An underwater pile foundation damage condition evaluation method based on a game theory-based GRA-KL-TOPSIS model

Abstract

The present application relates to the technical field of bridge pile foundation evaluation, and more particularly to an underwater pile foundation damage condition evaluation method based on a GRA-KL-TOPSIS model of game theory, and the specific steps are as follows: Step 1, determining the subjective weight by G1 method, including constructing a bridge underwater pile foundation damage state evaluation index system and determining damage grades and index classification standards; Step 2, calculating the objective weight by an improved CRITIC method, including index data processing and establishing a function based on blind number theory; Step 3, determining the comprehensive weight by game theory; Step 4, coupling GRA, KL and TOPSIS to establish a GRA-KL-TOPSIS comprehensive evaluation model, improving the traditional TOPSIS method and comprehensively determining the damage state ranking. The present application introduces game theory, G1 method and improved CRITIC method to consider the damage degree index layer 6 index weight vectors. By applying the method, the evaluator can quickly evaluate the pile foundation damage degree and determine the priority sequence of the pile foundation damage degree.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge pile foundation evaluation, and particularly relates to an underwater pile foundation damage condition evaluation method based on a GRA-KL-TOPSIS model of game theory. BACKGROUND

[0002] In order to more quickly and accurately evaluate the damage degree of the bridge pile foundation, the evaluation model is not only aimed at determining the damage condition grade of the bridge pile foundation, but also at formulating a corresponding pile foundation maintenance and reinforcement scheme in a timely manner according to the damage condition, so as to realize sustainable development.

[0003] At present, although some specifications at home and abroad have studied the evaluation of the damage degree of the pile foundation, a unified standard has not yet been formed, and there is a lack of a special evaluation method. SUMMARY

[0004] The present application aims to solve the problems in the prior art and provides an underwater pile foundation damage condition evaluation method based on a GRA-KL-TOPSIS model of game theory, which can avoid the problem of too large subjective weight proportion in the index of the traditional method, and realize the evaluation and sorting of the damage condition of the bridge pile foundation.

[0005] In order to achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0006] The underwater pile foundation damage condition evaluation method based on the GRA-KL-TOPSIS model of game theory specifically comprises the following steps:

[0007] Step 1, determining the subjective weight by the G1 method, comprising constructing an evaluation index system of the damage state of the underwater pile foundation of the bridge and determining the damage grade and index grading standard;

[0008] Step 2, calculating the objective weight by the improved CRITIC method, comprising index data processing and establishing a function based on the blind number theory;

[0009] Step 3, determining the comprehensive weight by game theory;

[0010] Step 4, coupling the GRA, KL and TOPSIS to establish a GRA-KL-TOPSIS comprehensive evaluation model, improving the traditional TOPSIS method, and comprehensively determining the damage state sorting.

[0011] Preferably, in step 1, the specific steps are as follows:

[0012] Step 1.1: Determine the relative importance of each pair of indicators. Suppose n evaluation indicators are selected and discussed by experts. After comparing and selecting the indicators pair by pair, the most important indicator x1 is determined and the corresponding weight is recorded as w1. Then, continue to compare and select the remaining n-1 indicators. Through continuous comparison and selection, we finally get a set of indicator sequences ranked by relative importance (X1, X2, ..., X n ), the corresponding weight set is expressed as (w1,w2,…,w n );

[0013] Step 1.2: Given the relative importance ratio, the relative importance ratio of the indicator r j The relative importance of the indicators is the key to the weighting of the G1 method indicators. It is determined according to the value standard and after discussion by experts. The relative importance ratio r j The calculation formula is:

[0014]

[0015] Where r j is the relative importance ratio of the jth indicator, w j is the corresponding weight of the jth evaluation index, w j-1 is the corresponding weight of the j-1th evaluation index.

[0016] Preferably, in step 2, the specific steps are as follows:

[0017] Step 2.1, the standard deviation of the indicator δ=(δ1,δ2,…,δ n ) is calculated using formula (2):

[0018]

[0019] Where a′ ij The object of evaluation after standardization is U i Corresponding indicator X j The value of θ j is the index X among the m evaluation objects after standardization j The mean of δ j is the indicator X j The standard deviation of , m is the number of indicators;

[0020] Step 2.2, the correlation coefficient matrix of the indicators R = (r ij ) m×n Calculate using formula (3):

[0021]

[0022] Where: a′ i 、a' j is the standardized value of the i-th and j-th indicators of the evaluation object; θi , θ j is the mean value of the standardized value of the i, jth evaluation index; r ij is the correlation coefficient between the index X i and X j ;

[0023] Step 2.3, the objective weight w = (w1, w2, …, w n ) is calculated by formula (4):

[0024]

[0025] w 客j is the objective weight of the jth evaluation index;

[0026] Step 2.4, normalize w by formula (5) to obtain W 客 = (W1, W2, …, W n );

[0027]

[0028] W j is the normalized objective weight of the jth index.

[0029] Preferably, in step 3, the specific steps are as follows:

[0030] Step 3.1, all weight vectors are combined into a set of strategies W = (w1, w2, …, w n ), and any linear combination of the N weight vectors is performed, that is, Based on the optimal strategy, the deviation minimization processing is performed on w and w k ( is the inverse matrix of w k ), that is:

[0031]

[0032] c k is the weight vector coefficient of the kth index, is the inverse of the kth index weight vector, is the inverse of the jth index weight vector;

[0033] Step 3.2, according to the differential properties of the matrix, the optimal first-order derivative condition satisfies the following formula:

[0034]

[0035] c1, c2, …, c N is the weight vector coefficient, w1, w2, …, w n is the weight vector matrix of the 1st, 2nd, … n th, is the weight vector inversion matrix of the first, second, …, nth weight vector;

[0036] Step 3.3, the weight vector coefficients c1, c2, …, cn are inverted, and the weight vector coefficients c1, c2, …, cn of the first, second, …, nth weight vector are obtained. N After normalization processing, the final optimization weight vector coefficients are determined, and the index comprehensive weight is:

[0037]

[0038] is the weight vector coefficient of the kth index after normalization, is the inversion of the weight vector of the kth index, w * is the index comprehensive weight after normalization;

[0039] Preferably, in step 4, the specific steps are as follows:

[0040] Step 4.1, calculate the weighted decision matrix, assuming that there are i evaluation objects and j evaluation indexes, according to the actual evaluation object, an initial evaluation matrix X is established, in order to eliminate the dimensional difference between indexes, all index data are normalized according to formula (9) to obtain an initial standard decision matrix Y, the initial standard decision matrix Y is multiplied by the index weight ω to calculate the weighted decision matrix Z:

[0041]

[0042] Z = (z ij ) m×n = y ij · w * j (10)

[0043] Z is the weighted decision matrix, x ij is the value of the jth evaluation index of the ith evaluation object in the evaluation matrix, y ij is the value of the jth evaluation index of the ith evaluation object in the initial standard decision matrix, w * j is the value of the jth evaluation index, z ij is the value of the jth evaluation index of the ith evaluation object in the weighted decision matrix;

[0044] Step 4.2, determine the positive and negative ideal solutions, according to the calculation results of the weighted decision matrix Z, combined with the index attribute characteristics (cost type or benefit type), the optimal value and the worst value of each index are determined as the positive ideal solution set Z + and the negative ideal solution set Z - :

[0045]

[0046] the value of the jth evaluation index in the positive ideal solution set, the value of the jth evaluation index in the negative ideal solution set, z ij the value of the jth evaluation index of the ith evaluation object in the weighted decision matrix,

[0047] Step 4.3, calculate the KL distance, according to formula (12) and formula (13), calculate the KL distance of each evaluation object and the positive and negative ideal solutions and

[0048]

[0049] the value of the jth evaluation index in the positive ideal solution set, the value of the jth evaluation index in the negative ideal solution set, z ij the value of the jth evaluation index of the ith evaluation object in the weighted decision matrix, the KL distance of the positive ideal solution, the KL distance of the negative ideal solution;

[0050] Step 4.4, construct the correlation matrix R of the evaluation object, based on the grey correlation principle, calculate the correlation coefficient of the evaluation object and the positive and negative ideal solutions, and construct the correlation matrix

[0051]

[0052] In the formula, p is the grey correlation resolution, the value range is 0-1, generally take 0.5; the value of the jth evaluation index in the positive ideal solution set, the value of the jth evaluation index in the negative ideal solution set, z ij the value of the jth evaluation index of the ith evaluation object in the weighted decision matrix, the correlation coefficient of the positive ideal solution, the correlation coefficient of the negative ideal solution;

[0053] Step 4.5, calculate the grey correlation degree, the grey correlation degree calculation formula is:

[0054]

[0055] the correlation coefficient of the positive ideal solution, the correlation coefficient of the negative ideal solution, r i * the grey correlation degree;

[0056] Step 4.6, calculate the grey correlation closeness degree, normalize the KL distance and the grey correlation degree, and the specific calculation formula is:

[0057]

[0058]

[0059] In the formula, is the normalized KL distance of the positive ideal solution, is the normalized KL distance of the negative ideal solution; is the normalized grey correlation degree of the positive ideal solution, is the normalized grey correlation degree of the negative ideal solution, is the KL distance of the positive ideal solution, is the KL distance of the negative ideal solution, r i + is the correlation coefficient of the positive ideal solution, r i - is the correlation coefficient of the negative ideal solution;

[0060] Step 4.7, calculate the closeness degree S of each object to be evaluated to the positive and negative ideal solutions i

[0061]

[0062] In the formula, respectively represent the closeness and distance of the ith object to be evaluated to the ideal solution; μ is a decision maker preference coefficient, generally taken as 0.5; is the normalized KL distance of the positive ideal solution, is the normalized KL distance of the negative ideal solution; is the normalized grey correlation degree of the positive ideal solution, is the normalized grey correlation degree of the negative ideal solution;

[0063] Step 4.8, according to the closeness calculation result, calculate the grey correlation relative closeness C i

[0064]

[0065] Step 4.9, finally, according to the size of the grey correlation relative closeness C i , determine the ranking of the objects to be evaluated.

[0066] By adopting the above technical scheme: the game theory, G1 method and improved CRITIC method are introduced to consider the weight vector of the 6 indexes of the damage degree index layer. By applying the method, the evaluator can quickly evaluate the damage degree of the pile foundation and determine the priority sequence of the damage degree of the pile foundation.​​

[0067] Compared with the prior art, the present application has the following beneficial effects:

[0068] 1、The present application utilizes the characteristics of the grey correlation method (GRA) in the aspects of strong adaptability in the processing of small amount of data, poor information and grey information, and the ability to map and evaluate the situation changes of different subsystems; and the Kullback-Leibler distance (KL) is used to replace the Euclidean distance in the traditional TOPSIS method, so as to solve the distance approximation problem.

[0069] 2、The model provided by the present application can quickly evaluate the damage degree of the pile foundation and determine the priority of the damage degree of the pile foundation for the evaluator, and provide a new idea for the evaluator to quickly evaluate. BRIEF DESCRIPTION OF DRAWINGS

[0070] Figure 1 The flowchart of the present application. DETAILED DESCRIPTION

[0071] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings, so that the advantages and features of the present application can be better understood by those skilled in the art, and the protection scope of the present application can be more clearly defined. The described embodiments of the present application are only a part of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0072] Referring to Figure 1 , a method for evaluating the damage condition of underwater pile foundation based on the GRA-KL-TOPSIS model of game theory, the specific steps are as follows:

[0073] Step 1, determining the subjective weight by G1 method, including constructing the evaluation index system of the damage state of the underwater pile foundation of the bridge and determining the damage grade and index grading standard;

[0074] Step 2, calculating the objective weight by the improved CRITIC method, including index data processing and the suggested function based on the blind number theory;

[0075] Step 3, determining the comprehensive weight by game theory;

[0076] Step 4, coupling GRA, KL and TOPSIS to establish the GRA-KL-TOPSIS comprehensive evaluation model, improving the traditional TOPSIS method, and comprehensively determining the damage state ranking.

[0077] Specifically, in step 1, the specific steps are as follows:

[0078] Step 1.1: Determine the relative importance of each pair of indicators. Suppose n evaluation indicators are selected and discussed by experts. After comparing and selecting the indicators pair by pair, the most important indicator x1 is determined and the corresponding weight is recorded as w1. Then, continue to compare and select the remaining n-1 indicators. Through continuous comparison and selection, we finally get a set of indicator sequences ranked by relative importance (X1, X2, ..., X n ), the corresponding weight set is expressed as (w1,w2,…,w n );

[0079] Step 1.2: Given the relative importance ratio, the relative importance ratio of the indicator r j The relative importance of the indicators is the key to the weighting of the G1 method indicators. It is determined according to the value standard and after discussion by experts. The relative importance ratio r j The calculation formula is:

[0080]

[0081] Where r j is the relative importance ratio of the jth indicator, w j is the corresponding weight of the jth evaluation index, w j-1 is the corresponding weight of the j-1th evaluation index.

[0082] Specifically, in step 2, the specific steps are as follows:

[0083] Step 2.1, the standard deviation of the indicator δ=(δ1,δ2,…,δ n ) is calculated using formula (2):

[0084]

[0085] Where a′ ij The object of evaluation after standardization is U i Corresponding indicator X j The value of θ j is the index X among the m evaluation objects after standardization j The mean of δ j is the indicator X j The standard deviation of m is the number of indicators;

[0086] Step 2.2, the correlation coefficient matrix of the indicators R = (r ij ) m×n Calculate using formula (3):

[0087]

[0088] Where: a′ i 、a' j is the standardized value of the i-th and j-th indicators of the evaluation object; θi ,θ j is the mean of the standardized values ​​of the i-th and j-th indicators of the evaluation object; r ij is the indicator X i With X j The correlation coefficient between

[0089] Step 2.3, objective weight w=(w1,w2,…,w n ) is calculated using formula (4):

[0090]

[0091] w 客j is the objective weight of the jth evaluation index;

[0092] Step 2.4: Normalize w by formula (5) to get W 客 =(W1,W2,…,W n );

[0093]

[0094] W j is the objective weight of the j-th indicator after normalization.

[0095] Specifically, in step 3, the specific steps are as follows:

[0096] Step 3.1: All weight vectors are combined into a set of strategy sets W = (w1, w2, ..., w n ), make any linear combination of these N weight vectors, and we have Based on the optimal strategy, w and w k ( w k The inverted matrix of is used to minimize the deviation, that is:

[0097]

[0098] c k is the weight vector coefficient of the kth indicator, is the inversion of the k-th indicator weight vector, is the inversion of the j-th indicator weight vector;

[0099] Step 3.2: According to the differential properties of the matrix, the optimal first-order derivative condition satisfies the following formula:

[0100]

[0101] c1,c2,…,c N are weight vector coefficients, w1,w2,…,w n is the weight vector matrix of the 1st, 2nd, ...nth, is the weight vector inversion matrix of the first, second, …, n-th weight vector;

[0102] Step 3.3, the weight vector coefficients c1, c2, …, c N is normalized to determine the final optimization weight vector coefficient, and the index comprehensive weight is:

[0103]

[0104] is the weight vector coefficient of the k-th index after normalization, is the inversion of the k-th index weight vector, w * is the normalized index comprehensive weight.

[0105] Specifically, in step 4, the specific steps are as follows:

[0106] Step 4.1, calculate the weighted decision matrix, assuming there are i evaluation objects and j evaluation indexes, according to the actual evaluation object, establish the initial evaluation matrix X, in order to eliminate the dimensional difference between indexes, according to formula (9), all index data are normalized to obtain the initial standard decision matrix Y, multiply the initial standard decision matrix Y by the index weight ω to calculate the weighted decision matrix Z:

[0107]

[0108] Z = (z ij ) m×n = y ij · w * j (10)

[0109] Z is the weighted decision matrix, x ij is the value of the j-th evaluation index of the i-th evaluation object in the evaluation matrix, y ij is the value of the j-th evaluation index of the i-th evaluation object in the initial standard decision matrix, w * j is the value of the j-th evaluation index, z ij is the value of the j-th evaluation index of the i-th evaluation object in the weighted decision matrix;

[0110] Step 4.2, determine the positive and negative ideal solutions, according to the calculation results of the weighted decision matrix Z, combined with the index attribute characteristics (cost type or benefit type), the optimal value and the worst value of each index are determined as the positive ideal solution set Z + and the negative ideal solution set Z - :

[0111]

[0112] the value of the jth evaluation index in the positive ideal solution set, the value of the jth evaluation index in the negative ideal solution set, z ij the value of the jth evaluation index of the ith evaluation object in the weighted decision matrix,

[0113] Step 4.3, calculate the KL distance, according to formula (12) and formula (13), calculate the KL distance of each evaluation object and the positive and negative ideal solutions and

[0114]

[0115] the value of the jth evaluation index in the positive ideal solution set, the value of the jth evaluation index in the negative ideal solution set, z ij the value of the jth evaluation index of the ith evaluation object in the weighted decision matrix, the KL distance of the positive ideal solution, the KL distance of the negative ideal solution;

[0116] Step 4.4, construct the correlation matrix R of the evaluation object, based on the grey correlation principle, calculate the correlation coefficient of the evaluation object and the positive and negative ideal solutions, and construct the correlation matrix

[0117]

[0118] In the formula, p is the grey correlation resolution, the value range is 0-1, generally take 0.5; the value of the jth evaluation index in the positive ideal solution set, the value of the jth evaluation index in the negative ideal solution set, z ij the value of the jth evaluation index of the ith evaluation object in the weighted decision matrix, the correlation coefficient of the positive ideal solution, the correlation coefficient of the negative ideal solution;

[0119] Step 4.5, calculate the grey correlation degree, the grey correlation degree calculation formula is:

[0120]

[0121] the correlation coefficient of the positive ideal solution, the correlation coefficient of the negative ideal solution, r i * the grey correlation degree;

[0122] Step 4.6, calculate the grey correlation closeness degree, normalize the KL distance and the grey correlation degree, and the specific calculation formula is:

[0123]

[0124] In the formula, is the normalized KL distance of the positive ideal solution, is the normalized KL distance of the negative ideal solution; is the normalized grey correlation degree of the positive ideal solution, is the normalized grey correlation degree of the negative ideal solution, is the KL distance of the positive ideal solution, is the KL distance of the negative ideal solution, r i + is the correlation coefficient of the positive ideal solution, r i - is the correlation coefficient of the negative ideal solution;

[0125] Step 4.7, calculate the closeness degree S of each object to be evaluated to the positive and negative ideal solutions i :

[0126]

[0127] In the formula, respectively represent the closeness and distance of the ith object to be evaluated to the ideal solution; μ is the decision maker's preference coefficient, generally taken as 0.5; is the normalized KL distance of the positive ideal solution, is the normalized KL distance of the negative ideal solution; is the normalized grey correlation degree of the positive ideal solution, is the normalized grey correlation degree of the negative ideal solution;

[0128] Step 4.8, according to the closeness calculation result, calculate the grey correlation relative closeness C i :

[0129]

[0130] Step 4.9, finally, according to the size of the grey correlation relative closeness C i , determine the ranking of the objects to be evaluated.

[0131] Embodiment:

[0132] Taking the bridge L2-1# pile (K1), L2-2# pile (K2), R2-1# pile (K3), and R2-2# pile (K4) as the research background, the GRA-KL-TOPSIS model based on game theory is used to comprehensively analyze the damage state of the pile foundation through relevant calculations.

[0133] According to the results of index data processing, based on the principle of interpolation, the midpoint value of the grading standard is used as the interpolation point, that is: b1 = 30, b2 = 65, b3 = 75, b4 = 85, b5 = 95, and the midpoint value b i Multiply it by the interval distribution probability to calculate the final score of the indicator. 11 For example, indicator X 11 The probabilities of falling into the five level intervals are 0, 0, 0.0815, 0.2089, and 0.0428, respectively. Then the index X 11 The comprehensive score is: X 11 =0×30+0×65+0.3711×75+0.4699×85+0.159×95=82.879. Following the same steps, determine the index scores of L2-1# pile (K1), L2-2# pile (K2), R2-1# pile (K3), and R2-2# pile (K4). The specific calculation results are shown in Table 1.

[0134] Table 1 Assignment of various pile foundation indicators

[0135]

[0136]

[0137] The subjective weights of the indicators determined by the G1 method are (0.2263, 0.1886, 0.1804, 0.1388, 0.1393, 0.1266). The objective weights of the indicators calculated by the improved CRITIC method are (0.1209, 0.2053, 0.2104, 0.1814, 0.1262, 0.1558). Finally, the comprehensive weights of the indicators are (0.1589, 0.2024, 0.1990, 0.1641, 0.1317, 0.1439).

[0138] According to the calculation principle of the GRA-KL-TOPSIS model, the index data of different coal mines are standardized according to formula (9) to obtain the initial standard decision matrix Y; according to formula (10), the weighted decision matrix is ​​calculated; according to formula (11), combined with the weighted decision matrix Z, the calculation results are calculated to determine the ideal solution Z of the index. + and negative ideal solution Z - The specific calculation results are shown in Table 2.

[0139] Table 2 Weighted standardized data and calculation results of positive and negative ideal solutions

[0140]

[0141] According to formula (12) and formula (13), the relative entropy KL distance of different coal mine indicators is calculated; according to formula (14) and formula (15), the grey correlation coefficient between different indicators and positive and negative ideal solutions is calculated; according to formula (16), formula (17) and formula (18), the KL distance and grey correlation coefficient are normalized, and according to formula (19) and formula (20), the grey correlation relative closeness is calculated. The specific calculation results are shown in Table 3.

[0142] Table 3 GRA-KL-TOPSIS calculation results

[0143]

[0144] In order to further verify the accuracy and reliability of the evaluation results based on the GRA-KL-TOPSIS evaluation model and compare the evaluation results of this application with the actual results, the specific comparison results are shown in Table 4.

[0145] Table 4 Comparison of evaluation results

[0146]

[0147] In summary, the present invention can avoid the problem of excessive subjective weight in indicators in traditional methods and realize the evaluation and ranking of bridge pile foundation damage conditions.

[0148] The descriptions and practices disclosed in this invention are easy to understand and comprehend for those skilled in the art, and modifications and refinements may be made without departing from the principles of the invention. Therefore, modifications and improvements made without departing from the spirit of the invention should also be considered within the scope of protection of this invention.

Claims

1. A method for evaluating underwater pile foundation damage based on the GRA-KL-TOPSIS model based on game theory, characterized in that: The specific steps are as follows: Step 1: Determine the subjective weight using the G1 method, including constructing an evaluation index system for the damage status of underwater bridge pile foundations and determining the damage level and index grading standards; Step 2: Improve the CRITIC method to calculate the objective weight, including indicator data processing and establishing a function based on blind number theory; Step 3: Determine the comprehensive weight using game theory; Step 4: GRA, KL, and TOPSIS are coupled to establish a GRA-KL-TOPSIS comprehensive evaluation model, which improves the traditional TOPSIS method and comprehensively determines the damage status ranking; In step 1, the specific steps are as follows: Step 1.1: Determine the relative importance of each pair of indicators. Suppose n evaluation indicators are selected and discussed by experts. After comparing and selecting the indicators pair by pair, the most important indicator x1 is determined and the corresponding weight is recorded as w1. Then, continue to compare and select the remaining n-1 indicators. Through continuous comparison and selection, we finally get a set of indicator sequences ranked by relative importance (X1, X2, ..., X n ), the corresponding weight set is expressed as (w1,w2,…,w n ); Step 1.2: Given the relative importance ratio, the relative importance ratio of the indicator r j Reflecting the relative importance of indicators is the key to the weighting of indicators in the G1 method. It is determined according to the value selection criteria and after discussion by experts; Relative importance ratio r j The calculation formula is: Where r j is the relative importance ratio of the jth evaluation index, w j is the corresponding weight of the jth evaluation index, w j-1 is the corresponding weight of the j-1th evaluation index; In step 2, the specific steps are as follows: Step 2.1, the standard deviation of the indicator δ=(δ1,δ2,…,δ n ) is calculated using formula (2): Where a′ ij The object of evaluation after standardization is U i Corresponding indicator X j The value of θ j is the index X among the m evaluation objects after standardization j The mean of δ j is the indicator X j The standard deviation of m is the number of indicators; Step 2.2, the correlation coefficient matrix of the indicators R = (r ij ) m×n Calculate using formula (3): Where: a′ i 、a' j is the standardized value of the i-th and j-th indicators of the evaluation object; θ i ,θ j is the mean of the standardized values ​​of the i-th and j-th indicators of the evaluation object; r ij is the indicator X i With X j The correlation coefficient between Step 2.3, objective weight w 客 =(w1,w2,…,w n ) is calculated using formula (4): w 客j is the objective weight of the jth evaluation index; Step 2.4: Normalize w by formula (5) to get W 客 =(W1,W2,…,W n ); W j is the objective weight of the jth indicator after normalization; In step 3, the specific steps are as follows: Step 3.1: All weight vectors are combined into a set of strategy sets W = (w1, w2, ..., w n ), make any linear combination of these N weight vectors, and we have Based on the optimal strategy, w and w k Perform deviation minimization processing, that is: c k is the weight vector coefficient of the kth indicator, is the inversion of the k-th indicator weight vector, is the inversion of the j-th indicator weight vector; Step 3.2: According to the differential properties of the matrix, the optimal first-order derivative condition satisfies the following formula: c1,c2,…,c N are weight vector coefficients, w1,w2,…,w n is the weight vector matrix of the 1st, 2nd, ...nth, Invert the matrix of the 1st, 2nd, ...nth weight vector; Step 3.3, weight vector coefficients c1, c2, ..., c N After normalization, the final optimization weight vector coefficient is determined, and the comprehensive weight of the indicators is: is the weight vector coefficient of the kth indicator after normalization, is the inversion of the kth indicator weight vector, w * is the comprehensive weight of the normalized indicators; In step 4, the specific steps are as follows: Step 4.1: Calculate the weighted decision matrix. Suppose there are i evaluation objects and j evaluation indicators. According to the actual situation of the object to be evaluated, establish the initial evaluation matrix X. To eliminate the dimensional differences between the indicators, normalize all indicator data according to formula (9) to obtain the initial standard decision matrix Y. Multiply the initial standard decision matrix Y by the indicator weight ω to calculate the weighted decision matrix Z: Z=(z ij ) m×n =y ij ·In * j (10) Z is the weighted decision matrix, x ij is the value of the jth evaluation index of the i-th evaluation object in the evaluation matrix, y ij is the value of the jth evaluation index of the i-th evaluation object in the initial standard decision matrix, w * j is the value of the jth comprehensive evaluation index, z ij Take the value of the jth evaluation index of the i-th evaluation object in the weighted decision matrix; Step 4.2: Determine the positive and negative ideal solutions. Based on the calculation results of the weighted decision matrix Z and the attribute characteristics of the indicators, the optimal and worst values ​​of each indicator are determined as the positive ideal solution set Z. + , negative ideal solution set Z - : is the value of the jth evaluation index in the positive ideal solution set, The value of the jth evaluation index in the negative ideal solution set, z ij Take the value of the jth evaluation index of the i-th evaluation object in the weighted decision matrix; Step 4.3: Calculate the KL distance. According to formula (12) and formula (13), calculate the KL distance between each object to be evaluated and the positive and negative ideal solutions. and is the value of the jth evaluation index in the positive ideal solution set, The value of the jth evaluation index in the negative ideal solution set, z ij is the value of the jth evaluation index of the i-th evaluation object in the weighted decision matrix, is the KL distance of the positive ideal solution, is the KL distance of the negative ideal solution; Step 4.4: Construct the correlation matrix R of the object to be evaluated. Based on the grey correlation principle, calculate the correlation coefficients between the object to be evaluated and the positive and negative ideal solutions, and construct the correlation matrix Where ρ is the grey relational resolution, ranging from 0 to 1, and is taken as 0.5; is the value of the jth evaluation index in the positive ideal solution set, The value of the jth evaluation index in the negative ideal solution set, z ij is the value of the jth evaluation index of the i-th evaluation object in the weighted decision matrix, is the correlation coefficient of the positive ideal solution, is the correlation coefficient of the negative ideal solution; Step 4.5: Calculate the grey relational degree. The grey relational degree calculation formula is: is the correlation coefficient of the positive ideal solution, is the correlation coefficient of the negative ideal solution, is the grey relational degree; Step 4.6: Calculate the grey relational closeness and normalize the KL distance and grey relational degree. The specific calculation formula is: Where, is the normalized KL distance of the positive ideal solution, is the normalized KL distance of the negative ideal solution; is the normalized grey relational degree of the positive ideal solution, The normalized grey relational degree of the negative ideal solution is is the KL distance of the positive ideal solution, is the KL distance of the negative ideal solution, is the correlation coefficient of the positive ideal solution, is the correlation coefficient of the negative ideal solution; Step 4.7: Calculate the degree of closeness S between each object to be evaluated and the positive and negative ideal solutions. i : Where, They represent the closeness and distance between the i-th object to be evaluated and the ideal solution respectively; μ is the decision maker's preference coefficient, which is 0.5; is the normalized KL distance of the positive ideal solution, is the normalized KL distance of the negative ideal solution; is the normalized grey relational degree of the positive ideal solution, Normalized grey relational degree of negative ideal solution; Step 4.8: Calculate the grey relational relative closeness C according to the result of closeness calculation. i : Step 4.9, finally, according to the grey relational relative closeness C i Size, determine the quality ranking of the objects to be evaluated.

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