Method for evaluating cable insulation performance based on fuzzy theory and grey game theory

Abstract

The application discloses a kind of cable insulation performance evaluation method based on fuzzy theory and grey game theory.First, according to the insulation property of single-core cable, effective performance index is screened out, and insulation performance evaluation matrix is established according to the associated performance evaluation index data through fuzzy theory, then normalized processing is carried out to obtain standard matrix.Second, through improved three-scale analytic hierarchy process and entropy weight method, the weight vector w1 and w2 of each effective evaluation index are calculated, the weight vector of each index is re-optimized using the idea of game theory combination weighting, and the optimal comprehensive weight result w3 is obtained.Finally, through the fuzzy operation of comprehensive weight and evaluation matrix, combined with the maximum membership degree criterion, the evaluation value of cable insulation performance is analyzed, and the diagnosis and evaluation of insulation performance are realized.The application avoids data redundancy, releases data storage resources, improves the running speed of system calculation, and provides a comprehensive and effective criterion for the insulation performance of cable.

Description

Technical Field

[0001] This invention belongs to the field of power equipment condition assessment, and in particular, it is a method for assessing cable insulation performance based on fuzzy theory and grey game theory. Background Technology

[0002] The safety of the power industry plays a vital and irreplaceable role in the nation's economic development. With my country's economic growth, the electricity load in large cities, coastal areas, and offshore islands is constantly increasing, and the widespread adoption of power cables has provided an effective guarantee for alleviating this load growth. However, the failure rate of power cables in my country is still several times higher than in developed countries. Furthermore, during operation, cables can age and deteriorate due to electrical, thermal, chemical, mechanical, and biological factors, sometimes even experiencing partial insulation breakdown. Therefore, it is urgent to conduct insulation assessments of power cables to prevent fires and explosions and achieve cable fault prevention. Developing an effective analytical method for comprehensive evaluation of cable insulation performance is therefore crucial.

[0003] Furthermore, existing technologies, when optimizing the solutions to the three fundamental elements of game theory, only consider the optimization of methods and payoffs, without comprehensively optimizing the participating decision-makers. When the amount of data from decision-makers is redundant, it not only increases computer memory usage but also slows down the computational speed. Effectively screening and eliminating decision-makers can significantly improve the efficiency of game theory methods, effectively saving computational resources and computer memory. Moreover, existing technologies, when evaluating research subjects, do not connect the ideas of fuzzy theory with game theory; they merely obtain the evaluation matrix through scoring criteria, which introduces a degree of subjectivity. Summary of the Invention

[0004] To address the aforementioned issues, this invention provides a cable insulation performance evaluation method based on fuzzy theory and grey game theory. It employs grey game theory to select effective attribute indicators and comprehensively optimizes two different evaluation methods, resulting in a complete and comprehensive analysis of multi-parameter evaluation information. This avoids the one-sidedness of single objective or subjective analysis, as well as data redundancy, effectively freeing up data storage resources and improving the system's computational speed. It provides power departments with comprehensive and effective criteria for understanding cable insulation performance, enabling operators to more accurately monitor and grasp the cable's operating status, and to a certain extent, effectively ensuring the safe operation of power lines.

[0005] Therefore, the technical solution adopted in this invention is a cable insulation performance evaluation method based on fuzzy theory and grey game theory, comprising the following steps:

[0006] 1) Determine the effective evaluation index of the insulation performance of single-core cables using the grey relational analysis method;

[0007] 2) Determine the evaluation matrix of the standard based on fuzzy theory;

[0008] 3) Calculate the first weight vector w1 for each evaluation index using the three-scale analytic hierarchy process;

[0009] 4) Calculate the second weight vector w2 for each evaluation index using the entropy weight method;

[0010] 5) The weighting was re-optimized using game theory to determine the comprehensive weight vector w3 for each indicator;

[0011] 6) Analyze the evaluation value of cable insulation performance based on the evaluation matrix determined in step 2) and the comprehensive weight result obtained in step 5);

[0012] 7) Based on the principle of maximum membership, complete the diagnosis and evaluation of cable insulation performance in step 6).

[0013] The advantages and beneficial effects of this invention are as follows:

[0014] First, this invention provides a method for evaluating the insulation performance of single-core cables based on fuzzy theory and grey game theory. It comprehensively optimizes various evaluation methods, enabling a complete and comprehensive analysis of multi-parameter evaluation information and avoiding the one-sidedness of single objective and subjective analysis.

[0015] Secondly, this invention uses the concept of grey game theory to filter out effective attribute indicators, avoids data redundancy, effectively releases data storage resources, and improves the system's computing speed.

[0016] Third, the improved analytic hierarchy process involved in this invention effectively eliminates data, freeing up a large amount of computer resources and effectively improving the solution processing speed.

[0017] In summary, this method provides a comprehensive and effective criterion for power departments to understand the insulation performance of cables, enabling operators to more accurately monitor and grasp the operating status of cables, and to a certain extent effectively ensuring the safe operation of power lines. It has high application value in the evaluation of cable insulation performance. Attached Figure Description

[0018] Figure 1 This is a flowchart of the cable insulation performance evaluation method based on fuzzy theory and grey game theory provided by the present invention. Detailed Implementation

[0019] like Figure 1 As shown, a method for evaluating cable insulation performance based on fuzzy theory and grey game theory includes the following steps:

[0020] 1) Determine the effective evaluation index of the insulation performance of single-core cables based on the grey relational analysis method.

[0021] 2) Determine the evaluation matrix of the standard based on fuzzy theory.

[0022] 3) Calculate the first weight vector w1 of each evaluation index according to the three-scale hierarchical analysis method.

[0023] 4) Calculate the second weight vector w2 for each evaluation index using the entropy weight method.

[0024] 5) The weighting was re-optimized using game theory to determine the comprehensive weight vector w3 for each indicator.

[0025] 6) Analyze the evaluation value of cable insulation performance based on the evaluation matrix determined in step 2) and the comprehensive weight result obtained in step 5).

[0026] 7) Based on the principle of maximum membership, complete the diagnosis and evaluation of cable insulation performance in step 6).

[0027] Preferably, according to step 1), the effective evaluation index of the insulation performance of a single-core cable is determined using the grey relational analysis method, forming the following insulation performance evaluation index matrix for the single-core cable:

[0028]

[0029] Where: x0(k) is the parent index, representing the insulation resistance value of a single-core cable measured at the k-th stage, k = (1, 2, ..., n). i (k) represents the sub-indicator, indicating the related indicator value to be screened, i = (1, 2, ..., m). Where n is the number of measurement time series corresponding to the indicator data, and m is the number of indicators to be screened.

[0030] The grey relational formula for the insulation performance evaluation index matrix of single-core cables is as follows:

[0031]

[0032] In the formula: r is the degree of correlation; ξ is the correlation coefficient.

[0033]

[0034]

[0035]

[0036] Wherein: ρ represents the influence coefficient. The introduction of ρ is to reduce the influence of extreme values ​​on the calculation results, and it is generally taken as 0.5. Based on equations (2) to (4), the correlation degree r between the parent index and the child index can be obtained.

[0037] In step 1), the effective coefficient α of the effective index formed based on the correlation degree i The formula is:

[0038]

[0039] Set the acceptance threshold β according to requirements. When α i When the value is greater than β, an effective evaluation index is obtained. Simultaneously, the single-core cable insulation performance evaluation index matrix X is updated promptly, and the latest effective evaluation index matrix L for cable insulation performance measured at the k-th time stage is obtained.

[0040] Based on the evaluation matrix determined by fuzzy theory as described in step 2), the fuzzy membership function formula formed by fuzzy theory is as follows:

[0041]

[0042]

[0043]

[0044] Where u(1), u(2), and u(3) represent three membership functions under excellent and poor conditions, respectively. a, b, c, and d are evaluation thresholds obtained from experiments or experience. x represents the actual value of the insulation performance index. Based on equations (6) to (8), the obtained index matrix L can be substituted to obtain the evaluation matrix V = [v ij ] p×q Where: p represents the number of effective evaluation indicators for the insulation performance of a single-core cable, and q represents the number of evaluation objects. ij This indicates the comparison value between two pairs of indicators.

[0045] The standard evaluation matrix formula formed in step 2) based on fuzzy theory is as follows:

[0046]

[0047] Based on step 3), the weight vector w1 of each evaluation index is calculated using the three-scale analytic hierarchy process, resulting in the following three-scale formula:

[0048]

[0049] Where: x ij For indicator x i Relative to index x j The degree of importance. When x i >x j When, it indicates that the index x i Relative to index x j It is important.

[0050] Step 3) uses the three-scale hierarchical analysis method to form a weight vector w1 = [c1, ..., c i ].

[0051] Where: c i The weight value of the effective evaluation index for the insulation performance of a single-core cable is given by the following formula:

[0052]

[0053]

[0054] Based on equations (11) to (12), the weight vector w1 of the insulation performance evaluation index for single-core cables can be obtained.

[0055] According to step 4), the second weight vector w2 of each evaluation index is calculated using the entropy weight method, and the resulting second weight vector w2 = [s1,…,s i ].

[0056] Where: s i The weight value of the effective evaluation index for the insulation performance of a single-core cable is given by the following formula:

[0057]

[0058]

[0059] In the formula: H i e represents the entropy value of each indicator. ij This represents the comparison value between two pairs of indicators after normalization. Based on equations (13) to (14), the weight vector w2 of the insulation performance evaluation index for single-core cables can be obtained.

[0060] Based on step 5), the weights are re-optimized using game theory to determine the comprehensive weight vector w3 for each indicator. The resulting comprehensive weight vector w3 = [z1, ..., z i ].

[0061] Where: z i The weight value of the effective evaluation index for the insulation performance of a single-core cable is given by the following formula:

[0062]

[0063] In the formula: w represents the optimal weighting coefficient. i Let z represent the weight vector obtained by the i-th method. i It is an element in the w3 vector.

[0064] According to the game theory model, the optimization algorithm for the optimal weight coefficients is as follows:

[0065]

[0066]

[0067]

[0068] error represents the minimum error value, k i This represents the coefficients of the linear combination.

[0069] Based on equations (16) to (18), the weight vector w3 of each indicator can be obtained.

[0070] The evaluation matrix G = [g1, g2, g3] of the cable insulation performance obtained by analysis and calculation in step 6) is specifically formulated as follows:

[0071]

[0072] Where: g j The membership values ​​represent the cable insulation performance as excellent, good, or very poor. i This represents the overall weight value after game theory optimization.

[0073] Step 7) describes the diagnosis and evaluation of cable insulation performance using the maximum membership principle, resulting in the final evaluation value g = max(G).

[0074] The above examples should be understood as merely illustrating the technical solutions of the present invention and not as limiting it. After reading the description of the present invention, those skilled in the art can still make various modifications or equivalent substitutions to the technical solutions of the present invention, and these equivalent transformations and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A method for evaluating cable insulation performance based on fuzzy theory and grey game theory, characterized in that, Includes the following steps: 1) Determine the effective evaluation index of the insulation performance of single-core cables using the grey relational analysis method; 2) Determine the evaluation matrix of the standard based on fuzzy theory; 3) Calculate the first weight vector w1 for each evaluation index using the three-scale analytic hierarchy process; 4) Calculate the second weight vector w2 for each evaluation index using the entropy weight method; 5) The weighting was re-optimized using game theory to determine the comprehensive weight vector w3 for each indicator; 6) Analyze the evaluation value of cable insulation performance based on the evaluation matrix determined in step 2) and the comprehensive weight result obtained in step 5); 7) Based on the principle of maximum membership, complete the diagnosis and evaluation of cable insulation performance in step 6).

2. The cable insulation performance evaluation method based on fuzzy theory and grey game theory according to claim 1, characterized in that: The evaluation index matrix X for the insulation performance of single-core cables is: Where: x0(k) is the parent index, representing the insulation resistance value of a single-core cable measured at the k-th stage, k = 1, 2, ..., n; x i (k) represents the sub-indicator, i = 1, 2, ..., m; n is the number of measurement time series corresponding to the indicator data, and m is the number of indicators to be screened.

3. The cable insulation performance evaluation method based on fuzzy theory and grey game theory according to claim 2, characterized in that: The formula for the grey relational degree in the grey relational method described in step 1) is: In the formula: r(x0,x i ) represents the correlation between the parent indicator and the child indicator; ξ represents the correlation coefficient; Where: ρ represents the influence coefficient.

4. The cable insulation performance evaluation method based on fuzzy theory and grey game theory according to claim 3, characterized in that: The effective coefficient α of the effective evaluation index in step 1) i The formula is: Set the acceptance threshold β according to the requirements, when α i When the value is greater than β, an effective evaluation index is obtained. At the same time, the single-core cable insulation performance evaluation index matrix X is updated in a timely manner, and the cable insulation performance effective evaluation index matrix L measured in the kth stage at the latest time is obtained.

5. The cable insulation performance evaluation method based on fuzzy theory and grey game theory according to claim 1, characterized in that: The formula for the fuzzy membership function formed in step 2) is: Where: u(1), u(2), u(3) represent three membership functions under the conditions of excellent, good, and poor evaluation, respectively; a, b, c, d are evaluation thresholds obtained from experiments or experience; and x represents the actual value of the insulation performance index. Substituting the obtained effective evaluation index matrix L of cable insulation performance into equations (6) to (8) yields the evaluation matrix V = [v ij ] p×q Where: p is the number of effective evaluation indicators for the insulation performance of a single-core cable, q is the number of evaluation objects, and v ij This indicates the comparison value between two pairs of indicators.

6. The cable insulation performance evaluation method based on fuzzy theory and grey game theory according to claim 5, characterized in that: The formula for the standard evaluation matrix constructed based on the aforementioned evaluation matrix is: e ij This represents the comparison value between two normalized indicators.

7. The cable insulation performance evaluation method based on fuzzy theory and grey game theory according to claim 1, characterized in that: Step 3) specifically includes: The three-scale formula in the three-scale hierarchical analytic hierarchy process is: Where: x ij For indicator x i Relative to index x j The degree of importance; The first weight vector formed is w1 = [c1, ..., c i ], c i The weight value of the effective evaluation index for the insulation performance of a single-core cable is given by the following formula:

8. The cable insulation performance evaluation method based on fuzzy theory and grey game theory according to claim 1, characterized in that: Step 4) The second weight vector w2 = [s1,…,s i ], s i The weight value of the effective evaluation index for the insulation performance of a single-core cable is given by the following formula: In the formula: H i Here are the entropy values ​​for each indicator.

9. The cable insulation performance evaluation method based on fuzzy theory and grey game theory according to claim 1, characterized in that: Step 5) The comprehensive weight vector w3 = [z1, ..., z i ], z i The weight value of the effective evaluation index for the insulation performance of a single-core cable is given by the following formula: In the formula: k i * w represents the optimal weighting coefficient. i This represents the weight vector obtained by the i-th method; The optimization algorithm for the optimal weight coefficients is as follows: error represents the minimum error value, k i This represents the coefficients of the linear combination.

10. The cable insulation performance evaluation method based on fuzzy theory and grey game theory according to claim 1, characterized in that: In step 6), the evaluation matrix G = [g1, g2, g3] for the cable insulation performance is obtained, and the specific formula is as follows: Where: g j The membership values ​​for cable insulation performance are excellent, good, and very poor. i This represents the overall weight value after game theory optimization.

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