CN104133985A - Evaluation method of geological disaster risk attribute interval of tunnel and underground construction - Google Patents

Abstract

The invention discloses an evaluation method of a geological disaster risk attribute interval of a tunnel and underground construction. The evaluation method comprises the following evaluation steps: (1) establishing a risk evaluation index system and a grading standard thereof; (2) constructing a single-index attribute measure function of the evaluation index; (3) determining a weight vector of a risk interval evaluation index; (4) determining a measurement value interval of the evaluation index, and calculating a single-index attribute measure value of the measurement value interval; and (5) according to a synthesized attribute, measuring a vector, and carrying out attribute recognition by adopting a confidence criterion. The complexity of tunnel and underground construction geological conditions and risk uncertainty are effectively considered, disaster risk levels in the tunnel and underground construction can be determined, and the probability of occurrence of each risk level of construction disasters can be given so as to better realize the quantitative evaluation of the construction disasters.

Description

Evaluation method between tunnel and underground works geological disaster risk attribute area

Technical field

The present invention relates to evaluation method between tunnel and underground works geological disaster risk attribute area.

Background technology

Tunnel and underground works relate to traffic engineering (railway, vcehicular tunnel), Hydraulic and Hydro-Power Engineering (water-conveyance tunnel, underground power house) the important engineering field such as, become gradually the important component part that national major infrastructure project is built, and along with the planning of strategic development in science and technology such as country " 12 " etc., the center of gravity of key project construction shifts to the extreme complicated western mountainous areas of topographic and geologic just gradually, in process of construction, be faced with " large buried depth, long hole line, heavily stressed, strong karst, high hydraulic pressure " etc. the huge challenge of extreme geologic condition, in addition construction geologic prospect work is in earlier stage difficult to engineering geology and the hydrogeological condition of investigating thoroughly that tunnel is along the line, cause will facing many serious geologic hazards in constructing tunnel, such as gushing water, gush mud, rock burst, landslide, Gas Outburst etc., cause great economic loss and heavy casualties.How the disaster risk of accurate evaluation tunnel and underground works, becomes one of key technical problem facing in tunnel and underground works exploitation gradually.

The research work of domestic venture analysis and assessment aspect is existing in developing stage.The nineties in 20th century, it is support that more domestic underground engineering projects be take in Tongji University, University Of Tianjin etc., and pilot study has been carried out in the aspects such as risk management theory and application, has stepped the first step of domestic civil engineering work risk management.The middle and later periods nineties, domestic scholars is introduced Structure Reliability Analytical Method in underground works, has enriched engineering risk organize content, further Supplementary and perfect risk management theory.At the beginning of 21 century, engineering circles and academia pay much attention to the Research on Risk Management of engineering field, and tunnel and the progressively refinement of underground engineering field risk management theory, in risk assessment pattern, several aspects such as prediction early warning and control decision are rapidly developed, and have obtained many achievements in research.

Yet, at present also not too perfect about the risk investigation of tunnel and underground works engineering, substantially rest on qualitative analysis or semi-quantitative analysis stage, still need to do a large amount of work.Current adopted risk assessment theory and problem of method ubiquity: in carrying out the Risk Analysis Process of tunnel and underground works disaster, the value of risk assessment index is an explicit value often, the complicacy of underground works geologic condition and the uncertainty of risk itself have been ignored, and most models can only be qualitative or sxemiquantitative provide disaster risk class, cannot provide probability of happening corresponding to disaster grade.

Summary of the invention

The deficiency existing for solving prior art, the invention discloses evaluation method between tunnel and underground works geological disaster risk attribute area, the present invention adopts comprehensive enabling legislation to determine the weight of evaluation index, both can consider disaster case history data factor, can to evaluation index, dynamically adjust according to field condition again, reduce the impact of expert's subjectivity on evaluation result.

For achieving the above object, concrete scheme of the present invention is as follows:

Evaluation method between tunnel and underground works geological disaster risk attribute area, comprises the following steps:

Step 1: set up Risk Assessment Index System according to the principal element of bringing out geologic hazard generation, according to subordinate function or the characterization of relation between the evaluation index in Risk Assessment Index System and disaster probability of happening and frequency, determine grade scale and the grade scale matrix corresponding to grade scale thereof of risk assessment index;

Step 2: according to the single index Attribute Measure function of the grade scale matrix construction evaluation index in step 1;

Step 3: adopt comprehensive enabling legislation to determine the weight vector of Risk interval evaluation index;

Step 4: the measured value that utilizes single index Attribute Measure function to carry out respectively calculative determination evaluation index for lower limit and the upper limit in measured value interval is interval, calculates synthesized attribute measure vector;

Step 5: according to synthesized attribute measure vector, adopt Reliability Code to carry out Attribute Recognition.

In described step 1, for a certain geologic hazard in tunnel and underground works, obtain and bring out the principal element that geologic hazard occurs, select typical effects factor and form Risk interval assessment indicator system; Statistical is separated out subordinate function or the characterization of relation between evaluation index and disaster probability of happening and frequency, thereby determines grade scale and the grade scale matrix corresponding to grade scale thereof of risk assessment index.

Bringing out the principal element that geologic hazard occurs is: formation lithology, unfavorable geology, underground water table, topography and geomorphology, the attitude of rocks, can lava and non-can lava contact zones, aspect and interlayer crack etc.

In described step 2, according to grade scale matrix, build the Attribute Measure function of each evaluation index to calculate single index Attribute Measure.

In described step 3, adopt comprehensive enabling legislation to determine the weight of evaluating in index, to reflect the significance level of index to evaluation object; Comprehensive enabling legislation weight vector is obtained by objective weight vector and subjective weight vector weighted sum.

In described step 4, the measured value of evaluation index is an interval, when single index Attribute Measure calculates, calculates respectively for lower limit and the upper limit in measured value interval; The respectively corresponding row vector of the lower limit in each evaluation index measured value interval and the upper limit; For each evaluation index, therefrom the row vector of the new matrix of an optional conduct, calculates the synthesized attribute of this matrix and estimates.By in measured value substitution single index Attribute Measure function formula, what the result calculating was evaluation index estimates.

In described step 5, gather the synthesized attribute calculating and estimate, the mean value of asking synthesized attribute that its each risk class is corresponding to estimate, adopts Reliability Code to carry out Attribute Recognition analysis, obtains the risk class of evaluation object; Then, adopt Reliability Code to calculate the risk class under each combination, the ratio that each risk class of statistical study is shared, thus obtain probability of happening corresponding to geologic hazard grade.

In described step 1, establish total m of Risk interval assessment indicator system risk evaluation index factor, risk class is divided into n grade, and evaluation index grade scale matrix A is expressed as follows:

In formula, in A, each row element all should meet a _i0<a _i1< ... <a _in, or a _i0>a _i1> ... >a _in; I=1,2 ..., m; J=1,2 ..., n.

In described step 2, the risk of establishing tunnel and underground works disaster is divided into 5 grades, i.e. n=5 in matrix A; The single index Attribute Measure function of structure evaluation index; b _ij, d _ijcan be calculated by following formula:

$b_{\mathrm{ij}}=\frac{a_{\mathrm{ij}-1}+a_{\mathrm{ij}}}{2}---\left(2\right)$

d _ij＝min{|b _ij-a _ij|，|b _ij+1-a _ij|} (3)

In formula (1), j meets j=1, and 2 ..., n; In formula (2), j meets, j=1, and 2 ..., n-1, μ _ijthe measured value t that is i evaluation index has attribute C _jbe the size of risk class, a _ij-1, a _ijbe respectively the capable j-1 row of i, j column element in matrix A, b _ij, b _ij+1, d _ijit is the parameter of introducing for structure single index Attribute Measure function.

In described step 3, comprehensive enabling legislation weight vector is obtained by objective weight vector P and subjective weight vector Q weighted sum:

ω＝ψ ₁·P+ψ ₂·Q＝ψ ₁·[p ₁，p ₂，…，p _m]+ψ ₂·[q ₁，q ₂，…，q _m] (4)

ψ ₁+ψ ₂＝1 (5)

In formula, ψ ₁, ψ ₂for the distribution weights of objective weight and subjective weight, by expert's confidence index method, obtained; ω is the weight vector of evaluation index, p ₁, p ₂..., p _mfor the objective weight-values of evaluation index, q ₁, q ₂..., q _msubjective weights for evaluation index.

Objective weight vector adopts Frequency statistics method to add up acquisition to typical project case:

$p_i=(N_i/N)/\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}(N_i/N)---\left(6\right)$

In formula: N is the sum of typical project case; N is the sum of evaluation index; N _ifor evaluation index frequency; p _ifor the shared frequency of evaluation index, i.e. objective weight-values.

Subjective weight vector adopts 1～9 calibration Judgement Matricies to calculate by analytical hierarchy process and obtains:

$q_i={\left(\underset{j=1}{\overset{m}{\mathrm{\&Pi;}}}{P}_{\mathrm{ij}}\right)}^{1/m}/\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left(\underset{j=1}{\overset{m}{\mathrm{\&Pi;}}}{P}_{\mathrm{ij}}\right)}^{1/m}---\left(7\right)$

${\mathrm{\&lambda;}}_{\max }=\left(\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}({\left(\mathrm{Aq}\right)}_i/q_i)\right)/m---\left(8\right)$

$\mathrm{CR}=\frac{\mathrm{CI}}{\mathrm{RI}}=\frac{({\mathrm{\&lambda;}}_{\max }-m)/(m-1)}{\mathrm{RI}}---\left(9\right)$

In formula, A is judgment matrix; λ _maxfor the eigenvalue of maximum of judgment matrix, CI is general coincident indicator; RI is mean random coincident indicator; CR is random Consistency Ratio.Judgment matrix must meet consistency check requirement, i.e. CR<0.1.Q _ifor the subjective weights of evaluation index, P _ijproduct for the capable all elements of i in judgment matrix.

In described step 4, the measured value of evaluation index is an interval, is shown below:

I _i＝[t _id，t _iu] (10)

In formula, t _id, t _iube respectively lower limit and the higher limit in measured value interval.When single index Attribute Measure calculates, for lower limit and the upper limit in measured value interval, calculate respectively, obtain t _id, t _iucorresponding single index attribute measure matrix:

U _d, U _ucan regard the matrix being formed by m 1 * n rank row vector as, total 2m row vector, the i.e. respectively corresponding row vector u of the lower limit in each evaluation index measured value interval and the upper limit _idj, u _iuj; For each evaluation index, from u _idj, u _iujin the i of the new matrix U of an optional conduct capable, can build 2 thus ^mindividual U matrix;

If u _jifor the j row of matrix U, by following formula, can compute matrix U j be listed as corresponding synthesized attribute and estimate

u _j＝ω·u _ji＝[ω ₁，ω ₂，…，ω _m]·[u _j1，u _j2，…，u _jm] ^T (12)

u _j＝[u ₁，u ₂，…，u _m] (13)

Wherein, ω ₁, ω ₂..., ω _mfor the weights of evaluation index, u _j1, u _j2..., u _jmfor the j column element of matrix U, u ₁, u ₂..., u _mfor the synthesized attribute of opinion rating is estimated.

In described step 5, the object of Attribute Recognition is to estimate μ by synthesized attribute _jwhich assessment grade C judgement evaluation object belongs to _j.In attribute Recognition Model, adopt Reliability Code: establish (C ₁, C ₂..., C _n) be an orderly collection of evaluating of attribute space F, λ is degree of confidence, and 0.5 < λ≤1, generally gets 0.6～0.7.

If meet

$j_0=\left\{\begin{array}{c}\min \{j:\underset{l=1}{\overset{j}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\mathrm{jl}}\&GreaterEqual;\mathrm{\&lambda;},1\&le;j\&le;n\},C_1>C_2>...>C_n\\ \max \{j:\underset{l=j}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\mathrm{jl}}\&GreaterEqual;\mathrm{\&lambda;},1\&le;j\&le;n\},C_1<C_2<...<C_n\end{array}\right.---\left(14\right)$

Think that evaluation object grade is C _j0rank.μ _jlthe synthesized attribute that is l grade is estimated.

In described step 4, can build 2 ^mindividual U matrix, thus obtain 2 ^mindividual synthesized attribute measure vector, gathers the synthesized attribute calculating and estimates 2 ^mindividual, to ask synthesized attribute that its each risk class is corresponding to estimate mean value, recycling formula (14) is carried out Attribute Recognition analysis, obtains the risk class of evaluation object; Then, utilize formula (14) to calculate the j under each combination ₀value, in like manner can obtain 2 ^mindividual value, statistical study j ₀get respectively 1,2,3 ..., during n, respectively there is how many kinds of combination, the ratio that calculation risk grade is shared, thus obtain probability of happening corresponding to geologic hazard grade.

Beneficial effect of the present invention:

Evaluation method between tunnel provided by the invention and underground works geological disaster risk attribute area, its usefulness is:

(1) can objectively analyze affecting the risk factors of geologic hazard, effectively select typical influence factor and build assessment indicator system, reduce the impact of secondary cause on evaluation result;

(2) adopt comprehensive enabling legislation to determine the weight of evaluation index, both can consider disaster case history data factor, can to evaluation index, dynamically adjust according to field condition again, reduced the impact of expert's subjectivity on evaluation result;

(3) evaluation index measured value is an interval, has effectively considered tunnel and the complicacy of underground works geologic condition and the uncertainty of risk, can to engineering project disaster risk, evaluate better;

(4) not only can determine the risk class of disaster in tunnel and underground works, can also provide the probability of happening of each risk class of engineering project disaster, thereby realize the quantitative identification of disaster risk class.

Accompanying drawing explanation

Fig. 1 is evaluation procedure process flow diagram of the present invention;

Fig. 2 (a) is single index Attribute Measure function computing formula figure mono-;

Fig. 2 (b) is single index Attribute Measure function computing formula figure bis-.

Embodiment:

Below in conjunction with accompanying drawing, the present invention is described in detail:

As shown in Figure 1, evaluation method between tunnel and underground works geological disaster risk attribute area, comprises the following steps:

(1) set up Risk Assessment Index System and grade scale thereof.

For a certain geologic hazard in tunnel and underground works, correlation engineering example data in systematic collection is external, and carry out classified finishing analysis, and obtain and bring out the principal element that geologic hazard occurs, select typical effects factor and form Risk interval assessment indicator system.Statistical is separated out subordinate function or the characterization of relation between evaluation index and disaster probability of happening and frequency, thereby determines the grade scale of risk assessment index.If total m of risk assessment index factor, risk class is divided into n grade, and evaluation index grade scale matrix A is expressed as follows:

In formula, in A, each row element all should meet a _i0<a _i1< ... <a _in, or a _i0>a _i1> ... >a _in; I=1,2 ..., m; J=1,2 ..., n.

(2) the single index Attribute Measure function of structure evaluation index.

According to evaluation index grade scale matrix A, build the Attribute Measure function of each evaluation index to calculate single index Attribute Measure.

If the risk of tunnel and underground works disaster is divided into 5 grades, i.e. n=5 in matrix A; Can be according to as shown in Fig. 2 (a)-2 (b), shown in the single index Attribute Measure function of method construct evaluation index.

In figure, μ _ijthe measured value t that is i evaluation index has attribute C _jthe size of (risk class); b _ij, d _ijcan be calculated by following formula:

$b_{\mathrm{ij}}=\frac{a_{\mathrm{ij}-1}+a_{\mathrm{ij}}}{2}---\left(2\right)$

d _ij＝min{|b _ij-a _ij|，|b _ij+1-a _ij|} (3)

In formula (1), j meets j=1, and 2 ..., n; In formula (2), j meets, j=1, and 2 ..., n-1.

(3) determine the weight vector of Risk interval evaluation index.

Adopt comprehensive enabling legislation to determine the weight of evaluating in index, the significance level with reflected appraisal index to evaluation object.Comprehensive enabling legislation weight vector is obtained by objective weight vector P and subjective weight vector Q weighted sum:

ω＝ψ ₁·P+ψ ₂·Q＝ψ ₁·[p ₁，p ₂，…，p _m]+ψ ₂·[q ₁，q ₂，…，q _m] (4)

ψ ₁+ψ ₂＝1 (5)

In formula, ψ ₁, ψ ₂for the distribution weights of objective weight and subjective weight, by expert's confidence index method, obtained.

Objective weight vector adopts Frequency statistics method to add up acquisition to typical project case:

$p_i=(N_i/N)/\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}(N_i/N)---\left(6\right)$

In formula: N is the sum of typical project case; N is the sum of evaluation index; N _ifor evaluation index frequency.

Subjective weight vector adopts 1～9 calibration Judgement Matricies to calculate by analytical hierarchy process and obtains:

$q_i={\left(\underset{j=1}{\overset{m}{\mathrm{\&Pi;}}}{P}_{\mathrm{ij}}\right)}^{1/m}/\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left(\underset{j=1}{\overset{m}{\mathrm{\&Pi;}}}{P}_{\mathrm{ij}}\right)}^{1/m}---\left(7\right)$

${\mathrm{\&lambda;}}_{\max }=\left(\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}({\left(\mathrm{Aq}\right)}_i/q_i)\right)/m---\left(8\right)$

$\mathrm{CR}=\frac{\mathrm{CI}}{\mathrm{RI}}=\frac{({\mathrm{\&lambda;}}_{\max }-m)/(m-1)}{\mathrm{RI}}---\left(9\right)$

In formula, A is judgment matrix; λ _maxfor the eigenvalue of maximum of judgment matrix, CI is general coincident indicator; RI is mean random coincident indicator; CR is random Consistency Ratio.Judgment matrix must meet consistency check requirement, i.e. CR<0.1.

(4) determine the measured value interval of evaluation index, calculate its single index Attribute Measure value.

The measured value of evaluation index is an interval, is shown below:

I _i＝[t _id，t _iu] (10)

In formula, t _id, t _iube respectively lower limit and the higher limit in measured value interval.When single index Attribute Measure calculates, for lower limit and the upper limit in measured value interval, calculate respectively, obtain t _id, t _iucorresponding single index attribute measure matrix:

U _d, U _ucan regard the matrix being formed by m 1 * n rank row vector as, total 2m row vector, the i.e. respectively corresponding row vector u of the lower limit in each evaluation index measured value interval and the upper limit _idj, u _iuj; For each evaluation index, from u _idj, u _iujin the i of the new matrix U of an optional conduct capable, can build 2 thus ^mindividual U matrix.

If u _jifor the j row of matrix U, by following formula, can compute matrix U j be listed as corresponding synthesized attribute and estimate

u _j＝ω·u _ji＝[ω ₁，ω ₂，…，ω _m]·[u _j1，u _j2，…，u _jm] ^T (12)

u _j＝[u ₁，u ₂，…，u _m] (13)

(5), according to synthesized attribute measure vector, adopt Reliability Code to carry out Attribute Recognition.

The object of Attribute Recognition is to estimate μ by synthesized attribute _jwhich assessment grade C judgement evaluation object belongs to _j.In attribute Recognition Model, adopt Reliability Code: establish (C ₁, C ₂..., C _n) be an orderly collection of evaluating of attribute space F, λ is degree of confidence, and 0.5 < λ≤1, generally gets 0.6～0.7.

If meet

$j_0=\left\{\begin{array}{c}\min \{j:\underset{l=1}{\overset{j}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\mathrm{jl}}\&GreaterEqual;\mathrm{\&lambda;},1\&le;j\&le;n\},C_1>C_2>...>C_n\\ \max \{j:\underset{l=j}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\mathrm{jl}}\&GreaterEqual;\mathrm{\&lambda;},1\&le;j\&le;n\},C_1<C_2<...<C_n\end{array}\right.---\left(14\right)$

Think that evaluation object grade is C _j0rank.

In step (4) computation process, can build 2 ^mindividual U matrix, thus obtain 2 ^mindividual synthesized attribute measure vector, gathers the synthesized attribute calculating and estimates (2 ^mindividual), the mean value of asking synthesized attribute that its each risk class is corresponding to estimate, recycling formula (14) is carried out Attribute Recognition analysis, obtains the risk class of evaluation object; Then, utilize formula (14) to calculate the j under each combination ₀value, in like manner can obtain 2 ^mindividual value, statistical study j ₀get respectively 1,2,3 ..., during n, respectively there is how many kinds of combination, the ratio that calculation risk grade is shared, thus obtain probability of happening corresponding to geologic hazard grade.

Claims (8)

1. evaluation method between tunnel and underground works geological disaster risk attribute area, is characterized in that, comprises the following steps:

Step 1: set up Risk Assessment Index System according to the principal element of bringing out geologic hazard generation, according to subordinate function or the characterization of relation between the evaluation index in Risk Assessment Index System and disaster probability of happening and frequency, determine grade scale and the grade scale matrix corresponding to grade scale thereof of risk assessment index;

Step 2: according to the single index Attribute Measure function of the grade scale matrix construction evaluation index in step 1;

Step 3: adopt comprehensive enabling legislation to determine the weight vector of Risk interval evaluation index;

Step 4: the measured value that utilizes single index Attribute Measure function to carry out respectively calculative determination evaluation index for lower limit and the upper limit in measured value interval is interval, calculates synthesized attribute measure vector;

Step 5: according to synthesized attribute measure vector, adopt Reliability Code to carry out Attribute Recognition.

2. evaluation method between tunnel as claimed in claim 1 and underground works geological disaster risk attribute area, it is characterized in that, in described step 1, for a certain geologic hazard in tunnel and underground works, the principal element that geologic hazard occurs is brought out in acquisition, selects typical effects factor and forms Risk interval assessment indicator system; Statistical is separated out subordinate function or the characterization of relation between evaluation index and disaster probability of happening and frequency, thereby determines grade scale and the grade scale matrix corresponding to grade scale thereof of risk assessment index.

3. evaluation method between tunnel as claimed in claim 1 and underground works geological disaster risk attribute area, is characterized in that, in described step 2, according to grade scale matrix, builds the Attribute Measure function of each evaluation index to calculate single index Attribute Measure.

4. evaluation method between tunnel as claimed in claim 1 and underground works geological disaster risk attribute area, is characterized in that, in described step 3, adopts comprehensive enabling legislation to determine the weight of evaluating in index, to reflect the significance level of index to evaluation object; Comprehensive enabling legislation weight vector is obtained by objective weight vector and subjective weight vector weighted sum.

5. evaluation method between tunnel as claimed in claim 1 and underground works geological disaster risk attribute area, it is characterized in that, in described step 4, the measured value of evaluation index is an interval, when single index Attribute Measure calculates, for lower limit and the upper limit in measured value interval, calculate respectively; The respectively corresponding row vector of the lower limit in each evaluation index measured value interval and the upper limit; For each evaluation index, therefrom the row vector of the new matrix of an optional conduct, calculates the synthesized attribute of this matrix and estimates.

6. evaluation method between tunnel as claimed in claim 1 and underground works geological disaster risk attribute area, it is characterized in that, in described step 5, gathering the synthesized attribute calculating estimates, the mean value of asking synthesized attribute that its each risk class is corresponding to estimate, adopt Reliability Code to carry out Attribute Recognition analysis, obtain the risk class of evaluation object; Then, adopt Reliability Code to calculate the risk class under each combination, the ratio that each risk class of statistical study is shared, thus obtain probability of happening corresponding to geologic hazard grade.

7. evaluation method between tunnel as claimed in claim 2 and underground works geological disaster risk attribute area, it is characterized in that, in described step 1, if total m of Risk interval assessment indicator system risk evaluation index factor, risk class is divided into n grade, and evaluation index grade scale matrix A is expressed as follows:

In formula, in A, each row element all should meet a _i0<a _i1< ... <a _in, or a _i0>a _i1> ... >a _in; I=1,2 ..., m; J=1,2 ..., n.

8. evaluation method between tunnel as claimed in claim 3 and underground works geological disaster risk attribute area, is characterized in that, in described step 2, the risk of establishing tunnel and underground works disaster is divided into 5 grades, i.e. n=5 in matrix A; The single index Attribute Measure function of structure evaluation index; b _ij, d _ijcan be calculated by following formula:

$b_{\mathrm{ij}}=\frac{a_{\mathrm{ij}-1}+a_{\mathrm{ij}}}{2}---\left(2\right)$

d _ij＝min{|b _ij-a _ij|，|b _ij+1-a _ij|} (3)

In formula (1), j meets j=1, and 2 ..., n; In formula (2), j meets, j=1, and 2 ..., n-1, μ _ijthe measured value t that is i evaluation index has attribute C _jbe the size of risk class, a _ij-1, a _ijbe respectively the capable j-1 row of i, j column element in matrix A, b _ij, b _ij+1, d _ijit is the parameter of introducing for structure single index Attribute Measure function.