Asphalt pavement preventive maintenance multi-attribute decision-making method based on optimized triangular fuzzy number

Abstract

The invention relates to the technical field of highway engineering maintenance, in particular to an asphalt pavement preventive maintenance multi-attribute decision-making method based on an optimized triangular fuzzy number, and the method comprises the steps: 1, collecting and processing initial data; step 2, carrying out normalization processing; step 3, similarity calculation; step 4, reliability calculation; and step 5, carrying out weighted post-processing. According to the method, the subjective degree of the score data can be further reduced, the more scientific weight of the evaluation index is obtained, the decision suggestion of the pavement maintenance scheme is obtained, and the maintenance scheme more suitable for road maintenance is selected. According to the method, consideration can be carried out from multiple dimensions, and subjectivity of expert scoring is scientifically reduced. By applying the calculation method provided by the invention, the optimal maintenance scheme for pavement maintenance can be quickly obtained.

Description

Technical Field

[0001] The invention relates to the technical field of highway engineering maintenance, and in particular to a multi-attribute decision-making method for preventive maintenance of asphalt pavement based on optimized triangular fuzzy numbers. Background Art

[0002] As a strategic and basic industry in the national economy, my country's highway transportation construction has made great achievements and effectively promoted the development of the economy and society. The highway density continues to increase, and asphalt pavement highways provide strong support for the construction of a modern comprehensive transportation system. However, with the rapid development of highway construction, there is also a peak in highway maintenance and management.

[0003] Preventive maintenance is an important technical measure that aims to protect the road surface and slow down the rate of deterioration of road performance. It can delay the decline in road quality caused by traffic and environmental loads and extend the service life. It is an effective measure to control highway diseases. Choosing a suitable preventive maintenance plan for asphalt pavement can reduce resource utilization, reduce environmental pollution, and extend the life of the road, which is of great significance to improving social sustainability.

[0004] At present, the selection of road maintenance plans mostly adopts multi-attribute decision-making methods, especially the analytic hierarchy process, which is often used. However, this method requires the use of expert scoring data, which has the disadvantages of strong subjectivity and poor reliability. Summary of the invention

[0005] The purpose of the present invention is to solve the shortcomings existing in the prior art, and to propose a multi-attribute decision-making method for preventive maintenance of asphalt pavement based on optimized triangular fuzzy numbers. This method can further reduce the subjectivity of score data, obtain more scientific weights of evaluation indicators, and derive decision recommendations for pavement maintenance plans, thereby selecting a maintenance plan that is more suitable for maintaining the road.

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

[0007] A multi-attribute decision-making method for preventive maintenance of asphalt pavement based on optimized triangular fuzzy numbers includes the following steps:

[0008] Step 1: Collection and processing of initial data;

[0009] The m alternative preventive maintenance technical solutions are sequentially matched to generate a solution set A = {A 1 ,A 2 ,…,A m};

[0010] The n factors that affect the selection of pavement maintenance schemes are sequentially generated into an index set B = {B 1 ,B 2,…,B n};

[0011] Summarize and analyze the scores of each expert to obtain the initial triangular fuzzy number decision matrix M of benefit-type indicators and cost-type indicators ori =[t′ ij ] m×n ;

[0012] Among them, A is the preventive maintenance technical scheme, B is the factor index affecting the selection of pavement maintenance scheme, m is the number of alternative preventive maintenance schemes, n is the number of factor indexes affecting the selection of pavement maintenance scheme, t′ ij is the initial triangular fuzzy number.

[0013] Step 2: Normalization processing;

[0014] Step 3: Similarity calculation;

[0015] Step 4: Reliability calculation;

[0016] Step 5: Weighted post-processing.

[0017] Preferably, in step 2, the specific method of normalization processing is as follows:

[0018] According to formula (1), the benefit index is normalized:

[0019]

[0020] According to formula (2), the cost-based index is normalized:

[0021]

[0022] Among them, t Lij is the lower bound of the normalized triangular fuzzy number, t Mij is the normalized triangular fuzzy number mode, t Uij is the upper bound of the normalized triangular fuzzy number, t′ Lij is the lower bound of the initial triangular fuzzy number, t′ Mij is the mode of the initial triangular fuzzy numbers, t′ Uij is the upper bound of the initial triangular fuzzy number. m is the number of alternative preventive maintenance plans, and i is the i-th element.

[0023] The normalized triangular fuzzy number decision matrix M of benefit-type index and cost-type index is obtained 1 and M 2 .

[0024] Preferably, in step 3, the specific method of similarity calculation is as follows:

[0025] For any two normalized triangular fuzzy numbers and The similarity is calculated using formula (3):

[0026]

[0027] in, represents the normalized triangular fuzzy number, is the similarity of any two normalized triangular fuzzy numbers, t L is the lower bound of the normalized triangular fuzzy number, t M is the normalized triangular fuzzy number mode, t U is the upper bound of the normalized triangular fuzzy number.

[0028] The i-th solution A can be calculated by formula (4): i For the jth indicator B j The similarity with all other solutions except the i-th solution is:

[0029]

[0030] Among them, B j is the jth indicator, is the normalized triangular fuzzy number of the jth index in the i-th scheme, is the canonical triangular fuzzy number of the jth indicator in the kth scheme, i is the ith element, k is the kth element, (i≠k), m is the number of alternative preventive maintenance schemes, 1≤i≤m,1≤j≤n,1≤k≤m;

[0031] For the jth indicator B j , all schemes are calculated separately according to formula (4), and the total similarity after aggregation is calculated by formula (5):

[0032]

[0033] The total similarity of all indicators for all solutions should be within R j The maximum similarity deviation maximization model and Lagrangian function are constructed as follows:

[0034]

[0035] make:

[0036] have to:

[0037] R j ′ is standardized, and the similarity calculation formula of the index can be obtained (6):

[0038]

[0039] Among them, maxD(Rj ) to make the total similarity in R j The similarity deviation maximization model of the maximum structure under the action, λ is the Lagrange multiplier, L(R j ,λ) is to make the total similarity in R j The Lagrangian function of the maximum structure under the action, R j is the total similarity of the jth index, is the similarity of two normalized triangular fuzzy numbers, j is the jth element, i is the ith element, k is the kth element, (i≠k), m is the number of alternative preventive maintenance schemes, and n is the number of factor indicators that affect the selection of pavement maintenance schemes.

[0040] Preferably, in step 4, the specific method of calculating the reliability is as follows:

[0041] In the normalized matrix, the indicator B j In the scheme A i The calculation formula of entropy is formula (7):

[0042]

[0043] in, is the normalized triangular fuzzy number of the jth index in the i-th scheme, t Lij is the lower bound of the normalized triangular fuzzy number, t Uij is the upper bound of the normalized triangular fuzzy number, and r is the similarity between two elements.

[0044] All indicators for the i-th solution X i The sum of the entropy is formula (8):

[0045]

[0046] Among them, S ij is the entropy of the jth indicator in the i-th solution, is the normalized triangular fuzzy number of the jth index in the i-th scheme, j is the jth element, i is the i-th element, and n is the number of factor indicators that affect the selection of pavement maintenance schemes.

[0047] Plan A i Medium Index B j Reliability F ij Formula (9):

[0048]

[0049] Among them, S ij is the entropy of the jth indicator in the i-th solution, is the normalized triangular fuzzy number of the jth index in the i-th scheme, S iis the sum of the entropy of all indicators in the i-th solution, F ij is the reliability of the jth indicator in the i-th solution.

[0050] Preferably, in step 5, the specific method of weighted post-processing is as follows:

[0051] According to formula (10), the weight of each indicator based on reliability is obtained:

[0052] w ij =R j (1-F ij ) (10)

[0053] Among them, w ij is the weight of the jth indicator in the i-th solution, R j is the total similarity of the jth index, F ij is the reliability of the jth indicator in the i-th solution.

[0054] The weighted comprehensive value of each solution is calculated according to formula (11):

[0055]

[0056] in, is the weighted comprehensive value of the ith solution, w i j is the weight of the jth indicator in the i-th solution, is the normalized triangular fuzzy number of the jth index in the i-th scheme, j is the jth element, and n is the number of factor indicators that affect the selection of pavement maintenance schemes.

[0057] According to formulas (12) and (13), the weighted comprehensive values ​​of the schemes are compared with each other in terms of the probability measurement values, and a probability comparison relationship matrix is ​​constructed:

[0058]

[0059] in, ρ is the decision maker’s risk preference, t L is the lower bound of the normalized triangular fuzzy number, t M is the normalized triangular fuzzy number mode, t U is the upper bound of the normalized triangular fuzzy number.

[0060]

[0061] Among them, A i is the i-th preventive maintenance technical solution, A k is the kth preventive maintenance technical solution, is the weighted comprehensive value of the ith solution, is the weighted comprehensive value of the kth solution, (i≠k).

[0062] According to formula (14), the overall comparative possibility of each scheme is calculated as follows:

[0063]

[0064] Where m is the number of alternative preventive maintenance plans. It is the possibility measurement value comparing the i-th and k-th preventive maintenance technical schemes. is the overall comparative possibility of the ith option.

[0065] right Sorting in descending order can get the optimal solution.

[0066] By adopting the above technical solution, it is possible to consider from multiple dimensions and scientifically reduce the subjectivity of expert scoring. The calculation method of the present invention can also quickly obtain the best maintenance plan for road maintenance.

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

[0068] 1. The method of the present invention can further reduce the subjectivity of expert scoring data when making preventive maintenance decisions for asphalt pavements, obtain more scientific weights of evaluation indicators, derive decision-making recommendations for pavement maintenance plans, and then select a maintenance plan that is more suitable for asphalt pavement projects.

[0069] 2. The method of the present invention can be used to improve multi-attribute decision-making methods that require expert scoring data, such as AHP, etc., and can make these methods more scientific and accurate.

[0070] 3. The method of the present invention is relatively simple to calculate, the original data is easy to obtain, and the data requirement is small. It is suitable for preliminary or emergency maintenance plan selection and is also suitable for roads with missing data. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 The figure is a flow chart of the calculation method 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] Example:

[0074] The road section in this example is a national and provincial trunk asphalt road in Jiangsu Province. It was built in 2010. The road surface is in good technical condition and has not undergone major or medium repairs. The total length of the two-way road from the starting point to the end point is 96km. The road section was tested in 2021, and the relevant data are shown in Table 1:

[0075] Table 1 Road surface condition indicators

[0076]

[0077] The overall pavement quality index (PQI) of the target road section is 95.34, and the road condition is relatively high. The road damage, flatness and rutting are all maintained at an excellent level, and the anti-skid is maintained at a good level. Among them, the total cracks are 3.31m 2 , strip repair 6125.4m, block repair 67.95m 2 .

[0078] Step 1: Initial data

[0079] At present, a variety of relatively mature preventive maintenance technologies have been formed, mainly including: grouting or sealing, micro-surfacing, slurry seal, gravel seal, composite seal, fog seal, thin layer cover, and in-situ thermal regeneration. 1 ,A 2 ,…,A 8}.

[0080] Through research, it is found that the factors affecting the selection of pavement maintenance schemes can be divided into benefit indicators and cost indicators, as shown in Table 2. Generate the indicator set B = {B 1 ,B 2 ,…,B 10}.

[0081] Table 2 Influencing indicators of scheme selection

[0082]

[0083] In this embodiment, an online and paper version of the questionnaire was developed to collect different people's views on the importance of each indicator to each option selection. The importance score is presented in the form of triangular fuzzy numbers, and the score should be between 0-1, 0 for the indicator is completely unimportant to the option selection, and 1 for the indicator completely determines the option selection. The questionnaire was distributed to 10 experts in different professional positions, only background information was provided to them, and expert opinions were solicited anonymously. Each expert scored each option based on his or her own opinions and experience, and tried to maintain their independence. Among them, relevant scientific researchers accounted for 30%, highway maintenance engineers accounted for 30%, college professors accounted for 20%, and road designers accounted for 20%. The final effective recovery rate of the questionnaire reached 80%. The upper limit, lower limit and median of each score in the questionnaire were averaged to obtain the initial decision matrix.

[0084] Step 2: Normalization

[0085] According to the scores of each expert in the returned questionnaire, the initial triangular fuzzy number decision matrix of benefit-type indicators and cost-type indicators is obtained after summary analysis. According to equations (1) and (2), each attribute indicator is normalized to obtain the normalized triangular fuzzy number decision matrix M of benefit-type indicators and cost-type indicators. 1 and M 2 , as shown in Table 3 and Table 4.

[0086] Table 3. Standardized matrix M of benefit-based indicators 1 (×10 -1 )

[0087]

[0088]

[0089] Table 4 Cost-based indicator normalization matrix M 2 (×10 -1 )

[0090]

[0091] Step 3: Similarity calculation Calculate the similarity R of the index from (3) to (6). j :

[0092] R 1 =0.0984,R 2 =0.0978,R 3 =0.1009,R 4 =0.1009,R 5 =0.1040

[0093] R 6 =0.0991,R 7=0.1022,R 8 =0.0984,R 9 =0.0984,R 10 =0.0997

[0094] Step 4: Reliability calculation

[0095] From (7) to (9), we can calculate the solution A = {A 1 ,A 2 ,…,A 8}Indicator set B={B 1 ,B 2 ,…,B 10 The reliability of F ij (1≤i≤8,1≤j≤10), as shown in Table 5.

[0096] Table 5 Reliability F ij (×10 -1 )

[0097]

[0098] Step 5: Weighted post-processing

[0099] According to formula (10), the weight w of each indicator based on reliability is obtained: ij , and then calculate the weighted comprehensive value of each solution according to formula (11) as follows:

[0100]

[0101]

[0102] Step 6: Relationship Matrix

[0103] According to equations (12) to (13), the weighted comprehensive values ​​of the schemes are compared with each other in terms of the probability measurement values. In this example, ρ = 0.5 is taken to construct the probability comparison relationship matrix G 8×8 =G(A i >A k ) 8×8 as follows:

[0104]

[0105] According to formula (14), the overall comparative possibility of each scheme is calculated as follows:

[0106]

[0107]

[0108] Step 7: Output the optimal solution

[0109] right Sorting in descending order, the available solutions from best to worst are:

[0110] A 6 >A 1 >A 2 >A 3 >A 4 >A 8 >A 7 >A 5 ,

[0111] Therefore, the optimal solution for the case project is fog seal layer A 6 .

[0112] In summary, the present invention can further reduce the subjectivity of expert scoring data when making preventive maintenance decisions for asphalt pavements, obtain more scientific weights of evaluation indicators, derive decision-making recommendations for pavement maintenance plans, and then select a maintenance plan that is more suitable for asphalt pavement projects.

[0113] 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 multi-attribute decision-making method for preventive maintenance of asphalt pavement based on optimized triangular fuzzy numbers, characterized in that: The steps include: Step 1: Collection and processing of initial data; The m alternative preventive maintenance technical solutions are sequentially matched to generate a solution set A = {A1, A2, ..., A m }; The n factors that affect the selection of pavement maintenance schemes are sequentially generated into an index set B = {B1, B2, ..., B n }; Summarize and analyze the scores of each expert to obtain the initial triangular fuzzy number decision matrix M of benefit-type indicators and cost-type indicators ori =[t i ' j ] m×n ; Among them, A is the preventive maintenance technical solution, B is the factor index that affects the selection of pavement maintenance solution, m is the number of alternative preventive maintenance solutions, n is the number of factor indexes that affect the selection of pavement maintenance solution, t i ' j is the initial triangular fuzzy number; Step 2: Normalization processing; Step 3: Similarity calculation; Step 4: Reliability calculation; Step 5: Weighted post-processing.

2. The method for multi-attribute decision-making for preventive maintenance of asphalt pavement based on optimized triangular fuzzy numbers according to claim 1 is characterized in that: In step 2, the specific method of normalization is as follows: According to formula (1), the benefit index is normalized: According to formula (2), the cost-based index is normalized: Among them, t Lij is the lower bound of the normalized triangular fuzzy number, t Mij is the normalized triangular fuzzy number mode, t Uij is the upper bound of the normalized triangular fuzzy number, t′ Lij is the lower bound of the initial triangular fuzzy number, t′ Mij is the mode of the initial triangular fuzzy numbers, t′ Uij is the upper bound of the initial triangular fuzzy number, m is the number of alternative preventive maintenance plans, and i is the i-th element; The normalized triangular fuzzy number decision matrices M1 and M2 of benefit-type indicators and cost-type indicators are obtained.

3. The method for multi-attribute decision-making for preventive maintenance of asphalt pavement based on optimized triangular fuzzy numbers according to claim 2 is characterized in that: In step 3, the specific method of similarity calculation is as follows: For any two normalized triangular fuzzy numbers and The similarity is calculated using formula (3): in, represents the normalized triangular fuzzy number, is the similarity of any two normalized triangular fuzzy numbers, t L is the lower bound of the normalized triangular fuzzy number, t M is the normalized triangular fuzzy number mode, t U is the upper bound of the normalized triangular fuzzy number; The i-th solution A can be calculated by formula (4): i For the jth indicator B j The similarity with all other solutions except the i-th solution is: Among them, B j is the jth indicator, is the normalized triangular fuzzy number of the jth index in the i-th scheme, is the canonical triangular fuzzy number of the jth indicator in the kth scheme, i is the ith element, k is the kth element, i≠k, m is the number of alternative preventive maintenance schemes, 1≤i≤m,1≤j≤n,1≤k≤m; For the jth indicator B j , all schemes are calculated separately according to formula (4), and the total similarity after aggregation is calculated by formula (5): The total similarity of all indicators for all solutions should be within R j The maximum similarity deviation maximization model and Lagrangian function are constructed as follows: make: have to: R j ′ is standardized, and the similarity calculation formula of the index can be obtained (6): Among them, maxD(R j ) to make the total similarity in R j The similarity deviation maximization model of the maximum structure under the action, λ is the Lagrange multiplier, L(R j ,λ) is to make the total similarity in R j The Lagrangian function of the maximum structure under the action, R j is the total similarity of the jth index, is the similarity of two normalized triangular fuzzy numbers, j is the jth element, i is the ith element, k is the kth element, i≠k, m is the number of alternative preventive maintenance schemes, and n is the number of factor indicators that affect the selection of pavement maintenance schemes.

4. The method for multi-attribute decision-making for preventive maintenance of asphalt pavement based on optimized triangular fuzzy numbers according to claim 3 is characterized in that: In step 4, the specific method of calculating the reliability is as follows: In the normalized matrix, the indicator B j In the scheme A i The calculation formula of entropy is formula (7): in, is the normalized triangular fuzzy number of the jth index in the i-th scheme, t Lij is the lower bound of the normalized triangular fuzzy number, t Uij is the upper bound of the normalized triangular fuzzy number, r is the similarity between two elements; All indicators for the i-th solution X i The sum of the entropy is formula (8): Among them, S ij is the entropy of the jth indicator in the i-th solution, is the normalized triangular fuzzy number of the jth index in the i-th scheme, j is the jth element, i is the i-th element, and n is the number of factor indicators that affect the selection of pavement maintenance schemes; Plan A i Medium Index B j Reliability F ij Formula (9): Among them, S ij is the entropy of the jth indicator in the i-th solution, is the normalized triangular fuzzy number of the jth index in the i-th scheme, S i is the sum of the entropy of all indicators in the i-th solution, F ij is the reliability of the jth indicator in the i-th solution.

5. The method for multi-attribute decision-making for preventive maintenance of asphalt pavement based on optimized triangular fuzzy numbers according to claim 4 is characterized in that: In step 5, the specific method of weighted post-processing is as follows: According to formula (10), the weight of each indicator based on reliability is obtained: w ij =R j (1-F ij ) (10) Among them, w ij is the weight of the jth indicator in the i-th solution, R j is the total similarity of the jth index, F ij is the reliability of the jth indicator in the i-th scheme; The weighted comprehensive value of each solution is calculated according to formula (11): in, is the weighted comprehensive value of the ith solution, w ij is the weight of the jth indicator in the i-th solution, is the normalized triangular fuzzy number of the jth index in the i-th scheme, j is the jth element, and n is the number of factor indexes that affect the selection of pavement maintenance schemes; According to formulas (12) and (13), the weighted comprehensive values ​​of the schemes are compared with each other in terms of the probability measurement values, and a probability comparison relationship matrix is ​​constructed: in, ρ is the decision maker’s risk preference, t L is the lower bound of the normalized triangular fuzzy number, t M is the normalized triangular fuzzy number mode, t U is the upper bound of the normalized triangular fuzzy number; Among them, A i is the i-th preventive maintenance technical solution, A k is the kth preventive maintenance technical solution, is the weighted comprehensive value of the ith solution, is the weighted comprehensive value of the kth solution, i≠k; According to formula (14), the overall comparative possibility of each scheme is calculated as follows: Where m is the number of alternative preventive maintenance plans, g(A i >A k ) is the probability measurement value of comparing the i-th and k-th preventive maintenance technical solutions, is the overall comparative possibility of the i-th option; right Sorting in descending order can get the optimal solution.

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