CN109345029A - A kind of constructing tunnel preferred method based on improvement Topsis method - Google Patents

A kind of constructing tunnel preferred method based on improvement Topsis method Download PDF

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CN109345029A
CN109345029A CN201811254362.8A CN201811254362A CN109345029A CN 109345029 A CN109345029 A CN 109345029A CN 201811254362 A CN201811254362 A CN 201811254362A CN 109345029 A CN109345029 A CN 109345029A
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王景春
黄文化
陈思博
刘超
马永利
薛佳龙
叶竹
王昕巍
赵子甲
郭献雪
罗富亮
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Shijiazhuang Tiedao University
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Abstract

The invention discloses a kind of based on the constructing tunnel preferred method for improving Topsis method, the following steps are included: choosing benching tunnelling method, three-drift method, central drift method, main hole CRD method and main 5 kinds of constructing tunnel schemes of hole Ring Cutting provided core soil method, and according to 8 Index Establishment assessment indicator systems below 5 kinds of selected constructing tunnel scheme selections: Surrounding Rock Engineering Geological Conditions, Vault settlement, ground settlement, inverted arch protuberance, Great Wall sedimentation, project progress, project cost, Great Wall local dip rate；Subjective weights omega is determined using AHP method1, information Entropy Method determines objective weight ω2, and introduce game theory aggregate model and determine comprehensive weight；The calculating error that each ATTRIBUTE INDEX is generated by unit difference is eliminated using improved Topsis method；Exchange premium degree is improved using grey relational grade.The present invention on the basis of safety of Great Wall, chooses more reasonable construction method, maximizes income on construction jobs in guaranteeing work progress.

Description

A kind of constructing tunnel preferred method based on improvement Topsis method
Technical field
The invention belongs to technical field of tunnel construction, specifically, be related to it is a kind of based on improve Topsis method tunnel apply Work preferred method.
Background technique
With the development of domestic economy, network of highways is constantly expanded, and vcehicular tunnel is also more and more.Constructing tunnel must Can so have an adverse effect to ambient enviroment, different degrees of disturbance is generated to ground and underground structure building, is especially worn down The construction in ancient Great Wall tunnel, protection historical relic of the ancient Great Wall as state key, of the remote past, weathering is serious, extremely be easy by Disturbance destroys.In constructing tunnel, wall rock loosening, surface subsidence etc. may cause ancient Great Wall and destroy, therefore preferably right Great Wall disturbance is minimum most important with the arrangement and method for construction of maximum revenue.Common construction method has step in constructing tunnel The construction methods such as method, three-drift method, central drift method, main hole CRD method, main hole Ring Cutting remaining core soil in advance.
As the Hot Contents of constructing tunnel Scheme Optimum Seeking Methods research, a variety of theories are applied to preferred method.At present Preferably there is certain research achievement to constructing tunnel scheme.But in general there are still 2 aspect problems: 1) lacking a set of Influence evaluating indexesto scheme system that is comprehensive and fully considering tunnel superstructure；2) the most qualitative analysis of Scheme Optimum Seeking Methods or Using step analysis (analytic hierarchy process, AHP) method, subjectivity is strong, and cannot fully consider each finger Incidence relation between mark, without according to scheme containing constructing tunnel to the setting of the influence index weight of superstructure and preferred method into Row processing.These problems are always the difficult point of the area research.
Summary of the invention
In view of this, the present invention provides a kind of constructing tunnel preferred method based on improvement Topsis method, this method is adopted Combined with APH method and entropy assessment, the subjective and objective comprehensive weight of each evaluation index sought using game theory method, recycle geneva away from Topsis method is improved from grey relational grade, acquires more reasonable exchange premium degree, it is preferred to carry out construction method sequence.
In order to solve the above-mentioned technical problem, it is preferably square based on the constructing tunnel for improving Topsis method that the invention discloses a kind of Method, comprising the following steps:
Step 1 chooses evaluation index: choosing benching tunnelling method, three-drift method, central drift method, main hole CRD method and main hole annular and opens 5 kinds of constructing tunnel schemes of provided core soil method are dug, and are built according to 8 indexs below 5 kinds of selected constructing tunnel scheme selections Vertical assessment indicator system: Surrounding Rock Engineering Geological Conditions, Vault settlement, ground settlement, inverted arch protuberance, Great Wall sedimentation, Great Wall part Slope, project progress, project cost；
Step 2 determines weight: determining subjective weights omega using AHP method1, information Entropy Method determines objective weight ω2, and introduce Game theory aggregate model determines comprehensive weight；
Step 3 eliminates the calculating error that each ATTRIBUTE INDEX is generated by unit difference using improved Topsis method；
Step 4 improves exchange premium degree using grey relational grade.
Optionally, the Surrounding Rock Engineering Geological Conditions of the benching tunnelling method in the step 1 are as follows: be useful in IV, V grades it is weaker and save The country rock that haircut is educated, the requirement of Vault settlement are as follows: 50mm, the requirement of ground settlement are as follows: 24mm, the requirement of inverted arch protuberance are as follows: 40mm, the requirement of Great Wall sedimentation are as follows: 6mm, the requirement of Great Wall local dip rate are as follows: 6, the requirement of project progress are as follows: 90 days, engineering The requirement of cost are as follows: 40,000/m；
The Surrounding Rock Engineering Geological Conditions of main hole CRD method are as follows: be suitable for IV, V grades of weak surrounding rocks, the requirement of Vault settlement are as follows: 20mm, the requirement of ground settlement are as follows: 10mm, the requirement of inverted arch protuberance are as follows: 15mm, the requirement of Great Wall sedimentation are as follows: 2mm, Great Wall office The requirement of portion's slope are as follows: 2, the requirement of project progress are as follows: 150 days, the requirement of project cost are as follows: 60,000/m；
The Surrounding Rock Engineering Geological Conditions of central drift method are as follows: be applicable in V, VI grade of country rock double-arched tunnel, the requirement of Vault settlement Are as follows: 35mm, the requirement of ground settlement are as follows: 18mm, the requirement of inverted arch protuberance are as follows: 30mm, the requirement of Great Wall sedimentation are as follows: 4mm, Great Wall The requirement of local dip rate are as follows: 4, the requirement of project progress are as follows: 110 days, the requirement of project cost are as follows: 50,000/m；
The Surrounding Rock Engineering Geological Conditions of three-drift method are as follows: be suitable for V, VI grade of country rock two-wire or multiple track tunnel engineering, vault The requirement of sedimentation are as follows: 30mm, the requirement of ground settlement are as follows: 15mm, the requirement of inverted arch protuberance are as follows: 28mm, the requirement of Great Wall sedimentation Are as follows: 4mm, the requirement of Great Wall local dip rate are as follows: 3, the requirement of project progress are as follows: 120 days, the requirement of project cost are as follows: 50,000/ m；
The Surrounding Rock Engineering Geological Conditions of main hole Ring Cutting provided core soil method are as follows: be suitable for VI grade of country rock single line and V- VI grade of country rock double track tunnel engineering, the requirement of Vault settlement are as follows: 35mm, the requirement of ground settlement are as follows: 15mm, inverted arch protuberance are wanted It asks are as follows: 10mm, the requirement of Great Wall sedimentation are as follows: 4mm, the requirement of Great Wall local dip rate are as follows: 4, the requirement of project progress are as follows: 110 It, the requirement of project cost are as follows: 50,000/m.
Optionally, weight is determined in the step 2 specifically:
Step 2.1 determines subjective weights omega using AHP method1: hierarchical structure is established according to n evaluation index of tunnel deformation, Evaluation index judgment matrix is constructed, while carrying out consistency check, and then acquire every evaluation index subjectivity weight W1(j), Middle j=1,2 ... n, n are index number；
Step 2.2 determines objective weight ω using information Entropy Method2:
Step 2.3, introducing game theory aggregate model determine comprehensive weight.
Optionally, hierarchical structure is established according to n evaluation index of tunnel deformation in the step 2.1, constructs evaluation index Judgment matrix, while consistency check is carried out, and then acquire every evaluation index subjectivity weight W1(j), specifically:
Step 2.1.1, judgment matrix A is established(k)。
The value of judgment matrix reflects people to the understanding of each element relative importance, generally uses 1~9 proportion quotiety pair Importance degree assignment.
Step 2.1.2, the weight of each layer index in AHP method is solved:
According to standard judgment matrix A, each factor is calculated in same substandard weight using feature vector method.First find out A Maximum eigenvalue λ max and corresponding this feature value feature vector, feature vector is normalized to obtain weight vectors For w1 (j)=(w1, w2 ..., wn), wherein j=1,2 ..., n；
Step 2.1.3, consistency check: AHP method requires to carry out consistency inspection after the weight vectors for obtaining judgment matrix It tests, to ensure the validity of every layer of judgment matrix.
Optionally, consistency check step in the step 2.1.3 specifically:
Step 2.1.3.1, the value of coincident indicator CI is calculated:
Step 2.1.3.2, corresponding Aver-age Random Consistency Index RI is calculated:
From 1,2 ..., 9 HesIt is pressed in totally 17 numbersAverage probability extract n uniformly randomly2It is a Number constitutes k rank pairwise comparison matrix A；It reruns repeatedly to generate the random judgment matrix A of multiple k ranksk, calculate each Coincident indicator is averaged, i.e.,
Step 2.1.3.3, the value of consistency ration CR is solved.
CR=CI/RI (3)
As consistency ration CR < 0.10, it is believed that the consistency of judgment matrix can receive, and otherwise cope with judgment matrix and make Appropriate amendment.
Optionally, objective weight ω is determined using information Entropy Method in the step 2.22Specifically:
Step 2.2.1, decision matrix is constructed:
Construct decision matrix A=(aij)m×n；I=1,2 ..., m；J=1,2 ..., n；Wherein, aijIndicate i-th kind of scheme J-th of index value, and standardized and turn to matrix R=(rij)m×n；That is:
J is profit evaluation model index:
J is cost type index:
Step 2.2.2, normalization matrix:
To Standard Process R=(rij)m×nIt is normalized to obtain matrix R '=(rij’)m×n；For rij: rij'= rij/∑rij；I=1,2 ..., m；J=1,2 ..., n；
Step 2.2.3, parameter rijComentropy EjWith index weights w2(j):
Particularly, work as rijWhen '=0, r is enabledij’lnrij'=0；W2It (j) is the weight coefficient of indices namely the power of index Weight, calculation formula are as follows:
Optionally, game theory aggregate model is introduced in the step 2.3 determine comprehensive weight specifically:
If determining the weight of n index using L kind method, then weight vectors are as follows: ω (k)=[ωk1, ωk2..., ωkn], k=1,2 ..., L；The linear combination of L weight vectors are as follows:
Wherein, ω indicates possible weight vectors collection, αkFor linear combination coefficient.Think of according to game theory aggregate model Think, exactly finds one group of linear combination coefficient αk, minimization ω and ωkDeviation between (k=1,2 ..., L), it may be assumed thatTo matrix derivation, the condition of optimal solution is obtained are as follows:
Solution equation group acquires linear combination coefficient (α1, α2..., αL), it is normalized to obtain:
So comprehensive weight are as follows:
Optionally, eliminate what each ATTRIBUTE INDEX was generated by unit difference using improved Topsis method in the step 3 Calculate error specifically:
Step 3.1 establishes decision matrix and is standardized
Establish decision matrix A=(aij)m×n, i=1,2 ..., m；J=1,2 ..., n, wherein aijIndicate jth kind scheme I index value；In order to eliminate influence of the different physical quantities guiding principle to the result of decision, needs to carry out standardization processing to it, be advised Generalized matrix R=(rij)m×n, detailed normalization method is as follows:
aijFor profit evaluation model index；aijFor cost type Index；
Step 3.2, construction weighted normal decision matrix
Known by step 2.3, the comprehensive weight determined by game theory aggregate model are as follows: ω*=(ω1, ω2..., ωn), n For scheme index number；If weighted normal decision matrix is G=(gij), wherein the element g in matrix GijAre as follows: gij=ωijrij, i=1,2 ..., m, j=1,2 ..., n；
Step 3.3 determines positive and negative ideal scheme and auxiliary ideal scheme
If positive ideal scheme are as follows: v+=(v1 +, v2 +..., vn +)T；Ill ideal solution are as follows: v?=(v1 -, v2 -..., vn -)T.? In m scheme, calculation method is as follows:
Step 3.4 calculates distance:
Known by step 2.2, the weighted normal decision matrix of evaluating indexesto scheme A is G=(gi1, gi2…gin)；
Mahalanobis distance its calculation formula is:
In formula, giThe vector of the n ATTRIBUTE INDEX composition of object is assessed for i-th；Covariance between each ATTRIBUTE INDEX Matrix is expressed as Σ i.e.: Σ=(σij)n×n
Wherein,
The mahalanobis distance of index system and plus-minus ideal solutions is calculated according to above formulaMahalanobis distance, which is applied, to be commented In valence analysis, the calculating error that each ATTRIBUTE INDEX is generated by unit difference is eliminated.
Optionally, exchange premium degree is improved using grey relational grade in the step 4 specifically:
Gray relative analysis method calculation of relationship degree formula are as follows:
In formula, wkFor index weights, xiIt (k) is assessment sequence, x0It (k) is reference sequence.According to above-mentioned calculated result, It willWithAfter progress unit unification simplifies, i-th of arrangement and method for construction A is constructediWith plus-minus ideal solutions S+、S-'s Synthesize approach degree are as follows:
Wherein, α 1, α 2 have been influence coefficient of the subjective factor to assessment object, work as α1+α2When=1, relative similarity degree are as follows:
Approach degree is based on mahalanobis distance and grey relational grade and improves, and it is excessively high and cause to compensate for correlation between ATTRIBUTE INDEX The excessive deficiency of Euclidean distance error；The sequence of m kind construction method exchange premium degree is preferred.
Compared with prior art, the present invention can be obtained including following technical effect:
1) weight of each evaluation index preferably influences constructing tunnel scheme very significant.Currently, the determination side of weight Method can divide 2 classes: subjective assignment method and objective assignment method.Subjective assignment method mainly relies on the knowledge and experience of expert to determine index Weight, weighted value can incorporation engineering actual conditions, but be easy influenced by expert individual's preference.Objective assignment method mainly from Mined information in objective data, objectivity is relatively strong but is easily separated from actual conditions.In order to make weights both refer to expert's meaning It is willing to be loyal to data itself again, the present invention determines subjective weights omega using AHP method1, information Entropy Method determines objective weight ω2, and introduce Game theory aggregate model determines comprehensive weight, which determines method than only by subjective and objective weight simple weighted average Method is more scientific, makes the preferred conclusion of scheme more closing to reality situation.
2) TOPSIS method is a kind of Multiattribute Decision analysis method, since it is easy, effective, and is answered extensively For solution optimal selection problem.But traditional TOPSIS decision-making technique cannot be evaluated positioned at positive ideal scheme and negative ideal Sample point on scheme perpendicular bisector, i.e., sample point close apart from positive ideal scheme are also close apart from ill ideal solution.This method passes through Horse formula distance and grey relational grade are combined and improve exchange premium degree, to solve perpendicular bisector contradictory problems instead of Euclidean distance.
3) present invention on the basis of safety of Great Wall, chooses more reasonable construction method, makes work in guaranteeing work progress Journey maximum revenue.To provide more systematic reference and solution in some reference selection of construction method problem.
Certainly, it implements any of the products of the present invention it is not absolutely required to while reaching all the above technical effect.
Specific embodiment
Carry out the embodiment that the present invention will be described in detail below in conjunction with embodiment, whereby to the present invention how application technology hand Section solves technical problem and reaches the realization process of technical effect to fully understand and implement.
The invention discloses a kind of based on the constructing tunnel preferred method for improving Topsis method, comprising the following steps:
Step 1): the selection of evaluation index:
Since the factor for influencing constructing tunnel scheme selection is various, including geological conditions, Lithology type, rainfall, Gu The excavation response on Great Wall, country rock and tunnel structure the factors such as deformation, environmental effect, the impact effect that every kind of arrangement and method for construction generates Not identical, therefore, scheme optimizing evaluation index should be chosen according to the de-stabilising effect of Specific construction scheme generation.Consider institute The 5 kinds of constructing tunnel schemes (as shown in table 1) chosen, obtain related data through expert consulting and using numerical simulation, according to finger The systematicness chosen, independence, 5 comparativity, objectivity and practicability principles are marked, following 8 Index Establishments evaluation is chosen and refers to Mark system: (1) Surrounding Rock Engineering Geological Conditions, (2) Vault settlement, (3) ground settlement, (4) inverted arch swell, (5) Great Wall settles, (6) project progress, (7) project cost, (8) Great Wall local dip rate.
Step 2): weight is determined
(1) AHP method.Each evaluation index subjectivity weight is determined using AHP method.AHP method by the simple stratification of challenge, Qualitative question quantification.It establishes hierarchical structure according to n evaluation index of tunnel deformation, constructs evaluation index judgment matrix, together Shi Jinhang consistency check, and then acquire every evaluation index subjectivity weight W1(j), (n is index by wherein j=1,2 ... n Number), specific calculating process is as follows:
(1.1) judgment matrix A is established(k)。
The value of judgment matrix reflects people to the understanding of each element relative importance, generally uses 1~9 proportion quotiety pair Importance degree assignment.
(1.2) weight of each layer index in AHP method is solved.
According to standard judgment matrix A, each factor is calculated in same substandard weight using feature vector method.First find out A Maximum eigenvalue λ max and corresponding this feature value feature vector, feature vector is normalized to obtain weight vectors For w1 (j)=(w1, w2 ..., wn), wherein j=1,2 ..., n.
(1.3) consistency check.
AHP method requires to carry out consistency check after the weight vectors for obtaining judgment matrix, to ensure every layer of judgment matrix Validity.Steps are as follows for consistency check:
The value of (1.3.1) calculating coincident indicator CI.
(1.3.2) calculates corresponding Aver-age Random Consistency Index RI.
From 1,2 ..., 9 HesIt is pressed in totally 17 numbersAverage probability extract n uniformly randomly2Number, Constitute k rank pairwise comparison matrix A；It reruns repeatedly to generate the random judgment matrix A of multiple k ranksk, calculate each consistent Property index, averages, i.e.,
11 rank of table~15 rank Aver-age Random Consistency Index tables
The value of (1.3.3) solution consistency ration CR.
CR=CI/RI (3)
As consistency ration CR < 0.10, it is believed that the consistency of judgment matrix can receive, and otherwise cope with judgment matrix and make Appropriate amendment.
(2) each evaluation index objective weight is determined using entropy assessment.Entropy assessment determines items by establishing evaluations matrix Evaluation criterion weight.Comentropy is for useful information amount size included in metric data, so that it is determined that the shared power of the information Weight.If a certain indication information entropy is smaller, illustrate that information content provided by this index is bigger, weight is bigger.
(2.1) decision matrix is constructed
Construct decision matrix A=(aij)m×n；I=1,2 ..., m；J=1,2 ..., n.Wherein, aijIndicate i-th kind of scheme J-th of index value, and standardized and turn to matrix R=(rij)m×n.That is:
J is profit evaluation model index:
J is cost type index:
(2.2) normalization matrix
To Standard Process R=(rij)m×nIt is normalized to obtain matrix R '=(rij’)m×n.For rij: rij'= rij/∑rij；I=1,2 ..., m；J=1,2 ..., n.
(2.3) parameter rijComentropy EjWith index weights w2(j)
Particularly, work as rijWhen '=0, r is enabledij’lnrij'=0.W2It (j) is the weight coefficient of indices namely the power of index Weight, calculation formula are as follows:
And
(3) game theory
It has differences, is found between each basic weight equal between the result obtained with different weighing computation methods Weighing apparatus, to achieve the purpose that the deviation between comprehensive weight and each basic weight minimizes, this is the principle of game theory aggregate model. If determining the weight of n index using L kind method, then weight vectors are as follows: ω (k)=[ωk1, ωk2..., ωkn], k=1, 2 ..., L.The linear combination of L weight vectors are as follows:
Wherein, ω indicates possible weight vectors collection, αkFor linear combination coefficient.Think of according to game theory aggregate model Think, exactly finds one group of linear combination coefficient αk, minimization ω and ωkDeviation between (k=1,2 ..., L), it may be assumed thatTo matrix derivation, the condition of optimal solution is obtained are as follows:
Solving equation group can be in the hope of linear combination coefficient (α1, α2..., αL), it is normalized to obtain:
So comprehensive weight are as follows:
Step 3): improved Topsis method calculates step
(1) it establishes decision matrix and is standardized
Establish decision matrix A=(aij)m×n, i=1,2 ..., m；J=1,2 ..., n, wherein aijIndicate jth kind scheme I index value.In order to eliminate influence of the different physical quantities guiding principle to the result of decision, needs to carry out standardization processing to it, be advised Generalized matrix R=(rij)m×n, detailed normalization method is as follows.
aijFor profit evaluation model index；aijFor cost type Index.
(2) weighted normal decision matrix is constructed
By (3) in step 2) it is found that the comprehensive weight determined by game theory aggregate model are as follows: ω*=(ω1, ω2..., ωn), n is scheme index number.If weighted normal decision matrix is G=(gij), wherein the element in matrix G gijAre as follows: gij=ωijrij, i=1,2 ..., m, j=1,2 ..., n.
(3) positive and negative ideal scheme and auxiliary ideal scheme are determined
If positive ideal scheme are as follows: v+=(v1 +, v2 +..., vn +)T；Ill ideal solution are as follows: v?=(v1 -, v2 -..., vn -)T.? In m scheme, calculation method is as follows:
(4) distance is calculated
By (2) in step 2) it is found that the weighted normal decision matrix of evaluating indexesto scheme A is G=(gi1, gi2…gin)
Mahalanobis distance its calculation formula is:
In formula, giThe vector of the n ATTRIBUTE INDEX composition of object is assessed for i-th.Covariance between each ATTRIBUTE INDEX Matrix is expressed as Σ i.e.: Σ=(σij)n×n
Wherein,Wherein, i, j=1,2 ..., n
The mahalanobis distance of index system and plus-minus ideal solutions is calculated according to above formulaMahalanobis distance, which is applied, to be commented In valence analysis, the calculating error that each ATTRIBUTE INDEX is generated by unit difference is eliminated.
Step 4): grey relational grade analysis
Gray relative analysis method calculation of relationship degree formula are as follows:
In formula, wkFor index weights, xiIt (k) is assessment sequence, x0It (k) is reference sequence.According to above-mentioned calculated result, It willWithAfter progress unit unification simplifies, i-th of arrangement and method for construction A is constructediWith plus-minus ideal solutions S+、S-'s Synthesize approach degree are as follows:
Wherein, α 1, α 2 have been influence coefficient of the subjective factor to assessment object, work as α1+α2When=1, relative similarity degree are as follows:
Approach degree is based on mahalanobis distance and grey relational grade and improves, and it is excessively high and cause to compensate for correlation between ATTRIBUTE INDEX The excessive deficiency of Euclidean distance error.The sequence of m kind construction method exchange premium degree is preferred.
Embodiment 1
1. data source
The present embodiment is calculated using Qinhuangdao Old Dragon's Head vcehicular tunnel as research background by FEM software ANSYS And the deformation size that related monitoring data obtain each evaluation index corresponding to each construction method is shown in Table 2.
2 construction method of table and corresponding requirement
2. determining weight
(1) AHP method.Each evaluation index subjectivity weight is determined using AHP method.It is according to 7 evaluation indexes of tunnel deformation Hierarchical structure is established, constructs evaluation index judgment matrix, while carrying out consistency check, and then it is subjective to acquire every evaluation index Weight W1(j), wherein j=1,2 ... 7.
1. establishing judgment matrix A according to each layer element(k)。
The value of judgment matrix reflects people to the understanding of each element relative importance, generally uses 1~9 proportion quotiety pair Importance degree assignment.
2. solving the weight of each layer index in AHP method.
According to standard judgment matrix A, each factor is calculated in same substandard weight using feature vector method.First with Matlab finds out the maximum eigenvalue λ max=7.12 of A, and feature vector is normalized to obtain weight vectors to be w1 (j)=(0.167,0.133,0.100,0.233,0.233,0.05,0.084).
3. consistency check.
AHP method requires to carry out consistency check after the weight vectors for obtaining judgment matrix, to ensure every layer of judgment matrix Validity.Steps are as follows for consistency check:
1) value of coincident indicator CI is calculated.
2) corresponding Aver-age Random Consistency Index RI is calculated.
7 rank Aver-age Random Consistency Index RI=1.36 can be obtained by table 1.
3) value of consistency ration CR is solved.
CR=CI/RI=0.02/1.36=0.0147 < 0.1
Consistency ration CR=0.0147 < 0.10, it is believed that the consistency of judgment matrix can receive.
(2) each evaluation index objective weight is determined using entropy assessment.Entropy assessment determines items by establishing evaluations matrix Evaluation criterion weight.Comentropy is for useful information amount size included in metric data, so that it is determined that the shared power of the information Weight.If a certain indication information entropy is smaller, illustrate that information content provided by this index is bigger, weight is bigger.
Construct decision matrix
Index weights can be obtained according to formula (4)~(7) to be respectively as follows:
w2(j)=(0.156,0.142,0.081,0.254,0.280,0.075,0.012)
(3) game theory
Weight combination coefficient: α is obtained according to game theory aggregate model formula (8)~(10)1 *=0.4372,To calculate comprehensive weight are as follows: w=(0.1608,0.1381,0.0893,0.2448,0.2595,0.0641, 0.0430)。
3. improved Topsis method calculates step
(1) decision matrix is standardized:
(2) weighted normal decision matrix is constructed
By (3) in step 2) it is found that the comprehensive weight determined by game theory aggregate model are as follows: w=(0.1608, 0.1381,0.0893,0.2448,0.2595,0.0641,0.0430).
Then weighted normal decision matrix are as follows:
(3) positive and negative ideal scheme and auxiliary ideal scheme are determined
In 5 schemes, positive ideal scheme is determined by formula (11)~(12) are as follows: v+=(0.0709,0.0292, 0.0315,0.0129,0.0137,0.0630,0.0019)T；Ill ideal solution are as follows: v?=(0.0211,0.0091,0.0076, 0.0032,0.0034,0.0509,0.0015)T。
(4) distance is calculated
The distance between each scheme and positive ill ideal solution are calculated separately out according to (13)~(14):
The distance value of each scheme of table 3
The mahalanobis distance of index system and plus-minus ideal solutions is calculated according to above formulaMahalanobis distance, which is applied, to be commented In valence analysis, the calculating error that each ATTRIBUTE INDEX is generated by unit difference is eliminated.
4. grey relational grade analysis
The grey relational grade of each scheme can be obtained by formula (15):
The grey relational grade of each scheme of table 4
The horse formula distance and grey relational grade of each scheme and plus-minus ideal solutions are normalized respectively.And it is general Subjective factor i.e. α identical to the influence degree of two kinds of approach degrees1=α2=0.5, using formula (16)~(18), find out each construction The synthesis approach degree of scheme and opposite exchange premium degree see the table below 5.
The synthesis approach degree of each arrangement and method for construction of table 5 and opposite exchange premium degree
Consideration sequence is successively as shown in Table 5 in this Great Wall tunnel, in 5 kinds of construction methods are as follows: three-drift method, main hole annular Excavate remaining core soil in advance, main hole CRD (intersecting median septum) method, central drift method, benching tunnelling method.Three-drift method construction safety, construction speed Degree is very fast, and cost is less, and is suitable for this area's ground matter, accurately quantifies this preferred construction party by improving Topsis method Case.
Approach degree is based on mahalanobis distance and grey relational grade and improves, and it is excessively high and cause to compensate for correlation between ATTRIBUTE INDEX The excessive deficiency of Euclidean distance error.5 kinds of construction method exchange premium degree sequences are preferred.
Above description has shown and described several preferred embodiments of invention, but as previously described, it should be understood that invention is not It is confined to form disclosed herein, should not be regarded as an exclusion of other examples, and can be used for various other combinations, modification And environment, and can be carried out within that scope of the inventive concept describe herein by the above teachings or related fields of technology or knowledge Change.And changes and modifications made by those skilled in the art do not depart from the spirit and scope of invention, then it all should be in the appended power of invention In the protection scope that benefit requires.

Claims (9)

1. a kind of based on the constructing tunnel preferred method for improving Topsis method, which comprises the following steps:
Step 1 chooses evaluation index: it is pre- to choose benching tunnelling method, three-drift method, central drift method, main hole CRD method and main hole Ring Cutting 5 kinds of constructing tunnel schemes of core local method are stayed, and are commented according to 8 Index Establishments below 5 kinds of selected constructing tunnel scheme selections Valence index system: Surrounding Rock Engineering Geological Conditions, Vault settlement, ground settlement, inverted arch protuberance, Great Wall sedimentation, Great Wall local dip Rate, project progress, project cost；
Step 2 determines weight: determining subjective weights omega using AHP method1, information Entropy Method determines objective weight ω2, and introduce game Comprehensive weight is determined by aggregate model；
Step 3 eliminates the calculating error that each ATTRIBUTE INDEX is generated by unit difference using improved Topsis method；
Step 4 improves exchange premium degree using grey relational grade.
2. constructing tunnel preferred method according to claim 1, which is characterized in that benching tunnelling method in the step 1 encloses Rock engineering geological condition are as follows: be useful in IV, V grades of weaker and joints development country rocks, the requirement of Vault settlement are as follows: 50mm, ground The requirement of table sedimentation are as follows: 24mm, the requirement of inverted arch protuberance are as follows: 40mm, the requirement of Great Wall sedimentation are as follows: 6mm, Great Wall local dip rate Requirement are as follows: 6, the requirement of project progress are as follows: 90 days, the requirement of project cost are as follows: 40,000/m；
The Surrounding Rock Engineering Geological Conditions of main hole CRD method are as follows: be suitable for IV, V grades of weak surrounding rocks, the requirement of Vault settlement are as follows: 20mm, The requirement of ground settlement are as follows: 10mm, the requirement of inverted arch protuberance are as follows: 15mm, the requirement of Great Wall sedimentation are as follows: 2mm, Great Wall local dip The requirement of rate are as follows: 2, the requirement of project progress are as follows: 150 days, the requirement of project cost are as follows: 60,000/m；
The Surrounding Rock Engineering Geological Conditions of central drift method are as follows: be applicable in V, VI grade of country rock double-arched tunnel, the requirement of Vault settlement are as follows: 35mm, the requirement of ground settlement are as follows: 18mm, the requirement of inverted arch protuberance are as follows: 30mm, the requirement of Great Wall sedimentation are as follows: 4mm, Great Wall office The requirement of portion's slope are as follows: 4, the requirement of project progress are as follows: 110 days, the requirement of project cost are as follows: 50,000/m；
The Surrounding Rock Engineering Geological Conditions of three-drift method are as follows: be suitable for V, VI grade of country rock two-wire or multiple track tunnel engineering, Vault settlement Requirement are as follows: 30mm, the requirement of ground settlement are as follows: 15mm, inverted arch protuberance requirement are as follows: 28mm, Great Wall sedimentation requirement are as follows: 4mm, the requirement of Great Wall local dip rate are as follows: 3, the requirement of project progress are as follows: 120 days, the requirement of project cost are as follows: 50,000/m；
The Surrounding Rock Engineering Geological Conditions of main hole Ring Cutting provided core soil method are as follows: be suitable for VI grade of country rock single line and V-VI grade Country rock double track tunnel engineering, the requirement of Vault settlement are as follows: 35mm, the requirement of ground settlement are as follows: 15mm, the requirement of inverted arch protuberance Are as follows: 10mm, the requirement of Great Wall sedimentation are as follows: 4mm, the requirement of Great Wall local dip rate are as follows: 4, the requirement of project progress are as follows: 110 days, The requirement of project cost are as follows: 50,000/m.
3. constructing tunnel preferred method according to claim 1, which is characterized in that determine that weight is specific in the step 2 Are as follows:
Step 2.1 determines subjective weights omega using AHP method1: hierarchical structure is established according to n evaluation index of tunnel deformation, is constructed Evaluation index judgment matrix, while consistency check is carried out, and then acquire every evaluation index subjectivity weight W1(j), wherein j= 1,2 ... n, n are index number；
Step 2.2 determines objective weight ω using information Entropy Method2:
Step 2.3, introducing game theory aggregate model determine comprehensive weight.
4. constructing tunnel preferred method according to claim 3, which is characterized in that become in the step 2.1 according to tunnel N evaluation index of shape establishes hierarchical structure, constructs evaluation index judgment matrix, while carrying out consistency check, and then acquires each Item evaluation index subjectivity weight W1(j), specifically:
Step 2.1.1, judgment matrix A is established(k)。
The value of judgment matrix reflects people to the understanding of each element relative importance, generally using 1~9 proportion quotiety to important Property assigning degrees.
Step 2.1.2, the weight of each layer index in AHP method is solved:
According to standard judgment matrix A, each factor is calculated in same substandard weight using feature vector method.First find out A most Feature vector is normalized to obtain weight vectors to be w1 by the feature vector of big eigenvalue λ max and corresponding this feature value (j)=(w1, w2 ..., wn), wherein j=1,2 ..., n；
Step 2.1.3, consistency check: AHP method requires to carry out consistency check after the weight vectors for obtaining judgment matrix, with Ensure the validity of every layer of judgment matrix.
5. constructing tunnel preferred method according to claim 4, which is characterized in that consistency is examined in the step 2.1.3 Test step specifically:
Step 2.1.3.1, the value of coincident indicator CI is calculated:
Step 2.1.3.2, corresponding Aver-age Random Consistency Index RI is calculated:
From 1,2 ..., 9 HesIt is pressed in totally 17 numbersAverage probability extract n uniformly randomly2Number is constituted K rank pairwise comparison matrix A；It reruns repeatedly to generate the random judgment matrix A of multiple k ranksk, calculate each consistency and refer to Mark, averages, i.e.,
Step 2.1.3.3, the value of consistency ration CR is solved.
CR=CI/RI (3)
As consistency ration CR < 0.10, it is believed that the consistency of judgment matrix can receive, and otherwise cope with judgment matrix and make suitably Amendment.
6. constructing tunnel preferred method according to claim 3, which is characterized in that use comentropy in the step 2.2 Method determines objective weight ω2Specifically:
Step 2.2.1, decision matrix is constructed:
Construct decision matrix A=(aij)m×n；I=1,2 ..., m；J=1,2 ..., n；Wherein, aijIndicate the jth of i-th kind of scheme A index value, and standardized and turn to matrix R=(rij)m×n；That is:
J is profit evaluation model index:
J is cost type index:
Step 2.2.2, normalization matrix:
To Standard Process R=(rij)m×nIt is normalized to obtain matrix R '=(rij’)m×n；For rij: rij'=rij/ ∑rij；I=1,2 ..., m；J=1,2 ..., n；
Step 2.2.3, parameter rijComentropy EjWith index weights w2(j):
Particularly, work as rijWhen '=0, r is enabledij’lnrij'=0；W2It (j) is the weight coefficient of indices namely the weight of index, meter It is as follows to calculate formula:
7. constructing tunnel preferred method according to claim 4, which is characterized in that introduce game theory in the step 2.3 Aggregate model determines comprehensive weight specifically:
If determining the weight of n index using L kind method, then weight vectors are as follows: ω (k)=[ωk1, ωk2..., ωkn], k =1,2 ..., L；The linear combination of L weight vectors are as follows:
Wherein, ω indicates possible weight vectors collection, αkFor linear combination coefficient.According to the thought of game theory aggregate model, it is exactly Find one group of linear combination coefficient αk, minimization ω and ωkDeviation between (k=1,2 ..., L), it may be assumed thatTo matrix derivation, the condition of optimal solution is obtained are as follows:
Solution equation group acquires linear combination coefficient (α1, α2..., αL), it is normalized to obtain:
So comprehensive weight are as follows:
8. constructing tunnel preferred method according to claim 4, which is characterized in that using improved in the step 3 Topsis method eliminates the calculating error that each ATTRIBUTE INDEX is generated by unit difference specifically:
Step 3.1 establishes decision matrix and is standardized
Establish decision matrix A=(aij)m×n, i=1,2 ..., m；J=1,2 ..., n, wherein aijIndicate i of jth kind scheme Index value；In order to eliminate influence of the different physical quantities guiding principle to the result of decision, needs to carry out standardization processing to it, be standardized Matrix R=(rij)m×n, detailed normalization method is as follows:
aijFor profit evaluation model index；aijFor cost type index；
Step 3.2, construction weighted normal decision matrix
Known by step 2.3, the comprehensive weight determined by game theory aggregate model are as follows: ω*=(ω1, ω2..., ωn), n is side Case index number；If weighted normal decision matrix is G=(gij), wherein the element g in matrix GijAre as follows: gij=ωijrij, i =1,2 ..., m, j=1,2 ..., n；
Step 3.3 determines positive and negative ideal scheme and auxiliary ideal scheme
If positive ideal scheme are as follows:Ill ideal solution are as follows: In m In a scheme, calculation method is as follows:
Step 3.4 calculates distance:
Known by step 2.2, the weighted normal decision matrix of evaluating indexesto scheme A is G=(gi1, gi2…gin)；
Mahalanobis distance its calculation formula is:
In formula, giThe vector of the n ATTRIBUTE INDEX composition of object is assessed for i-th；Covariance matrix table between each ATTRIBUTE INDEX It is shown as Σ i.e.: Σ=(σij)n×n
Wherein,Wherein, i, j=1,2 ..., n
The mahalanobis distance of index system and plus-minus ideal solutions is calculated according to above formulaMahalanobis distance is applied in evaluation point In analysis, the calculating error that each ATTRIBUTE INDEX is generated by unit difference is eliminated.
9. constructing tunnel preferred method according to claim 4, which is characterized in that use grey correlation in the step 4 Degree improves exchange premium degree specifically:
Gray relative analysis method calculation of relationship degree formula are as follows:
In formula, wkFor index weights, xiIt (k) is assessment sequence, x0It (k) is reference sequence.It, will according to above-mentioned calculated resultWith Roi +、Roi -After progress unit unification simplifies, i-th of arrangement and method for construction A is constructediWith plus-minus ideal solutions S+、S-Synthesis Approach degree are as follows:
Wherein, α 1, α 2 have been influence coefficient of the subjective factor to assessment object, work as α1+α2When=1, relative similarity degree are as follows:
Approach degree is based on mahalanobis distance and grey relational grade and improves, and it is excessively high and cause European to compensate for correlation between ATTRIBUTE INDEX The excessive deficiency of range error；The sequence of m kind construction method exchange premium degree is preferred.
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