invite them to score the current operation safety status of each second - level evaluation factor C within the initial layer C ij The state value x of the safety status of the η experts' scores for the same second - level evaluation factor C ij can be obtained by taking the arithmetic mean of the safety status scores ij ;

[0026] Step 403: Calculate the balance coefficient α of the j - th second - level evaluation factor C i under the i - th first - level evaluation factor B within the connection layer B ij ; ij

[0027] Step 404: Calculate the variable weight w of the j - th second - level evaluation factor C i under the i - th first - level evaluation factor B within the connection layer B ij ; ij

[0028] Among them, the specific steps for obtaining the constant weight w of each first - level evaluation factor B within the connection layer B i and the constant weight w of each second - level evaluation factor C within the initial layer C i 0 in step 401 are as follows: ij and the constant weight w of each second - level evaluation factor C within the initial layer ij 0 are as follows:

[0029] Step 401a: According to the hierarchical structure model of the reservoir dam safety status evaluation constructed in step 1, comprehensively consider the opinions of reservoir management personnel, on - site technical investigation personnel, and members of the safety appraisal expert group for this reservoir dam safety appraisal to evaluate each first - level evaluation factor B within the connection layer B i and each second - level evaluation factor C within the initial layer C​​​ij Conduct importance evaluation;

[0030] Step 401b: According to the relative importance of each first-level and second-level evaluation quantity obtained in Step 401a, combined with the nine-scale method, for each first-level evaluation quantity B within the connection layer B under the same final layer A i between and belonging to the same first-level evaluation quantity B i for each second-level evaluation quantity C within the initial layer C ij Compare them pairwise to construct the "connection layer B - final layer A" judgment matrix M B-A and the "initial layer C - connection layer B" judgment matrix According to the judgment matrix M B-A and Obtain the constant weight w of each first-level evaluation quantity B within the connection layer B i and i 0 the constant weight w of each second-level evaluation quantity C within the initial layer C ij and ij 0 .

[0031] Specifically, if the i-th first-level evaluation quantity within the connection layer B under the final layer A is denoted as B i , i = 1, 2,..., n, where n is the total number of first-level evaluation quantities within the connection layer B, then the constructed "connection layer B - final layer A" judgment matrix M B-A can be expressed as follows:

[0032]

[0033] In the formula: b ij represents the element value of the i-th row and j-th column of the judgment matrix M B-A . Its value reflects that for the final layer A, the first-level evaluation quantity B within its connection layer B i is relatively more important than B j . The larger b ij is, the greater the relative importance of B i . Among them, i, j = 1, 2,..., n, and n is the order of the judgment matrix, that is, the number of first-level evaluation quantities B within the connection layer B i .

[0034] Table 2 Meaning table of 1 - 9 scales

[0035] <![CDATA[b ij > Meaning 1 <![CDATA[B i Compared with B j equally important]]> 3 <![CDATA[B i Compared with B j is slightly more important]]> 5 <![CDATA[B i compared with B j is significantly more important]]> 7 <![CDATA[B i Compared with B j is strongly important]]> 9 <![CDATA[B i Compared with B j is extremely important]]> 2、4、6、8 Located in the middle of two adjacent scales <![CDATA[1 / b ij > <![CDATA[Given the value of b ij then 1 / b ij is its reciprocal]]>

[0036] The specific content of the said Step 401b is:

[0037] 1) There is a certain one-sidedness in the values of the relative importance of each first-level and second-level evaluation quantity, which may cause the judgment matrix to deviate from the consistency matrix, resulting in unreasonable weight allocation. Therefore, it is necessary to conduct a consistency test on the judgment matrix. If the consistency test fails, the judgment matrix needs to be continuously corrected until the test is passed. The specific steps for conducting a consistency test on matrix M are as follows:

[0038] ① Calculate the consistency index CI, and the formula is as follows:

[0039]

[0040] In the formula: CI is the consistency index, n is the order of the judgment matrix, and λ max is the largest eigenvalue of the judgment matrix M, that is:

[0041]

[0042] In the formula: W i is the normalized constant weight vector, and i = 1, 2,..., n

[0043] ② Determine the average random consistency index RI. The larger the order n of the judgment matrix, the greater the possibility of random deviation from consistency. The standard values of RI are shown in Table 3:

[0044] Table 3 Average Random Consistency Index Table

[0045] n 1 2 3 4 5 6 7 8 9 10 RI 0 0 0.52 0.89 1.12 1.26 1.36 1.41 1.46 1.49

[0046] ③ Calculate the test coefficient CR, and the formula is as follows:

[0047]

[0048] In the formula: When CR < 0.10, it means that the matrix passes the consistency test; otherwise, the judgment matrix M needs to be continuously corrected until the consistency test is passed.

[0049] 2) After all judgment matrices pass the consistency test, calculate the constant weight w i of each first-level evaluation quantity B i 0 in the connection layer B and the constant weight w ij of each second-level evaluation quantity C ij 0 in the initial layer C by the "square root method" or the "sum method":

[0050] Specifically, assume that for the n first-level evaluation vectors B i (i = 1, 2,..., n) in the connection layer B under the final layer A, there is a judgment matrix M B-A , then calculate the i-th first-level evaluation quantity B in the connection layer Bi The constant weight w i 0 The formula is as follows:

[0051] ① Root extraction method

[0052]

[0053] Each first-level evaluation index B within the connection layer B obtained from the above formula i The constant weight w i 0 can be comprehensively composed into the constant weight vector of the connection layer evaluation index, that is:

[0054] W 0 =(w 1 0 , w 2 0 , …, w n 0 ) T

[0055] ② Summation method

[0056] a. Perform column normalization on the elements in the judgment matrix M B-A to obtain the normalized matrix Q=(q ij ) n×n :

[0057]

[0058] b. Add the elements of matrix Q row by row to obtain the vector P=(p 1 , p 2 , …, p n ) T :

[0059]

[0060] c. Perform normalization on the vector P to obtain the index constant weight vector W 0 =(w 1 0 , w 2 0 , …, w n 0 ) T :

[0061]

[0062] The specific content of step 402 is as follows:

[0063] Step 402a: According to the hierarchical structure model for evaluating the safety status of the target reservoir dam constructed in Step 1 and the secondary evaluation variables C within the initial evaluation layer C determined in Step 3 ij and the comment set for the safety status and the scoring intervals corresponding to each comment, prepare η questionnaires, distribute them to reservoir management personnel, on-site technical investigation personnel, and members of the expert group for the current safety appraisal of the reservoir dam, and invite them to score the current operating safety status of the secondary evaluation variables C ij within the initial evaluation layer C;

[0064] Step 402b: To ensure that the magnitude x of the state value of the secondary evaluation variable C ij is as close as possible to its current safety status, in principle, it is required that decision-makers determine its risk level based on its current safety status and its influence on the fuzzy comprehensive score of the corresponding primary evaluation variable B ij before scoring each secondary evaluation variable C ij . After the risk levels of all secondary evaluation variables C i under the primary evaluation variable B i have been determined, adopt the form of "mutual comparison scoring" to score the safety status of each secondary evaluation variable C ij . During the scoring process, the mutual influence between the constant weight weights and the state values of each secondary evaluation variable should be considered as much as possible. The higher the score value, the better the safety status of the secondary evaluation variable C ij , and the lower the threat degree to the safety of the corresponding primary evaluation variable B ij . The lower the score value, the worse the safety status of the secondary evaluation variable C i , and the higher the threat degree to the safety of the corresponding primary evaluation variable B ij ; i

[0065] Step 402c: Take the arithmetic mean of the safety status scores of the η experts obtained in Step 402b for the same secondary evaluation variable C ij to obtain its state value x ij .

[0066] The specific steps for calculating the balance coefficient α i to be assigned to the j-th secondary evaluation variable C ij under the i-th primary evaluation variable B ij in the connection layer B described in Step 403 are as follows:

[0067] Step 403a: Calculate the state standard value x i of each primary evaluation variable B i 0 in the connection layer B. The formula is as follows:

[0068] ​

[0069] Where: w ij 0 is the constant weight of the j-th secondary evaluation index C under the first-level evaluation index B i ; x ij is the status value of the secondary evaluation index C ij ; n is the total number of first-level evaluation indexes in the connection layer B; m ij is the total number of secondary evaluation indexes under the first-level evaluation index B i ; i

[0070] Step 403b: Calculate the balance coefficient α to be assigned to the j-th secondary evaluation index C under the i-th first-level evaluation index B in the connection layer B i ; the formula is as follows: ij ij

[0071]

[0072] Where: μ is the adjustment coefficient for variable weight processing of the constant weights of the secondary evaluation indexes C in the initial layer C in the variable weight hierarchical model; the meanings of the other symbols are the same as before ij

[0073] The specific content of the said Step 404 is:

[0074] Assume that the i-th first-level evaluation index in the connection layer B is denoted as B i ; B i contains m i secondary evaluation indexes; denote the j-th secondary evaluation index under B i as C ij ; then the calculation formula for the variable weight w of the secondary evaluation index C ij is as follows: ij

[0075]

[0076] Where: w ij 0 is the constant weight of the j-th secondary evaluation index C under the first-level evaluation index B i ; x ij is the status value of the secondary evaluation index C ij ; α ij is the balance coefficient to be assigned to the secondary evaluation index C ij ; when α ij =1, it represents the constant weight mode ij

[0077] For an improved method for obtaining the balance coefficient value provided by the present invention, the idea is as follows: ​​​​​​

[0078] From the variable weight formula (Formula 3), it can be seen that the secondary evaluation parameters C in the initial layer C in the hierarchical structure model of the reservoir dam safety status evaluation are scientifically given. ij The equalization coefficient α ij It is the key to achieving reasonable weighting of various secondary evaluation quantities. According to the subjective will of the decision maker, the balance coefficient of each secondary evaluation quantity is independently assigned, which may cause the weight of the secondary evaluation quantity with a relatively small state value, that is, a relatively poor safety condition, which belongs to the same primary evaluation quantity to be further reduced after the weighting process, while the weight of the secondary evaluation quantity with a relatively large state value, that is, a relatively good safety condition, is increased after the weighting process, thereby covering up the current condition and danger of the reservoir. The safety score of the primary evaluation quantity finally obtained will increase unreasonably, which will affect the objectivity and authenticity of the reservoir safety evaluation results, and the determination of the subsequent construction focus of the risk elimination and reinforcement project will also be affected to a certain extent. In the actual engineering safety evaluation, the decision maker generally assigns the same balance coefficient to each secondary evaluation quantity based on engineering experience. Although this method can avoid the above-mentioned "state imbalance" problem, it fails to consider the mutual influence between the constant weights and the state values ​​of each secondary evaluation quantity under the same primary evaluation quantity. The weighting range of the secondary evaluation quantity with a relatively poor state value may be small, which is not enough to reflect the current safety hazards of the reservoir in the overall safety score of the reservoir, and there is a certain degree of blindness.

[0079] For the traditional variable-weight AHP, the purpose of variable-weight processing of each secondary evaluation quantity is to establish the connection between its weight and state value, aiming to emphasize that the weight should change with the change of state value. In order to reduce the adverse effects of the subjectivity and blindness of the above-mentioned traditional variable-weight AHP on the objectivity and authenticity of the reservoir safety evaluation results caused by the subjectivity and blindness of the balance coefficient, it is necessary to consider avoiding the "state imbalance" problem between the secondary evaluation quantities belonging to the same primary evaluation quantity due to the assignment of independent balance coefficients to each secondary evaluation quantity according to the subjective will of each decision maker, and also to consider how to increase the weight change range of the secondary evaluation quantity with relatively poor state value under the same primary evaluation quantity when variable-weight processing of each secondary evaluation quantity, so that the current safety hazards of the reservoir corresponding to the secondary evaluation quantity can be more clearly reflected in the reservoir safety evaluation results. Based on this, this paper proposes an improved method for determining the value of the balance coefficient, the steps are as follows: first, the decision maker determines the adjustment coefficient μ used for variable-weight processing of the constant weights of each secondary evaluation quantity based on engineering experience, and then determines the judgment of the primary evaluation quantity B belonging to the same primary evaluation quantity. i The following secondary evaluation quantities C ij The safety status of the state value x ij Good or bad "state standard value x i 0 ", and finally find out the secondary evaluation quantity C that should be given to eachij Equilibrium coefficient α ij 。

[0080] As can be seen from Equation (3), the variable weight formula contains three key parameters, namely the secondary evaluation quantity C ij constant weight w ij 0 , state value x ij and equilibrium coefficient α ij , where the constant weight w ij 0 is usually obtained from the judgment matrix. The determination of each element in the judgment matrix mainly depends on the assignment results of the importance of each secondary evaluation quantity under the same primary evaluation quantity by the expert group on the basis of detailed sorting, induction, analysis and summary of the general situation of the target reservoir project, long-term operation monitoring data and the results of previous dam safety appraisals. Therefore, the magnitude of the constant weight w ij 0 actually only reflects the degree of attention of the decision maker to the current safety status of the secondary evaluation quantity without considering the safety status, that is, the state value x ij . The larger the constant weight w ij 0 , the greater the degree of influence of the state value of this secondary evaluation quantity on the safety of its affiliated primary evaluation quantity is considered by the decision maker. On the other hand, the state value x ij of a certain secondary evaluation quantity is obtained by taking the arithmetic mean of the scores given by η decision makers on the basis of fully considering the current safety status of this secondary evaluation quantity. Therefore, the state value x ij is closer to the current safety status of this secondary evaluation quantity. Therefore, the constant weight comprehensive score of the primary evaluation quantity B ij to which this secondary evaluation quantity C i belongs, that is, the sum of the products of the state values of each secondary evaluation quantity under the primary evaluation quantity B i and the corresponding constant weights, is used as the "state standard value x i 0 " for judging the quality of the safety status or the goodness or badness of the state value of each secondary evaluation quantity under this primary evaluation quantity. The calculation formula is shown in Equation (1).

[0081] On this basis, a calculation formula for an improved method of determining the equilibrium coefficient value is further proposed and considered as follows:

[0082] For a certain secondary evaluation quantity C i belonging to the primary evaluation quantity B ij , if its state value x ij is less than the state standard value x i of the primary evaluation quantity B i 0 , it indicates that the secondary evaluation quantity Cij The current safety status is inferior to that of the first-level evaluation factor B i The comprehensive safety status, |x ij -x i 0 |The larger the value, the greater the safety threat level of the second-level evaluation factor C ij to the first-level evaluation factor B i should be considered to increase its balance coefficient α on the basis of the adjustment coefficient μ ij , and |α ij -μ| should be positively correlated with |x ij -x i 0 |. After variable weighting, the weight w ij should be increased compared with the constant weight w ij 0 The increase amplitude |w ij -w ij 0 | should also be positively correlated with |x ij -x i 0 |. If its state value x ij is greater than the state standard value x i of the first-level evaluation factor B i 0 , it indicates that the current safety status of the second-level evaluation factor C ij is better than that of the first-level evaluation factor B i The comprehensive safety status, |x ij -x i 0 |The larger the value, the smaller the safety threat level of this second-level evaluation factor C ij to the first-level evaluation factor B i Similarly, it should be considered to reduce its balance coefficient α on the basis of the adjustment coefficient μ ij , the variable weight w ij should be reduced compared with the constant weight w ij 0 |α ij -μ| and |w ij -w ij 0 | should also be positively correlated with |x ij -x i 0 |. Based on this, the calculation formula of an improved method for determining the balance coefficient proposed in this paper can be calculated according to Equation (2).

[0083] By improving the method for determining the balance coefficient, the constant weights w ij of each second-level evaluation factor C ij 0 can be balanced with their state values x ijThe relationship between them avoids the "state imbalance" problem that may occur among the secondary evaluation factors C under the same primary evaluation factor B caused by the decision-makers assigning independent equilibrium coefficients, and appropriately reduces the blindness that may be caused by assigning the same equilibrium coefficient α to each secondary evaluation factor C in the actual application of the traditional variable weight AHP. The state value x of a certain primary evaluation factor B may be relatively poor, and the variable weight range of the secondary evaluation factor with relatively poor performance is small, so it is not enough to highlight the impact of the current safety hazards of the reservoir corresponding to this secondary evaluation factor on the final result of the safety evaluation, and the current safety hazards of the reservoir can be better exposed. ij due to the possible "state imbalance" problem among the secondary evaluation factors under the same primary evaluation factor B caused by independent equilibrium coefficients, and i appropriately reduces the blindness that may be caused by assigning the same equilibrium coefficient α to each secondary evaluation factor C in the actual application of the traditional variable weight AHP. The state value x of a certain primary evaluation factor B ij may be relatively poor, and the variable weight range of the secondary evaluation factor with relatively poor performance is small, so it is not enough to highlight the impact of the current safety hazards of the reservoir corresponding to this secondary evaluation factor on the final result of the safety evaluation, and the current safety hazards of the reservoir can be better exposed. i under ij The variable weight range of the secondary evaluation factor with relatively poor performance is small, so it is not enough to highlight the impact of the current safety hazards of the reservoir corresponding to this secondary evaluation factor on the final result of the safety evaluation, and the current safety hazards of the reservoir can be better exposed.

[0084] Step 5 is further as follows:

[0085] Sort and summarize the scoring values of the η decision-makers on the secondary evaluation factors C in the initial layer C according to the evaluation set of the safety conditions of the secondary evaluation factors determined in Step 3 and the scoring interval corresponding to each comment, and then determine the fuzzy membership matrix of each secondary evaluation factor through the triangular membership function. The expression of the triangular membership function is as follows: ij Sort and summarize the scoring values of the η decision-makers on the safety conditions of the secondary evaluation factors C in the initial layer C according to the evaluation set of the safety conditions of the secondary evaluation factors determined in Step 3 and the scoring interval corresponding to each comment, and then determine the fuzzy membership matrix of each secondary evaluation factor through the triangular membership function. The expression of the triangular membership function is as follows:

[0086]

[0087] In the formula: a 1 , a 3 are the endpoint values of the segmented interval, and a 2 is the midpoint value of the interval.

[0088] Step 6 is further as follows:

[0089] Step 601: Fuzzy comprehensive operation of secondary evaluation factors

[0090] The calculation formula of the fuzzy comprehensive evaluation matrix W i of the i-th primary evaluation factor B Bi in the connection layer B is as follows:

[0091] W Bi = W i ·R i

[0092] In the formula: W i is the variable weight matrix of the secondary evaluation factors C i subordinate to the primary evaluation factor B ij relative to B i ; R i is composed of the secondary evaluation factors C i1 ~C imiThe membership matrix composed of the fuzzy membership matrices, expanded as follows:

[0093]

[0094] Where: j = 1, 2, …, m i , m i is the secondary evaluation quantity C under the first-level evaluation quantity B i ; ξ is the number of comments in the comment set of the safety status of each secondary evaluation quantity C within the initial evaluation layer C ij ; ξ is the number of comments in the comment set of the safety status of each secondary evaluation quantity C within the initial evaluation layer C ij for the safety status of the dam.

[0095] Step 602: Fuzzy comprehensive operation of the first-level evaluation quantity

[0096] The fuzzy comprehensive evaluation matrix W of the final layer A A is calculated as follows:

[0097] W A = W · R

[0098] Where: W is the constant weight matrix of the connection layer B relative to the final layer A; R is the matrix composed of the fuzzy evaluation matrices W of all the first-level evaluation quantities B within the connection layer B obtained from step (601), i = 1, 2, …, n; i for the safety status of the dam. Bi jointly composed matrix, i = 1, 2, …, n;

[0099]

[0100] Where: n is the total number of the first-level evaluation quantities B in the connection layer B i ; ξ is the number of comments in the comment set of the safety status of each secondary evaluation quantity C within the initial evaluation layer C

[0101] Step 603: During the dam safety evaluation process, the safety level of the reservoir dam to be evaluated is divided into five levels from A to E:

[0102] Level A, the comprehensive evaluation of the current safety status is "safe", and the scoring range is [σ 4 , 100];

[0103] Level B, the comprehensive evaluation of the current safety status is "relatively safe", scoring range: [σ 3 , σ 4 );

[0104] Level C, the comprehensive evaluation of the current safety status is "generally safe", scoring range: [σ 2 , σ 3 );

[0105] Level D, the comprehensive evaluation of the current safety status is "relatively dangerous", scoring range: [σ 1 , σ 2 );

[0106] Level E, the comprehensive evaluation of the current safety status is "dangerous", scoring range: [0, σ 1 )

[0107] Take the corresponding level parameter vector Calculate each first-level evaluation factor B within the connection layer B according to the following formula i The fuzzy comprehensive score of

[0108]

[0109] Similarly, the fuzzy comprehensive score of the final layer A, that is, the total goal of evaluating the safety status of the reservoir dam, can be calculated according to the following formula

[0110]

[0111] In view of the subjectivity and blindness problems existing in the process of assigning the balance coefficients of each secondary evaluation factor in the actual engineering application of the traditional variable weight AHP, the present invention proposes an improved method for obtaining the balance coefficients. By introducing this method into the traditional variable weight AHP based on the state variable weight vector and the balance function and combining it with the fuzzy comprehensive evaluation method, an improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing the safety status of the dam in the field of reservoir dam safety evaluation method is constructed

[0112] Compared with the prior art, the present invention has the following advantages

[0113] (1) Compared with the traditional AHP, the variable weight AHP takes into account the influence of the state values of the secondary evaluation factors on the change of their weights, avoiding the failure of a few specific scheme composite sorting methods that reflect the interaction mechanism between system elements caused by the construction of the fixed weight system of factors, thus preventing the influence on the objectivity and authenticity of the evaluation results of the reservoir dam safety status caused by the defect that the nonlinear and emergent nature and other essential characteristics of complex systems such as reservoir safety evaluation cannot be reflected

[0114] (2) An improved method for obtaining the balance coefficients proposed in this paper can avoid the "state imbalance" problem that may occur between the secondary evaluation factors belonging to the same first-level evaluation factor caused by the independent assignment of the balance coefficients of each secondary evaluation factor in the traditional variable weight AHP; at the same time, this method takes into account the mutual influence between the constant weights and the state values of the secondary evaluation factors belonging to the same first-level evaluation factor during the variable weight processing of the constant weights of each secondary evaluation factor, effectively reducing the blindness caused by assigning the same balance coefficients to each secondary evaluation factor in the actual engineering application of the traditional variable weight AHP, and can more effectively highlight the influence of the current safety hazards of the reservoir on the evaluation results, improving the degree of fit between the evaluation results and the actual operation safety status of the reservoir, and providing a certain reference basis for the formulation of subsequent reservoir reinforcement plans and the orderly development of work Description of the Drawings

[0115] Figure 1 is the basic flowchart of an improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing the safety status of a dam according to the present invention;

[0116] Figure 2 is the structural schematic diagram of the reservoir dam safety evaluation hierarchical structure model in this embodiment;

[0117] Figure 3 is the equilibrium coefficient α of each secondary evaluation index obtained according to formulas (1) and (2) when the adjustment coefficient μ = 0.2 and μ = 0.3 ij with |x ij - x i 0 | variation trend;

[0118] Figure 4 is the comparison chart of the variation trend of the weight change rate of the constant weight of each secondary evaluation index after variable weight processing by using two different methods of taking the equilibrium coefficient with |x ij - x i 0 | size; Detailed Implementation Manner

[0119] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0120] Embodiment

[0121] Step 1: Construct a hierarchical structure model for evaluating the safety status of the dam, including the final layer A, the connection layer B, and the initial layer C. The final layer A is the overall goal of evaluating the safety status of the reservoir dam; the connection layer B includes multiple primary evaluation indexes that may affect the fuzzy comprehensive score of the final layer A. Assume that there are n primary evaluation indexes in the connection layer B, and the i-th primary evaluation index is denoted as B i , where i = 1, 2,..., n; each primary evaluation index B i includes multiple secondary evaluation indexes that may affect the B i fuzzy comprehensive score. Assume that there are m i secondary evaluation indexes under B i , and the j-th secondary evaluation index is denoted as C ij , where j = 1, 2,..., m i , and all the secondary evaluation indexes C ij together constitute the initial layer C;

[0122] Step 2: Obtain the basic operation data of the target reservoir dam through on-site investigation, and respectively obtain the data related to each secondary evaluation index C in the initial layer C ijThe operation monitoring data of the reservoir in the relevant long period, the results of previous dam safety appraisals, and the current operation safety status;

[0123] Step 3: Divide the safety level of the dam of the reservoir to be evaluated into five levels from A to E. Taking the conclusions obtained after the detailed analysis of the basic operation data of the project and the results of previous dam safety appraisals by the expert group of this safety appraisal as the basic basis, determine the scoring intervals corresponding to each safety level. On this basis, determine each secondary evaluation quantity C within the evaluation initial layer C that matches the safety level and scoring interval of the safety status of the target reservoir dam to be evaluated. ij The comment set and corresponding scoring intervals for the safety status;

[0124] Step 4: Calculate the variable weight w of each secondary evaluation quantity C within the initial layer C. ij ; ij ;

[0125] Step 5: Calculate the fuzzy membership matrix of each secondary evaluation quantity C within the initial layer C. ij ;

[0126] Step 6: First, through the fuzzy comprehensive operation of multi-level evaluation quantities, obtain the fuzzy comprehensive evaluation matrices of each primary evaluation quantity B within the connection layer B and the final layer A respectively. Secondly, according to the safety level and scoring interval of the safety status of the target reservoir dam determined in Step 3, select the corresponding grade parameter vector V. Finally, multiply the n fuzzy comprehensive evaluation matrices within the connection layer B i and the fuzzy comprehensive evaluation matrix W of the final layer A by V respectively to obtain the fuzzy comprehensive scores of each primary evaluation vector B within the connection layer B A and the fuzzy comprehensive score F of the final layer A, that is, the total goal of evaluating the safety status of the reservoir dam. i ; ; A ;

[0127] As Figure 2 shown, according to the steps of reservoir safety evaluation, it is first necessary to construct an evaluation hierarchical structure model for the safety status of the target reservoir dam in accordance with principles such as scientificity, hierarchy, and completeness, including the final layer A, the connection layer B, and the initial layer C. The final layer A is the total goal of evaluating the safety status of the target reservoir dam; according to the factors that may affect the fuzzy comprehensive score of the final layer A, divide the connection layer B into engineering quality (B 1 ), operation management (B 2 ), flood control capacity (B 3 ), structural safety (B 4 ), seepage safety (B 5 ), and metal structure safety (B 6)There are 6 first-level evaluation factors in total; according to the specific evaluation content of each first-level evaluation factor, the initial layer C is divided into 25 second-level evaluation factors in total, among which the construction quality of dam seepage prevention (C 11 ), the rolling and ramming of the dam body (C 12 ), the construction quality of the dam foundation and bank slopes (C 13 ), the construction quality of other structures of the dam body (C 14 ), and the construction quality of water conveyance and discharge structures (C 15 ) are used as the second-level evaluation factors of the project quality (B 1 ); the daily operation management (C 21 ), the accident emergency plan (C 22 ), the equipment monitoring and maintenance (C 23 ), and the sorting out and rectification of potential safety hazards (C 24 ) are used as the second-level evaluation factors within the operation management (B 2 ); the flood control standard (C 31 ), the flood discharge capacity (C 32 ), the flood regulation calculation (C 33 ), and the daily maximum rainfall (C 34 ) are used as the second-level evaluation factors under the flood control capacity (B 3 ); the deformation of each part of the dam body (C 41 ), the anti-sliding stability of the dam body (C 42 ), the structural stability of the water conveyance and discharge structures (C 43 ), and the structural safety of other buildings (C 44 ) are used as the second-level evaluation factors under the structural safety (B 4 ); the seepage situation of the dam foundation of the dam (C 51 ), the seepage situation of the water conveyance and discharge structures (C 52 ), the finite element calculation results (C 53 ), and the permeability coefficient of the dam fill (C 54 ) are used as the second-level evaluation factors under the seepage safety (B 5 ); the on-site inspection (C 61 ), the safety monitoring (C 62 ), and the calculation and analysis (C 63 ) are used as the second-level evaluation factors under the metal structure safety (B 6 ), forming a hierarchical structure model for evaluating the safety status of the target reservoir dam.

[0128] Step 2 is specifically as follows: Obtain the basic operation data such as the project overview of the target reservoir dam through on-site investigation, and respectively obtain the reservoir operation monitoring data, the results of previous dam safety appraisals, and the current operation safety status within a relatively long period related to each second-level evaluation factor C ij in the initial layer C;

[0129] Step 3 includes the following steps:

[0130] Step 301: Determine the safety level of the target reservoir dam

[0131] To accurately describe the current safety status of the target reservoir dam, the safety levels of the reservoir dams to be evaluated are divided into five levels from A to E. Based on the basic data such as the project overview and current operation status of the reservoir dam by this safety appraisal expert group, as well as the results of previous dam safety appraisals, a detailed induction, digestion, analysis and demonstration, and summary are carried out, and the basic conclusions obtained are used as the basis to determine the scoring intervals corresponding to each safety level.

[0132] Table 4 shows the classification of the safety status evaluation levels of the reservoir dams in the embodiments of the present invention, the scoring intervals corresponding to each safety level, the reservoir operation status, and the countermeasures.

[0133] Table 4 Classification of Dam Safety Evaluation Levels

[0134]

[0135]

[0136] Step 302: Determine the set of evaluation comments for the safety status of the secondary evaluation variables

[0137] According to the safety level of the target reservoir dam to be evaluated and the scoring intervals corresponding to each safety level, determine the secondary evaluation variables C within the evaluation initial layer C that match them ij The set of evaluation comments for the safety status and the scoring intervals corresponding to each comment. Based on this and from step (301), the set of evaluation comments for determining the safety degree of each secondary evaluation variable C ij is expressed by the set expression φ = {safe, relatively safe, generally safe, relatively dangerous, dangerous}, where the scoring intervals corresponding to each comment match the scoring intervals corresponding to the safety levels of the evaluation of the reservoir dam safety status in Table 4.

[0138] Step 4 includes the following steps:

[0139] Step 401: According to the reservoir dam safety status evaluation hierarchical structure model established in step 1, invite reservoir management personnel, on-site technical investigation personnel, and members of this safety appraisal expert group to combine the nine-scale method based on the data sorted and summarized in step 2 for each primary evaluation variable B within the connection layer B i and each secondary evaluation variable C within the initial layer C ij to conduct importance evaluations, and construct the "connection layer B - final layer A" judgment matrix M B-A and the "initial layer C - connection layer B" judgment matrix Adopt the "square root method" or the "sum method" to calculate the constant weight w of each primary evaluation variable B within the connection layer B i respectivelyi 0 and the secondary evaluation variables C in the initial layer ij with constant weight w ij 0 , where i = 1, 2, …, n, j = 1, 2, …, m i , n is the total number of the primary evaluation variables B in the connection layer B i , m i is the number of the secondary evaluation variables C i contained in B ij ;

[0140] Step 402: Prepare η questionnaires and distribute them to reservoir management personnel, on-site technical investigation personnel, and members of the safety appraisal expert group for this time, and invite them to score the current operation safety status of the secondary evaluation variables C in the initial layer C ij . Take the arithmetic mean of the safety status scores of the η experts for the same secondary evaluation variable C ij to obtain its state value x ij ;

[0141] Step 403: Calculate the balance coefficient α i of the j-th secondary evaluation variable C ij under the i-th primary evaluation variable B in the connection layer B ij ;

[0142] Step 404: Calculate the variable weight w i of the j-th secondary evaluation variable C ij under the i-th primary evaluation variable B in the connection layer B ij .

[0143] In the said Step 401, the specific steps for obtaining the constant weights w i of the primary evaluation variables B in the connection layer B i 0 and the constant weights w ij of the secondary evaluation variables C in the initial layer C ij 0 are as follows:

[0144] Step 401a: According to the hierarchical structure model of the reservoir dam safety status evaluation constructed in Step 1, comprehensively consider the opinions of reservoir management personnel, on-site technical investigation personnel, and members of the safety appraisal expert group for this reservoir dam to evaluate the importance of the primary evaluation variables B in the connection layer B i and the secondary evaluation variables C in the initial layer C ij ;

[0145] Step 401b: According to the relative importance of the first-level and second-level evaluation metrics obtained in Step 401a, and in combination with the nine-scale method, pairwise comparisons are made between the first-level evaluation metrics B within the connection layer B under the same final layer A and between the second-level evaluation metrics C within the initial layer C under the same first-level evaluation metric B to construct the "connection layer B - final layer A" judgment matrix M i and the "initial layer C - connection layer B" judgment matrix i According to the judgment matrix M ij and B-A the constant weight w of each first-level evaluation metric B within the connection layer B is obtained B-A and the constant weight w of each second-level evaluation metric C within the initial layer C i i 0 ij ij 0 i B-A ij .

[0146] Specifically, if the i-th first-level evaluation metric within the connection layer B under the final layer A is denoted as B i , (i = 1, 2,..., n), where n is the total number of first-level evaluation metrics within the connection layer B, then the constructed "connection layer B - final layer A" judgment matrix M B-A can be expressed as follows:

[0147]

[0148] where: b ij represents the element value of the i-th row and j-th column of the judgment matrix M B-A , and its value reflects the importance degree of the first-level evaluation metric B within the connection layer B under the final layer A relative to B i . The larger b j is, the greater the relative importance of B ij . Among them, i, j = 1, 2,..., n, and n is the order of the judgment matrix, that is, the number of first-level evaluation metrics B within the connection layer B i . i

[0149] The specific content of Step 401b is as follows:

[0150] 1) The value of the relative importance of the indicators has a certain one-sidedness, which may cause the judgment matrix to deviate from the consistency matrix, resulting in unreasonable weight distribution. Therefore, it is necessary to conduct a consistency test on the judgment matrix. If the consistency test fails, the judgment matrix needs to be continuously corrected until it passes the test. The specific steps for conducting a consistency test on matrix M are as follows:

[0151] ① Calculate the consistency index CI, and the formula is as follows:​

[0152]

[0153] Where: CI is the consistency index, n is the order of the judgment matrix, and λ max is the maximum eigenvalue of the judgment matrix, that is:

[0154]

[0155] Where: W i is the normalized constant weight vector, and i = 1, 2,..., n

[0156] ② Determine the average random consistency index RI. The larger the order n of the judgment matrix M, the greater the possibility of random deviation from consistency. The standard values of RI are shown in Table 3:

[0157] ③ Calculate the test coefficient CR, and the formula is as follows:

[0158]

[0159] Where: when CR < 0.10, it means that the matrix passes the consistency test; otherwise, the judgment matrix needs to be corrected until it passes the consistency test.

[0160] 2) After all judgment matrices pass the consistency test, the embodiments of the present invention select to calculate the constant weight weights w i of each first-level evaluation quantity B i 0 in the connection layer B and the constant weight weights w ij of each second-level evaluation quantity C ij 0 in the initial layer C:

[0161] Specifically, assuming that for n first-level evaluation vectors B i (i = 1, 2,..., n) in the connection layer B under the final layer A, there is a judgment matrix M B-A , then calculate the constant weight weight w i of the i-th first-level evaluation vector B i 0 in the connection layer B. The "square root method" formula is as follows:

[0162]

[0163] The constant weight weights w i of each first-level evaluation quantity B i 0 obtained from the above formula can be comprehensively composed into the constant weight matrix W 0 of the connection layer B, that is:

[0164] W 0 =(w 1 0 , w 2 0 , …, w n 0 )

[0165] Similarly, the first-level evaluation factors B within the connection layer B can be obtained i and the second-level evaluation factors C ij under each of them ij 0 can be comprehensively composed into n constant weight matrices W 1 0 ~W n 0 , that is:

[0166]

[0167] In the formula: m i is the number of the second-level evaluation factors C i under the first-level evaluation factor B ij within the connection layer B

[0168] The "connection layer B - final layer A" judgment matrix M constructed in the embodiment of the present invention B-A and the "initial layer C - connection layer B" judgment matrix are as follows:

[0169] ① "Connection layer B - final layer A" judgment matrix M B-A :

[0170]

[0171] λ max = 6.1626, CI = 0.0330, CR = 0.0262 < 0.1

[0172] ② "Initial layer C - connection layer B" judgment matrix

[0173]

[0174] λ max = 5.0554, CI = 0.0138, CR = 0.0124 < 0.1

[0175]

[0176] λ max = 4.1964, CI = 0.0648, CR = 0.0728 < 0.1

[0177]

[0178] λ max = 4.1833, CI = 0.0604, CR = 0.0679 < 0.1

[0179]

[0180] λ max = 4.0248, CI = 0.0082, CR = 0.0092 < 0.1

[0181]

[0182] λ max = 4.1471, CI = 0.0484, CR = 0.0544 < 0.1

[0183]

[0184] λ max = 3, CI = 0.0000, CR = 0.0000 < 0.1

[0185] Determine each first-level evaluation index B within the connection layer B i of the constant weight w i 0 :

[0186] W 0 = (w 1 0 , w 2 0 , w 3 0 , w 4 0 , w 5 0 , w 6 0 ) = (0.1031, 0.0673, 0.1613, 0.3826, 0.2514, 0.0343)

[0187] Determine the constant weights of each second-level evaluation index within the initial layer C under the first-level evaluation index B: 1

[0188] W 1 0 = (w 11 0 , w, w 12 0 , w 13 0 , w 14 0 , w 15 0)=(0.2457, 0.4037, 0.2199, 0.0520, 0.0788)

[0189] Determine the constant weight of each secondary evaluation index in the initial layer C under the first-level evaluation index B 2 as follows:

[0190] W 2 0 =(w 21 0 , w 22 0 , w 23 0 , w 24 0 )=(0.5216, 0.2320, 0.1186, 0.1278)

[0191] Determine the constant weight of each secondary evaluation index in the initial layer C under the first-level evaluation index B 3 as follows:

[0192] W 3 0 =(w 31 0 , w 32 0 , w 33 0 , w 44 0 )=(0.4314, 0.1349, 0.3326, 0.1012)

[0193] Determine the constant weight of each secondary evaluation index in the initial layer C under the first-level evaluation index B 4 as follows:

[0194] W 4 0 =(w 41 0 , w 42 0 , w 43 0 , w 44 0 )=(0.2321, 0.4890, 0.1896, 0.0893)

[0195] Determine the constant weight of each secondary evaluation index in the initial layer C under the first-level evaluation index B 5 as follows:

[0196] W 5 0 =(w 51 0 , w 520 , w 53 0 , w 54 0 ) = (0.5380, 0.0595, 0.1285, 0.2740)

[0197] Calculate the first-level evaluation factor B 6 The constant weight of each secondary evaluation factor in the initial layer C under

[0198] W 6 0 = (w 61 0 , w 62 0 , w 63 0 ) = (0.3333, 0.3333, 0.33333)

[0199] The specific content of step 402 is as follows:

[0200] Step 402a: According to the dam safety status evaluation hierarchical structure model constructed in step (1) and the evaluation initial layer C determined in step (3), and the comment set of the safety status of each secondary evaluation factor C ij and the scoring interval corresponding to each comment, prepare η questionnaires (see Table 5), distribute them to reservoir management personnel, on-site technical investigation personnel, and members of the expert group for the current safety appraisal of the reservoir dam, and invite them to score the current operation safety status of each secondary evaluation factor C ij in the initial layer C;

[0201] Table 5 Membership Statistics Table

[0202]

[0203]

[0204] Step 402b: To ensure that the state value x ij of the secondary evaluation factor C ij is as close as possible to its current safety status, in principle, it is required that decision-makers should first determine its risk level according to its current safety status and its influence on the fuzzy comprehensive score of the first-level evaluation factor B ij before scoring each secondary evaluation factor C i . After the risk levels of all secondary evaluation factors C i under the first-level evaluation factor B ij have been determined, then adopt the form of "mutual comparison scoring" to score each secondary evaluation factor C ijThe safety status score of C. During the scoring process, the mutual influence between the constant weight weights and the status values of each secondary evaluation quantity should be considered as much as possible. The higher the score, the better the safety status of the secondary evaluation quantity C ij and the lower the safety threat level to the first-level evaluation quantity B i to which it belongs; the lower the score, the worse the safety status of the secondary evaluation quantity C ij and the higher the safety threat level to the first-level evaluation quantity B i to which it belongs;

[0205] Step 402c: Take the arithmetic mean of the safety status scores of the η experts for the same secondary evaluation quantity C ij to obtain the status value x i of the j-th secondary evaluation quantity C ij under the first-level evaluation quantity B ij , as shown in Table 6.

[0206] In the described Step 403, the specific steps for calculating the balance coefficient α i to be assigned to the j-th secondary evaluation quantity C ij under the i-th first-level evaluation quantity B ij in the connection layer B are as follows:

[0207] Step 403a: Calculate the status standard value x i of each first-level evaluation quantity B i 0 in the connection layer B:

[0208] Assume that there are m i secondary evaluation quantities C i under the i-th first-level evaluation quantity B ij (j = 1, 2,..., m i ), then the status standard value x i of the first-level evaluation quantity B i 0 is calculated as follows:

[0209]

[0210] In the formula: w ij 0 is the constant weight of the j-th secondary evaluation quantity C i under the i-th first-level evaluation quantity B ij in the connection layer; x ij is the status value of the secondary evaluation quantity C ij ; n is the total number of first-level evaluation quantities in the connection layer B; m i is the total number of secondary evaluation quantities C i under the first-level evaluation quantity B ij .

[0211] Step 403b: Calculate the equilibrium coefficient α to be assigned to the j-th secondary evaluation quantity C under the i-th primary evaluation quantity B within the connection layer B i as follows: ij of the equilibrium coefficient α ij , and the formula is as follows:

[0212]

[0213] In the formula: μ is the adjustment coefficient used for variable weight processing of the constant weight of each secondary evaluation quantity C within the initial layer C in the variable weight hierarchical model; the meanings of the other symbols are the same as before. ij

[0214] The specific content of the said step 404 is as follows:

[0215] Assume that the i-th primary evaluation quantity within the connection layer B is denoted as B i , and B i contains m i secondary evaluation quantities. Denote the j-th secondary evaluation quantity under B i as C ij . Then the calculation formula for the variable weight w ij of the secondary evaluation quantity C ij is as follows;

[0216]

[0217] In the formula: w ij 0 is the constant weight of the j-th secondary evaluation quantity C under the primary evaluation quantity B i ; x ij is the state value of the secondary evaluation quantity C ij ; α ij is the equilibrium coefficient to be assigned to the secondary evaluation quantity C ij . When α ij = 1, it represents the constant weight mode; the meanings of the other symbols are the same as before. ij

[0218] In the process of practical engineering application of an improved method for determining the value of the equilibrium coefficient proposed in this paper, first, the decision-maker needs to determine the adjustment coefficient μ used for variable weight processing of the constant weight of each secondary evaluation quantity C within the initial layer C according to engineering experience, and then calculate the state value x ij of each secondary evaluation quantity C ij and the absolute value of the difference |x ij - x i between the state standard value x i 0 of the primary evaluation quantity B to which each secondary evaluation quantity belongs calculated by formula (1) and ij -x​​i 0 |(difference of state values), and finally calculate the secondary evaluation quantities C that should be assigned to the initial layer C according to formula (2) ij The equalization coefficient α ij In actual safety assessment, decision makers should avoid ij The constant weight w ij 0 The process of weighting may lead to the problem of "state imbalance" among the secondary evaluation quantities under the same primary evaluation quantity. Usually, each secondary evaluation quantity is assigned C ij With the same equilibrium coefficient α, based on engineering experience and referring to the application results of variable weighted analytic hierarchy process in tailings dam break risk assessment, it can be seen that the value of α is generally 0.2-0.3, so the value range of the adjustment coefficient μ should also be 0.2-0.3.

[0219] When the adjustment coefficient μ = 0.2 and μ = 0.3, the secondary evaluation parameters C calculated according to formula (1) and formula (2) are ij The equalization coefficient α ij Follow|x ij -x i 0 |The trend of size change can be seen in Figure 3 .

[0220] Depend on Figure 3 It can be seen that the various secondary evaluation quantities C calculated by the improved method of balancing coefficients are ij The equalization coefficient α ij Fluctuates around the adjustment coefficient μ: when x ij ≥x i 0 When α ij ≤β; when x ij ≤x i 0 When α ij ≥β. In addition, α ij The change range of the relative adjustment coefficient β|α ij -β| and the secondary evaluation quantity C ij The state value x ij With its first-level evaluation quantity B i The state standard value x i 0 The absolute value of the difference |x ij -x i 0 | is positively correlated. In fact, after transformation, formula (2) can be obtained as follows:

[0221]

[0222] For each secondary evaluation quantity C i under the same primary evaluation quantity B ij when the adjustment coefficient μ and the status standard value x i of the primary evaluation quantity B i 0 are both determined, for a certain secondary evaluation quantity C ij under it, its status value x ij and the status standard value x i of its affiliated primary evaluation quantity B i 0 the absolute value of the difference |x ij -x i 0 | and |α ij -μ| are in a linearly proportional relationship, and the proportionality coefficient is For the same secondary evaluation quantity C ij when its status value x ij and the status standard value x i of its affiliated primary evaluation quantity B i 0 are both determined, |α ij -μ| and the adjustment coefficient μ are in a linearly proportional relationship, and the proportionality coefficient is

[0223] In practical engineering applications, traditional variable weight AHP usually assigns the same equilibrium coefficient α to each secondary evaluation quantity C ij by the decision maker according to engineering experience, which has a certain blindness. To illustrate that the improved equilibrium coefficient value-taking method provided by the present invention can effectively reduce the possibility that the current safety hazards of the reservoir cannot be reflected in the evaluation results caused by the above-mentioned blindness defect, two schemes are selected and the variable weight weights w ij of each secondary evaluation quantity C ij are calculated according to formula (3) respectively: Scheme 1 is to assign the same equilibrium coefficient α to each secondary evaluation quantity, α = 0.3; Scheme 2 is when the adjustment coefficient μ = 0.3, the equilibrium coefficient α ij that should be assigned to each secondary evaluation quantity C ij calculated according to formula (2).

[0224] The calculation results of the variable weight weights of each secondary evaluation quantity under the two schemes are shown in Table 6.

[0225] Table 6 Calculation results of variable weight weights

[0226]

[0227]

[0228] As can be seen from Table 6, similar to Scenario 1, when variable weight processing is performed on the constant weight w of each secondary evaluation index C under the same primary evaluation index B i , ij when x ij 0 <x ij <x i 0 , w ij >w ij 0 ; when x ij >x i 0 , w ij <w ij 0 . There is no "state imbalance" problem that may be caused by the decision maker independently assigning the balance coefficient of each secondary evaluation index

[0229] . Further, the weight change rate χ ij after variable weight processing of the constant weight w of a certain secondary evaluation index C ij 0 is defined by the following formula ij :

[0230]

[0231] The weight change rates of each secondary evaluation index under the two scenarios in Table 6 can be calculated from the above formula, as shown in Figure 4 :

[0232] It can be seen from Figure 4 that the weight change range of each secondary evaluation index C after variable weight by formula (3) is positively correlated with the absolute value of the difference |x ij -x ij | between its state value x and the state standard value x i of its primary evaluation index B i 0 . Compared with Scenario 1, the weight change ranges of each secondary evaluation index calculated by Scenario 2 are all greater than those obtained by Scenario 1, indicating that the improved balance coefficient value-taking method proposed in this paper, based on the adjustment coefficient μ, according to |x ij -x i 0 |, i 0 -x ijAssigning weights to the balance coefficients of the secondary evaluation quantities under the same primary evaluation quantity can effectively adjust the constant weight of each secondary evaluation quantity, thereby reducing the relatively small weight growth rate of the secondary evaluation quantity with relatively poor state values caused by the blindness defect in the way of obtaining the balance coefficient in Plan 1, which is insufficient to highlight the impact of the current safety hazards of the reservoir corresponding to this secondary evaluation quantity on the safety status evaluation results of its primary evaluation quantity and the overall reservoir.

[0233] Step 5 is specifically as follows:

[0234] Organize and summarize the scoring values of the η decision-makers for each secondary evaluation quantity C in the initial layer C according to the evaluation set for the current safety status of each secondary evaluation quantity and the scoring interval corresponding to each comment determined in Step 3, and then determine the fuzzy membership matrix of each secondary evaluation quantity C ij through the triangular membership function. The expression of the triangular membership function is as follows: ij

[0235]

[0236] In the formula: a 1 , a 3 are the endpoint values of the segmented interval, and a 2 is the midpoint value of the interval.

[0237] The calculation results of the fuzzy membership matrix of each secondary evaluation quantity C in the initial layer C obtained are shown in Table 7. ij

[0238] Table 7 Calculation Results of the Membership Degrees of Each Secondary Evaluation Quantity

[0239]

[0240]

[0241] Step 6 is specifically as follows:

[0242] Step 601: Fuzzy comprehensive operation of secondary evaluation quantities

[0243] The formula for the fuzzy comprehensive evaluation matrix i of the i-th primary evaluation quantity B in the connection layer B is as follows:

[0244]

[0245] In the formula: W i is the variable weight matrix of each secondary evaluation quantity C in the initial layer C belonging to the primary evaluation quantity B i ; R ij relative to B i ;​​i which is composed of the fuzzy membership degree matrix of the secondary evaluation indicators , and when expanded, it is as follows:

[0246]

[0247] In the formula: m i is the number of secondary evaluation indicators C i under the primary evaluation indicator B ij , and j = 1, 2,..., m i ; ξ is the number of evaluation comments in the comment set of the safety status of each secondary evaluation indicator C ij in the initial evaluation layer C.

[0248] Step 602: Fuzzy comprehensive operation of the primary evaluation indicator

[0249] The calculation formula of the fuzzy comprehensive evaluation matrix W A of the final layer A is as follows:

[0250] W A = W · R (6)

[0251] In the formula: W is the variable weight matrix of the connection layer B relative to the final layer A; R is the fuzzy evaluation matrix i formed by all the primary evaluation indicators B in the connection layer B calculated through step (601), and when expanded, it is as follows:

[0252]

[0253] In the formula: n is the total number of primary evaluation indicators B i in the connection layer B.

[0254] In the embodiment of the present invention, the fuzzy comprehensive evaluation matrix 1 ~B 6 of the primary evaluation indicators B in the connection layer B is as follows:

[0255]

[0256]

[0257] Comprehensively composed of to form the fuzzy membership degree judgment matrix R of the connection layer B:

[0258]

[0259] In the embodiment of the present invention, the fuzzy evaluation matrix W A of the final layer A is as follows:

[0260]

[0261] Step 603: Result analysis

[0262] In the process of dam safety assessment, the safety status of reservoir dams is divided into five levels from A to E:

[0263] Grade A: The overall safety status is evaluated as “safe”, with a score range of [90,100];

[0264] B level, the comprehensive evaluation of safety status is "relatively safe", the score range is: [70,90);

[0265] C level, the comprehensive evaluation of safety status is "generally safe", the score range is: [50,70);

[0266] D level, the overall safety status is evaluated as "relatively dangerous", the score range is: [30,50)

[0267] E level, the overall safety status is evaluated as "dangerous", the scoring range is: [0,30)

[0268] Take the corresponding level parameter vector V = (v 1 ,v 2 ,…,v n ) T =(95,80,60,40,15) T , the first-level evaluation quantities B in the connection layer B i The fuzzy comprehensive score is calculated as follows:

[0269]

[0270] Similarly, the fuzzy comprehensive score of the final layer A, i.e. the overall goal of evaluating the safety status of the reservoir dam, can be obtained by the following formula:

[0271]

[0272] In the embodiment of the present invention, when the adjustment coefficient μ=0.3 (Scheme 2), the primary evaluation quantity B in the connection layer B is obtained. 1 ~B 6 Fuzzy comprehensive score as follows:

[0273]

[0274]

[0275] In the embodiment of the present invention, when the adjustment coefficient μ=0.3 (Scheme 2), the final fuzzy comprehensive score F of layer A is obtained: A as follows:

[0276]

[0277] Similarly, when calculating the secondary evaluation parameters C within the initial layer C of the reservoir dam safety system ij for the connection layer B with the same equilibrium coefficient α, where α = 0.3 (Plan 1), and when the weights of all secondary evaluation parameters are constant weights, the primary evaluation parameters B 1 ~B 6 and the fuzzy comprehensive scores of the final layer A are shown in Table 8.

[0278] Furthermore, the score change rate is defined as follows:

[0279] Score change rate = (variable-weight fuzzy score - constant-weight fuzzy comprehensive score) / constant-weight fuzzy comprehensive score × 100% (8)

[0280] Based on Equation (8), the primary evaluation parameters B 1 ~B 6 and the fuzzy comprehensive score change rates of the final layer A under Plan 1 and Plan 2 are shown in Table 8.

[0281] Table 8 Calculation results of scores and score change rates

[0282]

[0283] Analyzing Table 8, it can be seen that substituting the variable-weight weights of the secondary evaluation parameters calculated under Plan 2 into the multi-level evaluation parameter fuzzy comprehensive operation, and finally combining with the selected grade parameter vector, the fuzzy comprehensive score of the target reservoir is 77.96 points. Therefore, according to the reservoir safety levels determined in Step 3 and the scoring intervals corresponding to each level, it can be determined that the current safety level of the target reservoir dam is Grade B, which is in a "relatively safe" state, indicating that the current operating state of the reservoir is good. Although there may be potential safety hazards inside, they do not affect the normal operation of the reservoir dam, and appropriate reinforcement measures need to be taken.

[0284] From the perspective of the fuzzy comprehensive scores of the primary evaluation parameters, in the case of constant weights, except for the primary evaluation parameter B 6 (metal structure safety) being in a "generally safe" state, the rest of the primary evaluation parameters are in a "relatively safe" state; for the two variable-weight cases (Plan 1 and Plan 2), except for the primary evaluation parameter B 6 (metal structure safety) being in a "generally safe" state, the primary evaluation parameter B 1(The quality of the dam project) is also classified as a "general safety" status, indicating that the status values of the secondary evaluation indicators have a certain impact on their weights. For the change rate of the overall score of the reservoir, the change rate of the score in the case of Plan 1 is only -0.81%, and the change rate of the score in the case of Plan 2 is -2.19%; for the change rate of the scores of each primary evaluation indicator, the absolute values of the change rates of the scores of each primary evaluation indicator calculated in the case of Plan 2 are all greater than those obtained in Plan 1. This is mainly because the improved method for determining the equilibrium coefficient takes into account the mutual influence between the constant weights and status values of the secondary evaluation indicators belonging to the same primary evaluation indicator. The above results show that the improved method for determining the equilibrium coefficient can effectively reduce the blindness of determining the equilibrium coefficient, enabling the potential safety hazards in the current status of the reservoir corresponding to the secondary evaluation indicators with relatively poor status values to be reflected in the overall safety scores of their respective primary evaluation indicators and the reservoir, and can provide a direction for determining the key points of subsequent danger removal and reinforcement projects.

[0285] From the application results of an improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing the dam safety status constructed in this paper in the safety evaluation of the example reservoir, the overall fuzzy comprehensive score of the target reservoir belongs to the "relatively safe" status, and the dam safety category is "Class II dam", which is consistent with the conclusion obtained by the expert group, indicating that this method has certain engineering applicability and reliability; the primary evaluation indicators "project quality" and "metal structure safety" both belong to the "general safety" status, and the conclusions obtained can provide a direction for determining the key points of construction for subsequent danger removal and reinforcement projects of this reservoir.

Claims

1. An improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing the safety status of dams, characterized in that: It includes the following steps: Step 1, construct a hierarchical structure model for evaluating the safety status of dams, including the final layer A, the connection layer B, and the initial layer C. The final layer A is the overall goal of evaluating the safety status of reservoir dams; The connection layer B contains multiple first-level evaluation factors that may affect the fuzzy comprehensive score of the final layer A. Assuming there are n first-level evaluation factors in the connection layer B, the i-th first-level evaluation factor is denoted as B i , where i = 1, 2, …, n; each first-level evaluation factor B i contains multiple second-level evaluation factors that may affect its fuzzy comprehensive score. Assuming there are m i second-level evaluation factors under B i , the j-th second-level evaluation factor is denoted as C ij , where j = 1, 2, …, m i , and all the second-level evaluation factors C ij together constitute the initial layer C; Step 2: Obtain the basic operation data of the target reservoir dam through on-site investigation, and respectively obtain the reservoir operation monitoring data, the results of previous dam safety appraisals, and the current operation safety status within the intervals related to each secondary evaluation quantity C in the initial layer C ij ; Step 3: Divide the safety level of the reservoir dam to be evaluated into five levels, A to E, and determine the scoring range corresponding to each safety level based on the conclusions obtained by the safety appraisal expert group after a detailed analysis of the basic operation data of the project and the results of previous dam safety appraisals. On this basis, determine the various secondary evaluation quantities C in the initial evaluation layer C that match the safety level and scoring range of the safety status of the target reservoir dam. ij The comment set of safety status and the corresponding scoring range; Step 4, obtain all secondary evaluation variables C in the initial layer C ij of the variable weight w ij ; The steps are as follows: Step 401: Based on the reservoir dam safety status evaluation hierarchical structure model established in step 1, invite reservoir management personnel, on-site technical survey personnel and members of the safety appraisal expert group to evaluate the various first-level evaluation quantities B in the connection layer B based on the data sorted and summarized in step 2 and combined with the nine-scale method. i And the various secondary evaluation quantities C in the initial layer C ij Carry out importance evaluation and construct the "connection layer B-final layer A" judgment matrix M B-A and the "initial layer C-connection layer B" judgment matrix Use the "square root method" or "sum method" to calculate the first-level evaluation quantity B in the connection layer B i The constant weight w i 0 and the secondary evaluation quantities C in the initial layer ij The constant weight w ij 0 , where i = 1, 2, ..., n, j = 1, 2, ..., m i , n is the first-level evaluation quantity B in the connection layer B i The total number of, m i Level 1 evaluation quantity B i Included secondary evaluation quantity C ij The number of Step 402: Prepare η questionnaires, distribute them to reservoir management personnel, on-site technical investigation personnel, and members of the safety appraisal expert group for this time, and invite them to score the current operating safety status of each secondary evaluation quantity C within the initial layer C ij . Take the arithmetic mean of the safety status scores given by η experts for the same secondary evaluation quantity C ij to obtain its state value x ij ; Step 403: Calculate the balance coefficient α of the j-th secondary evaluation quantity C under the i-th primary evaluation quantity B within the connection layer B i ij ij ;​​ Step 404: Calculate the $i$-th first-level evaluation quantity $B$ within the connection layer $B$ i and the $j$-th second-level evaluation quantity $C$ ij under it, with the variable weight $w$ ij ; Step 5, obtain the fuzzy membership degree matrix of each secondary evaluation quantity C within the initial layer C ij ; Step 6: First, obtain the first-level evaluation factors B within the connection layer B respectively through multi-level evaluation factor fuzzy comprehensive operation, and the fuzzy comprehensive evaluation matrix of the final layer A. Secondly, select the corresponding grade parameter vector V according to the safety grade and score range of the evaluation target reservoir dam safety status determined in Step 3. Finally, perform matrix multiplication operations on the n fuzzy comprehensive evaluation matrices i within the connection layer B and the fuzzy comprehensive evaluation matrix W of the final layer A with V respectively to obtain the fuzzy comprehensive scores A of the first-level evaluation vectors B within the connection layer B i and the fuzzy comprehensive score F of the final layer A, that is, the total target of evaluating the reservoir dam safety status . A .

2. The improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing the safety status of dams according to claim 1, characterized in that, Step 3 includes the following steps: Evaluate each secondary evaluation quantity C ij The set expression of the safety level comment set is φ, φ = {safe, relatively safe, generally safe, relatively dangerous, dangerous}, where the score interval corresponding to each comment matches the score interval of the five levels A to E for evaluating the safety status of the reservoir dam.

3. The improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing the safety status of dams according to claim 1, characterized in that, In step 401, the constant weight w of each first-level evaluation index B in the connection layer B i and the constant weight w of each second-level evaluation index C in the initial layer C i 0 are obtained specifically through the following steps: ij are obtained specifically through the following steps: ij 0 are obtained specifically through the following steps: Step 401a: Based on the hierarchical model for evaluating the safety status of reservoir dams constructed in step 1, the opinions of reservoir management personnel, on-site technical survey personnel and members of the reservoir dam safety appraisal expert group are comprehensively evaluated on the first-level evaluation parameters B in the connection layer B. i and the various secondary evaluation quantities C in the initial layer C ij Conduct importance assessment; Step 401b: According to the relative importance of the first-level and second-level evaluation metrics obtained in Step 401a, and in combination with the nine-scale method, pairwise comparisons are made between the first-level evaluation metrics B within the connection layer B under the same final layer A and between the second-level evaluation metrics C within the initial layer C under the same first-level evaluation metric B, to construct the "connection layer B - final layer A" judgment matrix M i and the "initial layer C - connection layer B" judgment matrix i According to the judgment matrix M ij and B-A the constant weight w of each first-level evaluation metric B within the connection layer B is obtained B-A and the constant weight w of each second-level evaluation metric C within the initial layer C i is obtained i 0 and ij the constant weight w of each second-level evaluation metric C within the initial layer C ij 0 .

4. The improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing the safety status of dams according to claim 1, characterized in that, In step 402, the state value x of each secondary evaluation parameter C within the initial layer C is obtained as follows: ij ij The specific steps are as follows:​ Step 402a: According to the hierarchical structure model for evaluating the safety status of the reservoir dam constructed in Step 1 and each secondary evaluation parameter C within the initial evaluation layer C determined in Step 3 ij Prepare η questionnaires based on the comment set for the safety status and the score intervals corresponding to each comment, and distribute them to reservoir management personnel, on-site technical investigation personnel, and members of the expert group for the current safety appraisal of the reservoir dam, and invite them to score the current operating safety status of each secondary evaluation parameter C within the initial evaluation layer C ij ; Step 402b: To ensure that the state value x ij of the secondary evaluation quantity C ij is close to its current safety status, in principle, it is required that decision-makers should first determine its risk level according to its current safety status and its influence on the fuzzy comprehensive score of the corresponding primary evaluation quantity B ij before scoring each secondary evaluation quantity C i . After the risk levels of all secondary evaluation quantities C i under the corresponding primary evaluation quantity B ij have been determined, the "mutual comparison and scoring" method is adopted to score the safety status of each secondary evaluation quantity C ij . During the scoring process, the mutual influence of the safety states among secondary evaluation quantities should be considered. The higher the score value, the better the safety status of the corresponding secondary evaluation quantity C ij , and the lower the threat degree to the corresponding primary evaluation quantity B i . The lower the score value, the worse the safety status of the secondary evaluation quantity C ij , and the higher the threat degree to the corresponding primary evaluation quantity B i . Step 402c: Take the arithmetic mean of the safety status scores of the η experts obtained in Step 402b for the same secondary evaluation quantity C ij to obtain the status value x i of the j-th secondary evaluation quantity C ij subordinate to the primary evaluation quantity B ij .

5. The improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing the safety status of dams according to claim 1, characterized in that, In step 403, calculate the balance coefficient α i of the j-th secondary evaluation quantity C ij under the i-th primary evaluation quantity B ij in the connection layer B, and the specific steps are as follows: Step 403a: Calculate each first-level evaluation quantity B within the connection layer B i of the status standard value x i 0 , and the formula is as follows: where: w ij 0 is the constant weight of the j-th secondary evaluation quantity C i under the first-level evaluation quantity B; x ij is the state value of the secondary evaluation quantity C ij ; n is the total number of first-level evaluation quantities in the connection layer B; m ij is the total number of secondary evaluation quantities i under the first-level evaluation quantity B i ; Step 403b: Calculate the equilibrium coefficient α to be assigned to the j-th secondary evaluation variable C under the i-th primary evaluation variable B within the connection layer B i The formula is as follows: ij for the equilibrium coefficient α ij of the j-th secondary evaluation variable C under the i-th primary evaluation variable B where: μ is the adjustment coefficient used to perform variable weight processing on the constant weight of each secondary evaluation index C within the initial layer C ij in the variable weight hierarchical model.

6. The improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing the safety status of dams according to claim 1, characterized in that, In step 404, the specific steps for obtaining the variable weight of each secondary evaluation quantity C in the initial layer C are as follows: ij ​ Suppose the \(i\)-th first-level evaluation quantity in the connection layer B is denoted as \(B_{i}\). i \(B_{i}\) i contains \(m\) i second-level evaluation quantities. Denote the \(j\)-th second-level evaluation quantity under \(B_{i}\) as \(C_{ij}\). i Then the calculation formula for the variable weight \(w_{ij}\) of the second-level evaluation quantity \(C_{ij}\) is as follows: ij \(C_{ij}\) ij The variable weight \(w_{ij}\) ij is as follows; where: w ij 0 is the j-th secondary evaluation quantity C i under the first-level evaluation quantity B ij with its constant weight; x ij is the state value of the secondary evaluation quantity C ij ; α ij is the balance coefficient to be assigned to the secondary evaluation quantity C ij ; when α ij = 1, it represents the constant weight mode; i = 1, 2, …, n, j = 1, 2, …, m i , n is the number of the first-level evaluation quantities B i within the connection layer B i , m i is the total number of the secondary evaluation quantities C ij under the first-level evaluation quantity B 7. The improved variable weight AHP-fuzzy comprehensive evaluation method for analyzing the safety status of dams according to claim 1, characterized in that, Step 6 includes the following steps: Step 601: Fuzzy comprehensive operation of secondary evaluation variables The i-th first-level evaluation quantity B in the connection layer B i of the fuzzy comprehensive evaluation matrix The calculation formula is as follows: Where: W i is the various secondary evaluation quantities C i subordinate to the primary evaluation quantity B ij and the variable weight weight matrix relative to B i ; R i is the membership matrix jointly composed of the fuzzy membership matrices of the secondary evaluation metrics , and when expanded, it is as follows: where: j = 1, 2, …, m i , m i is the number of secondary evaluation variables C i under the primary evaluation variable B ij ; ξ is the number of comments in the comment set of the safety status of each secondary evaluation variable C ij in the initial evaluation layer C Step 602: Fuzzy comprehensive operation of primary evaluation variables The fuzzy comprehensive evaluation matrix W of the final layer A A The calculation formula is as follows: W A = W · R Where: W is the variable weight matrix of the connection layer B relative to the final layer A; R is all the first-level evaluation factors B within the connection layer B obtained from step 601 i of the fuzzy comprehensive evaluation matrix collectively form a matrix, where i = 1, 2,..., n; where: n is the total number of first-level evaluation factors B in the connection layer B i ; Step 603: During the evaluation process of the safety status of reservoir dams, divide the safety status level of the reservoir dam to be evaluated into five levels from A to E: Level A, the comprehensive safety status evaluation is "safe", and the scoring range is [σ 4 , 100]; Level B, the comprehensive safety status evaluation is "relatively safe", scoring range: [σ 3 , σ 4 ); Level C, the comprehensive evaluation of the current safety status is "general safety", scoring range: [σ 2 , σ 3 ); Level D, the comprehensive evaluation of the current safety situation is "relatively dangerous", scoring range: [σ 1 , σ 2 ); Level E, the comprehensive safety status evaluation is "dangerous", scoring range: [0, σ 1 ) Take the corresponding level parameter vector: The first-level evaluation factors B within the connection layer B can be calculated according to the following formula i for the fuzzy comprehensive score: Similarly, the fuzzy comprehensive score of the final layer A, that is, the overall goal of evaluating the safety status of the reservoir dam, can be obtained according to the following formula:

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