Four-new pavement maintenance technology post-evaluation method for improving clustering iteration and preference

Abstract

The invention relates to the technical field of road maintenance, in particular to a four-new road surface maintenance technology post-evaluation method for improving clustering iteration and preference, which comprises the following steps: step 1, assuming that w four-new technology project samples form a set, and the four-new technology samples comprise u index characteristic values; performing normalization processing on each sample index value in the w sample matrixes so as to eliminate the influence of dimensions among the indexes, and obtaining an index characteristic value normalization matrix; according to the method, an augmented Lagrangian multiplier meeting the preference constraint of a decision maker is added to a target function of a fuzzy clustering iteration model, and a relaxation factor is introduced to obtain an iteration formula of an optimal fuzzy clustering center, an optimal fuzzy membership matrix and an optimal index weight which meet the preference of the decision maker; the problem that the secondary index weight is too large when a traditional fuzzy clustering iteration model is used for clustering is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of highway maintenance, and particularly to a post-evaluation method for four-new pavement maintenance technology that improves clustering iteration and preference, which can, on the basis of considering the preferences of decision-makers, avoid the problem of excessive weights of secondary indicators in traditional methods and realize the post-evaluation of the maintenance effects of multiple four-new technology projects for pavement maintenance. Background Technique

[0003] The introduction of new technologies, new materials, new processes, and new equipment ("four new technologies") has brought new changes to the field of road maintenance. The application of these innovative technologies not only aims to improve the accuracy and efficiency of road maintenance, but also to optimize resource allocation, reduce the impact on the environment, and achieve sustainable development.

[0004] At present, although some experts at home and abroad have conducted research on pavement maintenance evaluation, as an emerging technology classification, the "four new" technologies have not yet formed a unified standard and lack a dedicated evaluation method. Summary of the Invention

[0005] The purpose of the present invention is to solve the deficiencies in the prior art and propose a post-evaluation method for four-new pavement maintenance technology that improves clustering iteration and preference. This method can, on the basis of considering the preferences of decision-makers, avoid the problem of excessive weights of secondary indicators in traditional methods and realize the post-evaluation of the maintenance effects of multiple four-new technology projects for pavement maintenance.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A post-evaluation method for four-new pavement maintenance technology that improves clustering iteration and preference includes the following steps:

[0008] Step 1, data definition:

[0009] Assume that there are w four-new technology project samples that form a set, and the four-new technology samples contain u index eigenvalue:

[0010] B=(b ij )(i = 1, 2,..., u, j = 1, 2,..., w)

[0011] Among them, B is the initial matrix of index eigenvalues, b ij is the initial index value of each sample, i is the i-th index eigenvalue, j is the j-th four-new technology sample, w is the number of four-new technology project samples, and u is the number of index eigenvalues;

[0012] Step 2, normalization processing:

[0013] According to the fuzzy set optimization theory, normalize the index values of each sample in the above w sample matrices to eliminate the influence of the dimension between each index, and obtain the normalized matrix A=(aij ):

[0014]

[0015] Among them, A is the matrix for normalizing the index eigenvalue, and a ij is the normalized number of the index eigenvalue; 0 ≤ a ij ≤ 1; i = 1, 2,..., u, j = 1, 2,..., w;

[0016] Step 3, clustering:

[0017] Suppose w samples are classified into v categories according to u indicators for clustering, then the fuzzy clustering matrix C = (c kj ):

[0018]

[0019] Among them, C is the fuzzy clustering matrix, and c kj is the relative membership degree of sample j belonging to category v, v is the number of categories, k = 1, 2,..., v, j = 1, 2,..., u, c kj satisfies the following condition (1):

[0020]

[0021] Suppose the normalized numbers of the u index eigenvalues of category v are the clustering centers of category k, then the clustering centers of v categories can be represented by the u×v order fuzzy clustering center matrix D = (d ik ):

[0022]

[0023] Among them, D is the fuzzy clustering center matrix, and d ik is the normalization of the clustering center of index i of category k, 0 ≤ d ik ≤ 1; i = 1, 2,..., u, k = 1, 2,..., v;

[0024] Step 4, establish the objective function;

[0025] Step 5, constraint solution.

[0026] Preferably, in step 3, the generalized Euclidean distance (2) is used to represent the difference between sample j and category k:

[0027]

[0028] Among them, e kj is the generalized Euclidean distance formula representing the difference between sample j and category k, w i is the weight of the i-th index, a ijis the normalized number of index eigenvalues, d ik is the normalization of the clustering center of index i in category k, i is the i-th index eigenvalue, u is the number of index eigenvalues, and the weight vector W=(w1, w2,..., w u ), then w i satisfies the constraint (3):

[0029]

[0030] where w i is the weight of the i-th index, i is the i-th index eigenvalue, and u is the number of index eigenvalues.

[0031] Preferably, in step 4, the specific method includes: the relative membership degree of sample j belonging to category k is c kj , to solve the optimal relative membership degree of sample j belonging to category k. For a given c kj , c kj and w i , the smaller F(c kj , d ik , w i ) is, the closer sample j is to category k, and the better the clustering result. Therefore, the following objective function can be established:

[0032]

[0033] where w i is the weight of the i-th index, a ij is the normalized number of index eigenvalues, d ik is the normalization of the clustering center of index i in category k, c kj is the relative membership degree of sample j belonging to category v, i is the i-th index eigenvalue, j is the j-th "four new" technology sample, u is the number of index eigenvalues, w is the number of "four new" technology project samples, and v is the number of categories.

[0034] Preferably, in step 5, the specific method includes: the sum of squares of the weighted generalized Euclidean weights of the "four new" technology sample set for all categories is the smallest. According to the Lagrange function method, under the condition of satisfying the constraint conditions (1) and (3), the elements in the weight vector W, the fuzzy membership degree matrix C, and the fuzzy clustering center matrix D are obtained according to formulas (5) - (7):

[0035]

[0036] Preferably, for the convenience of calculation, it is assumed that the decision maker believes that the first index is the most important, that is, the weight of the first index is the largest, w1≥w i , i = 2, 3,..., u. Therefore, here it is necessary to separate w1 and add a relaxation factor αi (α i ≥ 0), the inequality constraint \(w_1\geq w\) i is transformed into an equality constraint \(w_1 - w\) i = α i , that is, making \(w_1 - w\) i equal to a number not less than 0 can achieve the decision-maker preference constraint of \(w_1\geq w\) i ;

[0037] Let:

[0038]

[0039] In the first step: Assume other variables are known, combine the objective function formula (4) and the constraint condition formula (3) to construct the Lagrangian function \(L\) as formula (9), and find the expression of \(w\) i :

[0040] Let:

[0041]

[0042] where α is the Lagrange multiplier, \(w\) i is the weight of the \(i\)-th index, \(w_1\) is the weight of the first index, \(a\) ij is the normalized number of index eigenvalue specifications, \(d\) ik is the normalized clustering center of the \(i\)-th index of category \(k\), \(c\) kj is the relative membership degree of sample \(j\) belonging to category \(v\), \(i\) is the \(i\)-th index eigenvalue, \(j\) is the \(j\)-th "four new" technology sample, \(u\) is the number of index eigenvalues, \(w\) is the number of "four new" technology project samples, and \(v\) is the number of categories;

[0043] Take the partial derivative of \(w\) i (\(i = 2, 3,..., u\)) according to formula (9), and let the partial derivative be equal to 0, that is:

[0044]

[0045] where \(g\) i is the constraint condition of the \(i\)-th index, α is the Lagrange multiplier, \(w\) i is the weight of the \(i\)-th index, \(i\) is the \(i\)-th index eigenvalue, and \(u\) is the number of index eigenvalues;

[0046] The expression of \(w\) i can be obtained as formula (11):

[0047]

[0048] Take the partial derivative of α according to formula (9):

[0049]

[0050] Then we can get:

[0051]

[0052] Substitute equation (11) into equation (13), that is:

[0053]

[0054] Then:

[0055]

[0056] Substitute equation (15) into equation (11) again, we can get:

[0057]

[0058] Move the term g in front of the summation symbol i into and change the summation subscript i in the term to l, then: That is, the expression of w i is equation (17):

[0059]

[0060] where w1 is the weight of the first index, a ij is the normalized number of index eigenvalues, d ik is the normalized clustering center of index i of category k, c kj is the relative membership degree of sample j belonging to category v, i is the i-th index eigenvalue, j is the j-th "four new" technology sample, u is the number of index eigenvalues, w i is the number of "four new" technology project samples, and v is the number of categories;

[0061] Step 2: Assume that other variables are known. Combine the objective function equation (4) with the constraint equation w1 - w i = β i to construct the Lagrangian function L′ and find the expression of w1 in equation (18):

[0062]

[0063] where β i is the relaxation factor (β i ≥ 0), and χ i is the constraint coefficient;

[0064] According to equation (18), take the partial derivative of w1 and set the partial derivative equal to 0, that is:

[0065]

[0066] Among them, \(w_1\) is the weight of the first index,

[0067] It can be obtained that:

[0068]

[0069] According to Equation (18), taking the partial derivative of \(\chi\) i gives:

[0070]

[0071] Substitute Equation (20) into Equation (21), that is:

[0072]

[0073] Then:

[0074]

[0075] Furthermore, it can be obtained that:

[0076]

[0077] Substitute Equation (24) into Equation (20), then the expression of \(w_1\) can be obtained:

[0078]

[0079] \(w_1\) is the weight of the first index, \(a\) ij is the normalized number of index eigenvalue specifications, \(d\) ik is the normalized clustering center of index \(i\) of category \(k\), \(c\) kj is the relative membership degree of sample \(j\) belonging to category \(v\), \(i\) is the \(i\)-th index eigenvalue, \(j\) is the \(j\)-th four-new technology sample, \(u\) is the number of index eigenvalues, \(w\) i is the weight of the \(i\)-th index, \(v\) is the number of categories, \(\beta\) i is the relaxation factor.

[0080] Step 3: Find the expression of the relaxation factor \(\beta\) i Since \(w_1 - w\) i -\(\beta\) i = 0, and \(\beta\) i ≥ 0, then the possible expression of \(\beta\) i is:

[0081] \(\beta\) i = |\(w_1 - w\) i |, (\(i = 2, 3, \cdots, u\)) (26)

[0082] Among them, \(\beta\) i is the relaxation factor, \(w_1\) is the weight of the first index, \(w\)i is the weight of the i-th index, i is the eigenvalue of the i-th index, and u is the number of index eigenvalues.

[0083] Therefore, the optimal weight vector expression (5) obtained by solving is changed to equations (17), (25), and (26). The steps to solve the fuzzy clustering loop iteration model are as follows:

[0084] 1. Set the maximum number of iterations Z of the model;

[0085] 2. Let the iteration number n = 0, and randomly generate a

[0086] 3. Substitute into equation (6) to find the corresponding fuzzy membership matrix

[0087] 4. Substitute into equation (7) to find the next fuzzy clustering center matrix

[0088] 5. Substitute into equation (17) to find the next partial index weight

[0089] 6. Substitute into equation (26) to find the next deviation perturbation term

[0090] 7. Substitute into equation (25) to find the next index weight

[0091] 8. Substitute into equation (6) to find the next approximate fuzzy clustering matrix

[0092] 9. Judge whether the constraint conditions are satisfied. If satisfied, output the obtained Otherwise, n = n + 1, and return to (3);

[0093] 10. Assign the finally output by the model to c p , assign to d p , and assign to w p ;

[0094] To improve the accuracy of the model, it is recommended to repeat the above process multiple times, compare the objective function values obtained from multiple results, and use the optimal relative membership degree matrix c corresponding to the minimum objective function value p , the optimal fuzzy clustering center matrix d p and the optimal weight vector w p as the final result of the model;

[0095] Step 4: Calculate the comprehensive evaluation value of each maintenance plan, as shown in Equation (27):

[0096]

[0097] where Q i is the comprehensive evaluation value of the i-th maintenance plan, w pj is the optimal weight vector of the j-th new technology and new material sample under the decision maker's preference, R is the index feature normalization matrix, and w is the number of index feature values.

[0098] Compared with the prior art, the present invention has the following beneficial effects:

[0099] 1. By adding an augmented Lagrangian multiplier that satisfies the decision maker's preference constraint to the objective function of the fuzzy clustering iteration model, and introducing a relaxation factor to obtain the iterative formulas for the optimal fuzzy clustering center, optimal fuzzy membership degree matrix, and optimal index weight that satisfy the decision maker's preference, the present invention overcomes the problem of excessive weight of secondary indicators when clustering with the traditional fuzzy clustering iteration model.

[0100] 2. The present invention provides a theoretical basis for determining the decision-making priority order under different preferences of decision makers, can be applied to different preference situations, formulate different preference schemes according to the characteristics of different regions, and provide a technical basis for the decision-making of decision makers. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 is the flow chart of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0102] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, so that those skilled in the art can better understand the advantages and features of the present invention, and thus make 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, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0103] An evaluation method for the post-evaluation of new technology and new material pavement maintenance that improves clustering iteration and preference includes the following steps:

[0104] Step 1, Data Definition:

[0105] Assume there is a set composed of w "Four New" technology project samples, where the "Four New" technology samples contain u index eigenvalue:

[0106] B = (b ij )(i = 1, 2, …, u, j = 1, 2,..., w)

[0107] Among them, B is the initial matrix of index eigenvalues, b ij is the initial index value of each sample, i is the i-th index eigenvalue, j is the j-th "Four New" technology sample, w is the number of "Four New" technology project samples, and u is the number of index eigenvalues;

[0108] Step 2: Normalization Processing:

[0109] According to the fuzzy set optimization theory, normalize the index values of each sample in the above w sample matrices to eliminate the influence of the dimension between each index, and obtain the normalized matrix A = (a ij ):

[0110]

[0111] Among them, A is the normalized matrix of index eigenvalues, a ij is the normalized number of index eigenvalues; 0 ≤ a ij ≤ 1; i = 1, 2,..., u, j = 1, 2,..., w;

[0112] Step 3, Clustering:

[0113] Suppose w samples are classified into v categories according to u indexes for clustering, then the fuzzy clustering matrix C = (c kj ):

[0114]

[0115] Among them, C is the fuzzy clustering matrix, c kj is the relative membership degree that sample j belongs to category v, v is the number of categories, k = 1, 2,..., v, j = 1, 2,..., u, c kj satisfies the following condition (1):

[0116]

[0117] Suppose the normalized numbers of u index eigenvalues of category v are the clustering centers of category k, then the clustering centers of v categories can be represented by a u×v order fuzzy clustering center matrix D = (d ik ):

[0118]

[0119] Among them, D is the fuzzy clustering center matrix, and d ik is the normalization of the clustering center of index i in category k, where 0 ≤ d ik ≤ 1; i = 1, 2,..., u, k = 1, 2,..., v;

[0120] Step 4: Establish the objective function;

[0121] Step 5: Solve the constraints.

[0122] Specifically, in Step 3, the generalized Euclidean distance (2) is used to represent the difference between sample j and category k:

[0123]

[0124] Among them, e kj is the generalized Euclidean distance formula representing the difference between sample j and category k, w i is the weight of the i-th index, a ij is the normalization number of the index eigenvalue, d ik is the normalization of the clustering center of index i in category k, i is the i-th index eigenvalue, u is the number of index eigenvalues, and the weight vector W = (w1, w2,..., w u ), then w i satisfies the constraint (3):

[0125]

[0126] Among them, w i is the weight of the i-th index, i is the i-th index eigenvalue, and u is the number of index eigenvalues.

[0127] Specifically, in Step 4, the specific method includes: the relative membership degree of sample j belonging to category k is c kj , to solve the optimal relative membership degree of sample j belonging to category k. For a given c kj , c kj and w i , the smaller F(c kj , d ik , w i ) is, the closer sample j is to category k, and the better the clustering result. Therefore, the following objective function can be established:

[0128]

[0129] Among them, w i is the weight of the i-th index, a ij is the normalization number of the index eigenvalue, d ik is the normalization of the clustering center of index i in category k, ckj is the relative membership degree of sample j belonging to category v, i is the i-th index eigenvalue, j is the j-th "Four New" technology sample, u is the number of index eigenvalues, w is the number of "Four New" technology project samples, and v is the number of categories.

[0130] Specifically, in step 5, the specific method includes: the sum of squares of the weighted generalized Euclidean weights of the "Four New" technology sample set for all categories is the smallest. According to the Lagrange function method, under the condition of satisfying constraints (1) and (3), the elements of the weight vector W, the fuzzy membership matrix C, and the fuzzy clustering center matrix D are obtained according to formulas (5) to (7):

[0131]

[0132] Specifically, for the convenience of calculation, it is assumed that the decision maker believes that the first index is the most important, that is, the weight of the first index is the largest w1≥w i , i = 2, 3,..., u. Therefore, it is necessary to separate w1 here and add a relaxation factor α i (α i ≥0), and transform the inequality constraint w1≥w i into an equality constraint w1 - w i = α i , that is, making w1 - w i equal to a number not less than 0 can achieve the decision maker's preference constraint condition of w1≥w i ;

[0133] Let:

[0134]

[0135] The first step: Assume that other variables are known, combine the objective function formula (4) with the constraint condition formula (3), construct the Lagrange function L as formula (9), and find the expression of w i :

[0136] Let:

[0137]

[0138] Among them, α is the Lagrange multiplier, w i is the weight of the i-th index, w1 is the weight of the first index, a ij is the normalized number of index eigenvalues, d ik is the normalization of the clustering center of category k for index i, c kj is the relative membership degree of sample j belonging to category v, i is the i-th index eigenvalue, j is the j-th "Four New" technology sample, u is the number of index eigenvalues, w is the number of "Four New" technology project samples, and v is the number of categories;

[0139] Take the partial derivative of \(w\) according to Equation (9) i (where \(i = 2, 3, \cdots, u\)) and set the partial derivative equal to 0, that is:

[0140]

[0141] where \(g\) i is the constraint condition of the \(i\)-th index, \(\alpha\) is the Lagrange multiplier, \(w\) i is the weight of the \(i\)-th index, \(i\) is the eigenvalue of the \(i\)-th index, and \(u\) is the number of eigenvalue of the index;

[0142] The expression of \(w\) i can be obtained as Equation (11):

[0143]

[0144] Take the partial derivative of \(\alpha\) according to Equation (9):

[0145]

[0146] Then we can get:

[0147]

[0148] Substitute Equation (11) into Equation (13), that is:

[0149]

[0150] Then:

[0151]

[0152] Substitute Equation (15) into Equation (11) again, we can get:

[0153]

[0154] Move the term \(g\) in front of the summation symbol i into and change the summation subscript \(i\) in the term to \(l\), then: That is, the expression of \(w\) i is Equation (17):

[0155]

[0156] where \(w1\) is the weight of the first index, \(a\) ij is the normalized number of the eigenvalue of the index, \(d\) ik is the normalized clustering center of the \(i\)-th index of category \(k\), \(c\) kjis the relative membership degree that sample j belongs to category v, i is the i-th index eigenvalue, j is the j-th "Four New" technology sample, u is the number of index eigenvalues, w is the number of "Four New" technology project samples, and v is the number of categories;

[0157] Step 2: Assume that other variables are known. The objective function formula (4) combines with the constraint formula w1 - w i = β i Construct the Lagrangian function L′ and obtain the expression (18) of w1:

[0158]

[0159] where β i is the relaxation factor (β i ≥ 0), and χ i is the constraint coefficient;

[0160] According to formula (18), take the partial derivative of w1 and set the partial derivative equal to 0, that is:

[0161]

[0162] where w1 is the weight of the first index,

[0163] It can be obtained that:

[0164]

[0165] According to formula (18), take the partial derivative of χ i and the result is:

[0166]

[0167] Substitute formula (20) into formula (21), that is:

[0168]

[0169] Then:

[0170]

[0171] Furthermore, it can be obtained that:

[0172]

[0173] Substitute formula (24) into formula (20), and then the expression of w1 can be obtained:

[0174]

[0175] Step 3: Find the expression of the relaxation factor β i Since w1 - w i - β i= 0, and β i ≥ 0, then it is possible that β i The expression of:

[0176] β i = |w1 - w i |, (i = 2, 3, …, u) (26)

[0177] Therefore, the obtained optimal weight vector expression (5) is changed to equations (17)(25)(26). The steps to solve the fuzzy clustering cyclic iteration model are as follows:

[0178] 1. Set the maximum number of iterations Z of the model;

[0179] 2. Let the number of iterations n = 0, and randomly generate a

[0180] 3. Substitute into equation (6) to find the corresponding fuzzy membership matrix

[0181] 4. Substitute into equation (7) to find the next fuzzy clustering center matrix

[0182] 5. Substitute into equation (17) to find the next partial index weight

[0183] 6. Substitute into equation (26) to find the next deviation perturbation term

[0184] 7. Substitute into equation (25) to find the next index weight

[0185] 8. Substitute into equation (6) to find the next approximate fuzzy clustering matrix

[0186] 9. Judge whether the constraint conditions are satisfied. If satisfied, output the obtained Otherwise, n = n + 1, and return to (3);

[0187] 10. Assign the finally output by the model to c p , assign to d p , and assign to wp ;

[0188] To improve the accuracy of the model, it is recommended to repeat the above process multiple times, compare the objective function values obtained from multiple results, and take the optimal relative membership degree matrix c corresponding to the minimum objective function value p , the optimal fuzzy clustering center matrix d p and the optimal weight vector w p as the final result of the model;

[0189] Step 4: Calculate the comprehensive evaluation value of each maintenance plan, as shown in Equation (27):

[0190]

[0191] where Q i is the comprehensive evaluation value of the i-th maintenance plan, w pj is the optimal weight vector of the j-th new technology and new material sample under the decision-maker's preference, R is the index feature normalization matrix, and w is the number of index feature values.

[0192] Example:

[0193] The index values of material performance and adaptability degree are obtained by the Delphi method; the pavement condition, service life, manager cost, user cost, and carbon emission indexes are calculated from the reported data of the sample road sections. The data is normalized, and the specific case data is shown in Table 1.

[0194] Table 1 Case road sample data

[0195]

[0196]

[0197] Pavement performance evaluation is the basis for pavement maintenance and repair. Therefore, the pavement condition index is set to the maximum. That is, w2≥w i (i≠2). The obtained weights are shown in the table, the sorting results are shown in the table, and the optimal membership degree matrix is shown in Table 2.

[0198] Table 2 Index weights with and without preference

[0199]

[0200] It can be seen that under the condition of no preference constraint, the two cost indexes of manager cost and user cost are relatively large, while the pavement condition is relatively small. When the road performance is the preference, the pavement condition is the largest, followed by the manager cost index and the carbon emission index. It can be seen that the index weights with preference are more suitable for the post-evaluation of the "four new" technology pavement maintenance of asphalt pavement.

[0201] To verify the effectiveness of the method proposed in the present invention, it was compared with other methods, and the results are shown in Table 3.

[0202] Table 3 Comparison of Weights of Different Methods

[0203]

[0204] It can be seen that the weight trend of Document 1 is generally the same as that of the present invention, but the weights obtained from Document 1 are close, and the discrimination is small.

[0205] For the two objective weighting methods of the CRITIC method and Document 2, the calculation results show that the management cost is the largest, followed by the pavement condition. However, the pavement condition index is an important index for judging pavement performance. Secondly, it is necessary to achieve the goals of reducing management costs, carbon emissions, environmental pollution, etc. as much as possible. Therefore, compared with the objective weighting method, the weights obtained by the present invention are more scientific and reasonable.

[0206] The comprehensive evaluation values of each maintenance plan are calculated according to formula (27) as follows:

[0207] Q1 = 66.82

[0208] Q2 = 72.42

[0209] After obtaining the comprehensive evaluation values, referring to the evaluation grade table (Table 4), the evaluation of the maintenance plan is obtained. In this case, both plans are in the rating interval of [60, 80], and both are of good grades.

[0210] Table 4 Evaluation Grade Table

[0211]

[0212] In summary, the present invention provides a theoretical basis for decision-makers to determine the decision priority order under different preferences, can be applied to different preference situations, formulate different preference plans according to the characteristics of different regions, and provide a technical basis for decision-makers' decisions.

[0213] The descriptions and practices disclosed in the present invention are easy to think and understand for ordinary technical personnel in the technical field. And without departing from the principle of the present invention, several improvements and retouches can be made. Therefore, the modifications or improvements made without deviating from the spirit of the present invention should also be regarded as within the protection scope of the present invention.

Claims

1. A post-evaluation method for four new pavement maintenance technologies with improved clustering iteration and preference, characterized in that: The steps include: Step 1: Data definition: Assume that there are w four-new technology project samples forming a set, where the four-new technology samples contain u indicator characteristic values: B=(b ij )(i=1,2,…,u,j=1,2,…,w) Among them, B is the initial matrix of indicator eigenvalues, b ij is the initial index value of each sample, i is the characteristic value of the i-th index, j is the j-th four new technology sample, w is the number of samples of the four new technology projects, and u is the number of indicator characteristic values; Step 2: Normalization: According to the fuzzy set optimization theory, the index values ​​of each sample in the above w sample matrix are normalized to eliminate the influence of the dimensions between the indicators, and the index eigenvalue normalization matrix A is obtained. ij ): Among them, A is the normalized matrix of indicator eigenvalues, a ij is the normalized number of the indicator eigenvalue; 0≤a ij ≤1;i=1,2,…,u,j=1,2,…,w; Step 3: Clustering: Assume that w samples are divided into v categories according to u indicators for clustering, then the fuzzy clustering matrix C = (c kj ): Among them, C is the fuzzy clustering matrix, c kj is the relative membership of sample j to category v, v is the number of categories, k = 1, 2, ..., v, j = 1, 2, ..., u, c kj The following condition formula (1) is satisfied: Assume that the normalized number of u index eigenvalues ​​of category v is the cluster center of category k, then the cluster centers of v categories are represented by the u×v order fuzzy cluster center matrix D = (d ik )express: Where D is the fuzzy cluster center matrix, d ik is the normalized cluster center of category k index i, 0≤d ik ≤1;i=1,2,…,u,k=1,2,…,v; Step 4: Establish the objective function; Step 5: Solve the constraints.

2. The improved clustering iteration and preference post-evaluation method of four new pavement maintenance technologies according to claim 1 is characterized in that: In step 3, the generalized Euclidean distance formula (2) is used to express the difference between sample j and category k: Among them, e kj is the generalized Euclidean distance formula representing the difference between sample j and category k, w i is the weight of the ith indicator, a ij is the normalized number of the indicator eigenvalue, d ik is the normalized cluster center of category k index i, i is the i-th index eigenvalue, u is the number of index eigenvalues, and the weight vector W = (w1, w2, ..., w u ), then w i Satisfy the constraint formula (3): Among them, w i is the weight of the ith indicator, i is the eigenvalue of the ith indicator, and u is the number of eigenvalues ​​of the indicator.

3. The improved clustering iteration and preference post-evaluation method of four new pavement maintenance technologies according to claim 2 is characterized in that: In step 4, the specific method includes: the relative membership degree of sample j to category k is c kj , in order to find the optimal relative membership of sample j to category k, for a given c kj , c kj and w i ,F(c kj ,d ik ,w i ) is smaller, indicating that the sample j is closer to the category k, and the clustering result is better. Therefore, the following objective function is established: Among them, w i is the weight of the ith indicator, a ij is the normalized number of the indicator eigenvalue, d ik is the normalized cluster center of category k index i, c kj is the relative membership of sample j to category v, i is the ith indicator characteristic value, j is the jth four new technology sample, u is the number of indicator characteristic values, w is the number of four new technology project samples, and v is the number of categories.

4. The improved clustering iteration and preference post-evaluation method of four new pavement maintenance technologies according to claim 3 is characterized in that: In step 5, the specific method includes: the sum of squares of weighted generalized Euclidean weighted distances of the four new technology sample sets for all categories is minimized, and according to the Lagrangian function method, under the condition of satisfying constraints (1) and (3), the weight vector W, the fuzzy membership matrix C and the fuzzy cluster center matrix D are obtained according to formulas (5) to (7):

5. The improved clustering iteration and preference post-evaluation method of four new pavement maintenance technologies according to claim 4 is characterized in that: For ease of calculation, assume that the decision maker believes that the first indicator is the most important, that is, the first indicator has the largest weight w1≥w i ,i=2,3,…,u, so here we need to separate w1 and add a relaxation factor α i , α i ≥0, and constrain the inequality w1≥w i Transformed into the equality constraint w1-w i =α i , that is, w1-w i If it is equal to a number not less than 0, w1≥w can be achieved i The decision maker's preference constraints; make: Step 1: Assume that other variables are known, combine the objective function formula (4) with the condition formula (3), construct the Lagrangian function L as formula (9), and calculate w i The expression is: make: Among them, α is the Lagrange multiplier, w i is the weight of the i-th indicator, w1 is the weight of the first indicator, a ij is the normalized number of the indicator eigenvalue, d ik is the normalized cluster center of category k index i, c kj is the relative membership of sample j to category v, i is the ith indicator characteristic value, j is the jth four new technology sample, u is the number of indicator characteristic values, w is the number of four new technology project samples, and v is the number of categories; According to formula (9), w i (i=2,3,…,u) find the partial derivative and set it equal to 0, that is: Among them, g i is the constraint condition of the i-th index, α is the Lagrange multiplier, w i is the weight of the i-th indicator, i is the i-th indicator eigenvalue, and u is the number of indicator eigenvalues; Get w i The expression of is as follows: According to formula (9), the partial derivative of α is: Then we can get: Substituting equation (11) into equation (13), we get: but: Substituting (15) into (11) we can obtain: Put the summation symbol The preceding term g i Move to within, will If the summation subscript i in the term is changed to l, then: That is w i The expression of is (17): Among them, w1 is the weight of the first indicator, a ij is the normalized number of the indicator eigenvalue, d ik is the normalized cluster center of category k index i, c kj is the relative membership of sample j to category v, i is the ith indicator characteristic value, j is the jth four-technical sample, u is the number of indicator characteristic values, w is i is the weight of the i-th indicator, and v is the number of categories; Step 2: Assume that other variables are known, and the objective function (4) is combined with the constraint condition w1-w i =β i Construct the Lagrangian function L′ and find the expression (18) for w1: Among them, β i is the relaxation factor, β i ≥0, χ i is the constraint coefficient; According to formula (18), the partial derivative of w1 is calculated and set to 0, that is: Among them, w1 is the weight of the first indicator, We can get: According to formula (18), i Taking partial derivatives we get: Substituting formula (20) into formula (21), we get: but: Then we can get: Substituting formula (24) into formula (20), we can get the expression of w1: w1 is the weight of the first indicator, a ij is the normalized number of the indicator eigenvalue, d ik is the normalized cluster center of category k index i, c kj is the relative membership of sample j to category v, i is the ith indicator characteristic value, j is the jth four-technical sample, u is the number of indicator characteristic values, w is i is the weight of the i-th indicator, v is the number of categories, β i is the relaxation factor; Step 3: Find the relaxation factor β i The expression of w1-w i -β i =0, and β i ≥0, then it is possible that β i The expression is: β i =|w1-w i |,(i=2,3,…,u) (26) Among them, β i is the relaxation factor, w1 is the weight of the first indicator, and w i is the weight of the i-th indicator, i is the i-th indicator eigenvalue, and u is the number of indicator eigenvalues; Therefore, the optimal weight vector expression (5) obtained by solving is changed to equation (17)(25)(26). The steps for solving the fuzzy clustering iterative model are as follows:

1. Set the maximum number of iterations Z of the model; 2. Let the number of iterations n = 0, and randomly generate a 3. Substitute into equation (6) to obtain the corresponding fuzzy membership matrix 4. Substitute into formula (7) to obtain the fuzzy clustering center matrix for the next step:

5. Substitute into formula (17) to find the weights of some indicators in the next step 6. Substitute into equation (26) to obtain the deviation disturbance term for the next step:

7. Substitute into formula (25) to find the indicator weight for the next step 8. Substitute into equation (6) to obtain the approximate fuzzy clustering matrix for the next step:

9. Determine whether the constraints are met, and output the results if they are met Otherwise n=n+1, return to (3); 10. Output the model Assign to c p , Assign to d p , and Assign to w p ; To improve the accuracy of the model, it is recommended to repeat the above process multiple times, compare the objective function values ​​obtained from multiple results, and select the optimal relative membership matrix c corresponding to the minimum objective function value. p , the optimal fuzzy clustering center matrix d p and the optimal weight vector w p As the final result of the model; Step 4: Calculate the comprehensive evaluation value of each maintenance plan, as shown in formula (27): Among them, Q i is the comprehensive evaluation value of the ith maintenance plan, w pj is the optimal weight vector of the jth four new technology samples under the decision maker’s preference, R is the indicator feature normalization matrix, and w is the number of indicator eigenvalues.

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