Underwater pile foundation damage condition evaluation method of GRA-KL-TOPSIS model based on game theory

Abstract

The invention relates to the technical field of bridge pile foundation evaluation, in particular to an underwater pile foundation damage condition evaluation method based on a GRA-KL-TOPSIS model of the game theory, and the method comprises the following specific steps: 1, determining a subjective weight through a G1 method, including constructing a bridge underwater pile foundation damage state evaluation index system and determining a damage grade and an index grading standard; step 2, improving a CRITIC method to calculate objective weights, including index data processing and function establishment based on a blind number theory; 3, a comprehensive weight is determined through the game theory; and step 4, coupling the GRA, the KL and the TOPSIS, establishing a GRA-KL-TOPSIS comprehensive evaluation model, improving a traditional TOPSIS method, and comprehensively determining a damage state sequence. According to the method, the game theory and the G1 method are introduced, and the CRITIC method is improved to consider six index weight vectors of a damage degree index layer. By means of the method, the pile foundation damage degree can be rapidly evaluated for an evaluator, and the pile foundation damage degree priority sequence can be determined.

Description

Technical Field

[0001] The invention relates to the technical field of bridge pile foundation evaluation, and in particular to an underwater pile foundation damage status evaluation method based on a GRA-KL-TOPSIS model of game theory. Background Art

[0003] In order to evaluate the damage degree of bridge pile foundation more quickly and accurately, the evaluation model is constructed not only to determine the damage condition level of bridge pile foundation, but also to formulate corresponding pile foundation maintenance and reinforcement plans in time according to the damage condition to achieve sustainable development.

[0004] At present, although there are some specifications at home and abroad that have studied the evaluation of pile foundation damage, there is no unified standard and a lack of specialized evaluation methods. Summary of the invention

[0005] The purpose of the present invention is to solve the shortcomings existing in the prior art and propose a method for evaluating the damage condition of underwater pile foundations based on the GRA-KL-TOPSIS model of game theory. This method can avoid the problem of excessive subjective weight in indicators in traditional methods and realize the evaluation and ranking of the damage condition of bridge pile foundations.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for evaluating the damage condition of underwater pile foundation based on the GRA-KL-TOPSIS model of game theory is proposed. The specific steps are as follows:

[0008] Step 1: G1 method is used to determine the subjective weight, including constructing an evaluation index system for the damage state of underwater pile foundations of bridges and determining the damage level and index classification standard;

[0009] Step 2: Improve the CRITIC method to calculate objective weights, including indicator data processing and establishing functions based on blind number theory;

[0010] Step 3: Determine the comprehensive weight using game theory;

[0011] Step 4: Couple GRA, KL and TOPSIS to establish a GRA-KL-TOPSIS comprehensive evaluation model, improve the traditional TOPSIS method, and comprehensively determine the damage status ranking.

[0012] Preferably, in step 1, the specific steps are as follows:

[0013] Step 1.1: Determine the relative importance of each pair of indicators. Suppose n evaluation indicators are selected, and experts discuss and compare and select the indicators pair by pair to determine the most important indicator x. 1 , the corresponding weight is recorded as w 1, and then continue to compare and select from the remaining n-1 indicators. Through continuous comparison and selection, we finally get a set of indicator sequences sorted by relative importance (X 1 ,X 2 ,…,X n ), the corresponding weight set is expressed as (w 1 ,w 2 ,…,w n );

[0014] Step 1.2: Given the relative importance ratio, the relative importance ratio of the indicator r j It reflects the relative importance of the index and is the key to the weighting of the G1 method index. It is given according to the value selection criteria and after discussion by experts; the relative importance ratio r j The calculation formula is:

[0015]

[0016] 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.

[0017] Preferably, in step 2, the specific steps are as follows:

[0018] Step 2.1, the standard deviation of the indicator δ = (δ 1 ,δ 2 ,…,δ n ) is calculated using formula (2):

[0019]

[0020] In the formula, a′ ij The standardized evaluation object 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 j For indicator X j The standard deviation of , m is the number of indicators;

[0021] Step 2.2, the correlation coefficient matrix of the indicators R = (r ij ) m×n Calculate using formula (3):

[0022]

[0023] 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 For indicator X i With X j The correlation coefficient between

[0024] Step 2.3, objective weight w = (w 1 ,w 2 ,…,w n ) is calculated using formula (4):

[0025]

[0026] w 客j is the objective weight of the jth evaluation index;

[0027] Step 2.4: Normalize w by formula (5) to get W 客 =(W 1 ,W 2 ,…,W n );

[0028]

[0029] W j is the normalized objective weight of the j-th indicator.

[0030] Preferably, in step 3, the specific steps are as follows:

[0031] Step 3.1: All weight vectors are combined into a set of strategy sets W = (w 1 ,w 2 ,…,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:

[0032]

[0033] c k is the weight vector coefficient of the kth indicator, is the inversion of the kth indicator weight vector, is the inversion of the j-th indicator weight vector;

[0034] Step 3.2: From the differential properties of the matrix, we know that the optimal first-order derivative condition satisfies the following formula:

[0035]

[0036] c 1 ,c 2 ,…,c N is the weight vector coefficient, w 1 ,w 2 ,…,w n is the weight vector matrix of the 1st, 2nd, ...nth, Invert the matrix of the 1st, 2nd, ...nth weight vectors;

[0037] Step 3.3: weight vector coefficient c 1 ,c 2 ,…,c N After normalization, the final optimization weight vector coefficient is determined, and the comprehensive weight of the indicator is:

[0038]

[0039] 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;

[0040] Preferably, in step 4, the specific steps are as follows:

[0041] 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. In order to eliminate the dimensional differences between the indicators, all indicator data are normalized according to formula (9) to obtain the initial standard decision matrix Y. Multiply the initial standard decision matrix Y with the indicator weight ω to calculate the weighted decision matrix Z:

[0042]

[0043] Z=(z ij ) m×n =y ij ·w * j (10)

[0044] 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 The initial standard decision matrix is ​​the value of the jth evaluation index of the i-th evaluation object, 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;

[0045] Step 4.2: Determine the positive and negative ideal solutions. According to the calculation results of the weighted decision matrix Z and the attribute characteristics of the indicators (cost type or benefit type), the optimal value and the worst value of each indicator are determined as the positive ideal solution set Z. + 、Negative ideal solution set Z - :

[0046]

[0047] 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;

[0048] Step 4.3: Calculate the KL distance. According to equations (12) and (13), calculate the KL distance between each object to be evaluated and the positive and negative ideal solutions. and

[0049]

[0050] 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;

[0051] 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

[0052]

[0053] Where, ρ is the grey relational resolution, ranging from 0 to 1, and generally 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;

[0054] Step 4.5, calculate the grey correlation degree. The grey correlation degree calculation formula is:

[0055]

[0056] is the correlation coefficient of the positive ideal solution, is the correlation coefficient of the negative ideal solution, r i * is the grey relational degree;

[0057] Step 4.6, calculate the grey relational closeness, normalize the KL distance and grey relational degree, the specific calculation formula is:

[0058]

[0059]

[0060] 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 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, r i + is the correlation coefficient of the positive ideal solution, r i - is the correlation coefficient of the negative ideal solution;

[0061] Step 4.7: Calculate the degree of closeness S between each object to be evaluated and the positive and negative ideal solutions. i :

[0062]

[0063] In the formula, 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 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 relational degree of the positive ideal solution, Normalized grey relational degree of negative ideal solution;

[0064] Step 4.8: Calculate the grey relational relative closeness C according to the result of the closeness calculation. i :

[0065]

[0066] Step 4.9: Finally, according to the grey relational relative closeness Ci Size, determine the order of merit of the objects to be evaluated.

[0067] By adopting the above technical solutions: introducing game theory, G1 method, and improved CRITIC method to consider the weight vectors of 6 indicators in the damage degree index layer. By applying this method, the assessor can quickly assess the damage degree of the pile foundation and determine the priority of the damage degree of the pile foundation.

[0068] Compared with the prior art, the present invention has the following beneficial effects:

[0069] 1. The present invention utilizes the characteristics of grey relational analysis (GRA) which is highly adaptable in dealing with problems such as small amount of data, poor information, and grey information, and can map and evaluate the situation changes of different subsystems; and uses Kullback-Leibler distance (KL) instead of the Euclidean distance in the traditional TOPSIS method to solve the problem of close distance.

[0070] 2. The model proposed in the present invention can help assessors quickly assess the degree of pile foundation damage and determine the priority of pile foundation damage, providing assessors with a new idea for rapid assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0072] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings, so that those skilled in the art can better understand the advantages and features of the present invention, thereby making a clearer definition of the protection scope of the present invention. The embodiments described in the present invention are only a part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present invention.

[0073] Reference Figure 1 , a damage evaluation method for underwater pile foundation based on the GRA-KL-TOPSIS model of game theory, the specific steps are as follows:

[0074] Step 1: G1 method is used to determine the subjective weight, including constructing an evaluation index system for the damage state of underwater pile foundations of bridges and determining the damage level and index classification standard;

[0075] Step 2: Improve the CRITIC method to calculate objective weights, including indicator data processing and a suggested function based on blind number theory;

[0076] Step 3: Determine the comprehensive weight using game theory;

[0077] Step 4: Couple GRA, KL and TOPSIS to establish a GRA-KL-TOPSIS comprehensive evaluation model, improve the traditional TOPSIS method, and comprehensively determine the damage status ranking.

[0078] Specifically, in step 1, the specific steps are as follows:

[0079] Step 1.1: Determine the relative importance of each pair of indicators. Suppose n evaluation indicators are selected, and experts discuss and compare and select the indicators pair by pair to determine the most important indicator x. 1 , the corresponding weight is recorded as w 1 , and then continue to compare and select from the remaining n-1 indicators. Through continuous comparison and selection, we finally get a set of indicator sequences sorted by relative importance (X 1 ,X 2 ,…,X n ), the corresponding weight set is expressed as (w 1 ,w 2 ,…,w n );

[0080] Step 1.2: Given the relative importance ratio, the relative importance ratio of the indicator r j It reflects the relative importance of the index and is the key to the weighting of the G1 method index. It is given according to the value selection criteria and after discussion by experts; the relative importance ratio r j The calculation formula is:

[0081]

[0082] 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.

[0083] Specifically, in step 2, the specific steps are as follows:

[0084] Step 2.1, the standard deviation of the indicator δ = (δ 1 ,δ 2 ,…,δ n ) is calculated using formula (2):

[0085]

[0086] In the formula, a′ ij The standardized evaluation object 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 jFor indicator X j The standard deviation of; m is the number of indicators;

[0087] Step 2.2, the correlation coefficient matrix of the indicators R = (r ij ) m×n Calculate using formula (3):

[0088]

[0089] 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 For indicator X i With X j The correlation coefficient between

[0090] Step 2.3, objective weight w = (w 1 ,w 2 ,…,w n ) is calculated using formula (4):

[0091]

[0092] w 客j is the objective weight of the jth evaluation index;

[0093] Step 2.4: Normalize w by formula (5) to get W 客 =(W 1 ,W 2 ,…,W n );

[0094]

[0095] W j is the normalized objective weight of the j-th indicator.

[0096] Specifically, in step 3, the specific steps are as follows:

[0097] Step 3.1: All weight vectors are combined into a set of strategy sets W = (w 1 ,w 2 ,…,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:

[0098]

[0099] c k is the weight vector coefficient of the kth indicator, is the inversion of the kth indicator weight vector, is the inversion of the j-th indicator weight vector;

[0100] Step 3.2: From the differential properties of the matrix, we know that the optimal first-order derivative condition satisfies the following formula:

[0101]

[0102] c 1 ,c 2 ,…,c N is the weight vector coefficient, w 1 ,w 2 ,…,w n is the weight vector matrix of the 1st, 2nd, ...nth, Invert the matrix of the 1st, 2nd, ...nth weight vectors;

[0103] Step 3.3: weight vector coefficient c 1 ,c 2 ,…,c N After normalization, the final optimization weight vector coefficient is determined, and the comprehensive weight of the indicator is:

[0104]

[0105] is the weight vector coefficient of the kth indicator after normalization, is the inversion of the kth indicator weight vector, w * is the normalized comprehensive weight of the indicators.

[0106] Specifically, in step 4, the specific steps are as follows:

[0107] 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. In order to eliminate the dimensional differences between the indicators, all indicator data are normalized according to formula (9) to obtain the initial standard decision matrix Y. Multiply the initial standard decision matrix Y with the indicator weight ω to calculate the weighted decision matrix Z:

[0108]

[0109] Z=(z ij ) m×n =y ij ·w * j (10)

[0110] 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 The initial standard decision matrix is ​​the value of the jth evaluation index of the i-th evaluation object, 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;

[0111] Step 4.2: Determine the positive and negative ideal solutions. According to the calculation results of the weighted decision matrix Z and the attribute characteristics of the indicators (cost type or benefit type), the optimal value and the worst value of each indicator are determined as the positive ideal solution set Z. + 、Negative ideal solution set Z - :

[0112]

[0113] 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;

[0114] Step 4.3: Calculate the KL distance. According to equations (12) and (13), calculate the KL distance between each object to be evaluated and the positive and negative ideal solutions. and

[0115]

[0116] 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;

[0117] 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

[0118]

[0119] Where, ρ is the grey relational resolution, ranging from 0 to 1, and generally 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;

[0120] Step 4.5, calculate the grey correlation degree. The grey correlation degree calculation formula is:

[0121]

[0122] is the correlation coefficient of the positive ideal solution, is the correlation coefficient of the negative ideal solution, r i * is the grey relational degree;

[0123] Step 4.6, calculate the grey relational closeness, normalize the KL distance and grey relational degree, the specific calculation formula is:

[0124]

[0125] 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 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, r i + is the correlation coefficient of the positive ideal solution, r i - is the correlation coefficient of the negative ideal solution;

[0126] Step 4.7: Calculate the degree of closeness S between each object to be evaluated and the positive and negative ideal solutions. i :

[0127]

[0128] In the formula, 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 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 relational degree of the positive ideal solution, Normalized grey relational degree of negative ideal solution;

[0129] Step 4.8: Calculate the grey relational relative closeness C according to the result of the closeness calculation. i :

[0130]

[0131] Step 4.9: Finally, according to the grey relational relative closeness C i Size, determine the order of merit of the objects to be evaluated.

[0132] Example:

[0133] 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 was used to comprehensively analyze the damage status of the pile foundation through relevant calculations.

[0134] According to the results of indicator data processing, based on the principle of interpolation, the midpoint value of the grading standard is used as the interpolation point, that is: b 1 =30, b 2 =65, b 3 =75, b 4 =85, b 5 =95, 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 probability of falling into the five level intervals is 0, 0, 0.0815, 0.2089, and 0.0428 respectively, so the indicator 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.

[0135] Table 1 Assignment of pile foundation indicators

[0136]

[0137]

[0138] 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).

[0139] According to the calculation principle of 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 combined to determine the positive ideal solution Z of the index. + and negative ideal solution Z - The specific calculation results are shown in Table 2.

[0140] Table 2 Weighted standardized data and calculation results of positive and negative ideal solutions

[0141]

[0142] 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.

[0143] Table 3 GRA-KL-TOPSIS calculation results

[0144]

[0145] 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.

[0146] Table 4 Comparison of evaluation results

[0147]

[0148] In summary, the present invention can avoid the problem of excessive subjective weight in the indicators of traditional methods and realize the evaluation and ranking of the damage status of bridge pile foundations.

[0149] The description and practice disclosed in the present invention are easy to think and understand for ordinary technicians in the technical field, and several improvements and modifications can be made without departing from the principles of the present invention. Therefore, modifications or improvements made without departing from the spirit of the present invention should also be regarded as the protection scope of the present 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: G1 method is used to determine the subjective weight, including constructing an evaluation index system for the damage state of underwater pile foundations of bridges and determining the damage level and index classification standard; Step 2: Improve the CRITIC method to calculate objective weights, including indicator data processing and establishing functions based on blind number theory; Step 3: Determine the comprehensive weight using game theory; Step 4: Couple GRA, KL and TOPSIS to establish a GRA-KL-TOPSIS comprehensive evaluation model, improve the traditional TOPSIS method, and comprehensively determine the damage status ranking.

2. The underwater pile foundation damage evaluation method based on the GRA-KL-TOPSIS model of game theory according to claim 1 is characterized in that: In step 1, the specific steps are as follows: Step 1.1, determine the relative importance of each pair of indicators. Assume that 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 (X1, X2, ..., X1) ranked by relative importance. 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 given according to the value selection criteria 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.

3. The underwater pile foundation damage evaluation method based on the GRA-KL-TOPSIS model of game theory according to claim 1 is characterized in that: In step 2, the specific steps are as follows: Step 2.1, standard deviation of the indicator δ = (δ1, δ2,…,δ n ) is calculated using formula (2): In the formula, a′ ij The standardized evaluation object 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 j For 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 For 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 normalized objective weight of the j-th indicator.

4. The underwater pile foundation damage evaluation method based on the GRA-KL-TOPSIS model of game theory according to claim 1 is characterized in that: In step 3, the specific steps are as follows: Step 3.1: All weight vectors are combined into a set of strategies 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 Minimize the deviation, that is: c k is the weight vector coefficient of the kth indicator, is the inversion of the kth indicator weight vector, is the inversion of the j-th indicator weight vector; Step 3.2: From the differential properties of the matrix, we know that 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 vectors; Step 3.3: For the weight vector coefficients c1, c2, ..., c N After normalization, the final optimization weight vector coefficient is determined, and the comprehensive weight of the indicator is: is the weight vector coefficient of the kth indicator after normalization, is the inversion of the kth indicator weight vector, w * is the normalized comprehensive weight of the indicators.

5. The underwater pile foundation damage evaluation method based on the GRA-KL-TOPSIS model of game theory according to claim 1 is characterized in that: 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. In order to eliminate the dimensional differences between the indicators, all indicator data are normalized according to formula (9) to obtain the initial standard decision matrix Y. Multiply the initial standard decision matrix Y with the indicator weight ω to calculate the weighted decision matrix Z: From=(from 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. According to 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 equations (12) and (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 In the formula, 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 correlation degree. The grey correlation degree calculation formula is: is the correlation coefficient of the positive ideal solution, is the correlation coefficient of the negative ideal solution, * r i is the grey relational degree; Step 4.6, calculate the grey relational closeness, normalize the KL distance and grey relational degree, the specific calculation formula is: 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 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, r i + is the correlation coefficient of the positive ideal solution, r i - 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 : In the formula, 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 the closeness calculation. i : Step 4.9: Finally, according to the grey relational relative closeness C i Size, determine the order of merit of the objects to be evaluated.

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