CN104504482A - Fuzzy comprehensive assessment method for railway snow disaster risk - Google Patents

Abstract

The invention discloses a fuzzy comprehensive assessment method for a railway snow disaster risk. The method comprises the following steps: establishing a factor set for measuring the railway snow disaster risk; setting a railway snow disaster risk assessment level; collecting expert opinions, performing secondary risk evaluation matrix assessment, and establishing a railway snow disaster fuzzy expert evaluation matrix; determining each risk indicator weight based on an improved group analytic hierarchy process; determining a secondary fuzzy assessment vector; determining the membership vector of a railway disaster risk factor set specific to a comment set; and determining a railway snow disaster risk assessment level by comprehensively adopting a confidence criterion and a level characteristic value formula. According to the method, the improved group analytic hierarchy process is combined with a fuzzy comprehensive evaluation method, so that accurate assessment of the railway snow disaster risk is realized, and the influence of a snow disaster on railway transportation and the society is lowered. The method has important theoretical significance to scientific and accurate formulation of disaster prevention and disaster preparedness measures and prevention of possible railway sudden accidents.

Description

A kind of railway heavy snow calamity source Fuzzy Synthetic Evaluation

Technical field

The present invention relates to railway system's risk assessment technology field, particularly a kind of railway heavy snow calamity source Fuzzy Synthetic Evaluation.

Background technology

Snow disaster risk assessment is a requisite basic work in disaster management, the great realistic problem of government and society extensive concern, to science formulate exactly preparedness measure of taking precautions against natural calamities organize snow disaster automatic rescue work and calamity in time after restoration and reconstruction decision-making have important supporting role.

Risk assessment is a kind of by analyzing potential Flood inducing factors, assesses the fragility existence condition that can work the mischief to human life's property and living environment, determines the method for risk property and scope degree.Usually, snowfall intensity is larger, and accumulated snow is darker, and the loss that disaster causes is more serious, and the risk of snow disaster is also larger.

The research of the calamity source assessment of current Chinese Railway is also in the starting stage, lacks the theoretical research of system.For snow disaster risk assessment, the index selected by different survey regions, method and classification standard are not quite similar, but are mostly that the danger or combine with hazard-affected body vulnerability inder causing calamity from snow disaster judges.The method can be used for the assessment of hazard-affected body fragility and snow disaster risk height on the one hand, also can calculate synthetic disaster condition index in the condition of a disaster comprehensive assessment on the other hand, but need the evaluation index Data support dynamically updated.Existing snow disaster risk assessment study mainly concentrates on pastoral area research, has and relates to, but also do not form unified method and index set in evaluation index assessment models etc., then relatively less for non-snow disaster in pastoral area evaluation studies.Traditional calamity source assessment generally judges disaster rank according to maximum membership grade principle, but when the largest component in fuzzy comprehensive evoluation matrix and second largest component are more or less the same, show that evaluation conclusion is slightly reluctantly aobvious according to maximum membership grade principle.

Summary of the invention

The object of the present invention is to provide a kind of science, accurately railway heavy snow calamity source Fuzzy Synthetic Evaluation, based on improved fuzzy comprehensive evaluation method and group decision analytical hierarchy process, risk assessment is carried out to railway heavy snow disaster, prevent contingent all kinds of railway accident, eliminate the impact on transportation by railroad and society of heavy snow disaster, reduce all kinds of loss, guarantee that circuit is unimpeded, train running on scheduled time runs.

The technical solution realizing the object of the invention is: a kind of railway heavy snow calamity source Fuzzy Synthetic Evaluation, comprises the following steps:

1st step, sets up the set of factors U of tolerance railway heavy snow calamity source;

2nd step, setting railway heavy snow calamity source evaluation grade V;

3rd step, data craft's suggestion, carries out the assessment of secondary risk Judgement Matrix, sets up railway heavy snow disaster fuzzy expert Judgement Matrix R _i;

4th step, determines each risk indicator weight based on the group decision analytical hierarchy process improved;

5th step, determines secondary fuzzy evaluation vector B _i;

6th step, determines the Membership Vestor b of Railway Disaster risk revulsion U to Comment gathers V;

7th step, comprehensive employing Reliability Code and rank feature values formula determination railway heavy snow calamity source level of evaluation.

The present invention compared with prior art, its remarkable advantage is: (1) does not need the support of dynamic data, railway heavy snow calamity source rank can be judged rationally, reliably, reduce all kinds of loss, guarantee that circuit is unimpeded, train running on scheduled time runs very necessary; (2) assess for non-pastoral area heavy snow calamity source, group decision analytical hierarchy process after improving is combined with fuzzy synthetic appraisement method, realize accurate evaluation to high-speed railway heavy snow calamity source, reduce the impact of heavy snow disaster on transportation by railroad and society; (3) by judging the validity of maximum membership grade principle, comprehensive employing rank feature values formula and Reliability Code judge railway heavy snow calamity source, assessment result more accurately, rationally, preparedness measure of taking precautions against natural calamities is formulated exactly for science, prevents contingent railway accident to have important theory significance.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of railway heavy snow calamity source appraisal procedure of the present invention.

Fig. 2 is railway heavy snow calamity source evaluation system hierarchy Model of the present invention.

Embodiment

Below in conjunction with drawings and the specific embodiments, the present invention is described in further detail.

Composition graphs 1 ~ 2, railway heavy snow calamity source Fuzzy Synthetic Evaluation of the present invention, first set of factors and the risk assessment grade of tolerance railway heavy snow calamity source is set up, secondly multidigit expert is invited to assess Railway Disaster risk level, again adopt the group decision analytical hierarchy process determination railway heavy snow disaster primary risk of improvement and corresponding secondary risk index weights, and then try to achieve the Membership Vestor of secondary fuzzy evaluation vector and one-level evaluation index, thus obtain risk factors to the Membership Vestor of Comment gathers, finally by the availability calculating maximum membership grade principle, comprehensive employing Reliability Code and rank feature values formula determination railway heavy snow calamity source level of evaluation.

Composition graphs 2, railway heavy snow calamity source evaluation system hierarchy Model comprises rule layer and operation layer, comprise first class index 4, two-level index 13, rule layer has environmental factor, apparatus factor, human factor and answers calamity power factor four primary risk evaluation indexes; Environmental factor comprises snow depth, accumulated snow duration, temperature and topographic relief amplitude four secondary risk evaluation indexes, and apparatus factor comprises line conditions, bridge tunnel situation and communication facilities three secondary risk evaluation indexes; Human factor comprises Employee Security sense of risk, ' professional and personnel's labor discipline idea three secondary risk evaluation indexes; Calamity power factor is answered to comprise in prevention ability before calamity, calamity recovery capability three secondary risk evaluation indexes after emergency relief ability and calamity.

Railway heavy snow calamity source Fuzzy Synthetic Evaluation of the present invention, comprises the following steps:

1st step, sets up the set of factors U of tolerance railway heavy snow calamity source;

Determine railway heavy snow calamity source set of factors U={u _i, i=1,2 ... I, I are the u of one-level evaluation index _inumber, u _i={ u _ij, j=1,2 ... J, J are one-level evaluation index u _iunder secondary evaluation index u _ijnumber.

If first class index 4, two-level index 13, railway heavy snow disaster one-level evaluation index risk revulsion U={u ₁, u ₂, u ₃, u ₄, secondary evaluation index is respectively u ₁={ u ₁₁, u ₁₂, u ₁₃, u ₁₄, u ₂={ u ₂₁, u ₂₂, u ₂₃, u ₃={ u ₃₁, u ₃₂, u ₃₃, u ₄={ u ₄₁, u ₄₂, u ₄₃.

2nd step, setting railway heavy snow calamity source evaluation grade V;

According to the needs that actual conditions and railway heavy snow calamity source are assessed, be L grade: V={V by railway heavy snow Hazard Risk Assessment grade classification _l, l=1,2 ..., L.The present invention is divided into 5 grade: V ₁=high, V ₂=higher, V ₃=general, V ₄=lower, V ₅=low, i.e. V={V ₁, V ₂..., V ₅.

3rd step, data craft's suggestion, carries out the assessment of secondary risk Judgement Matrix, sets up railway heavy snow disaster fuzzy expert Judgement Matrix R _i:

$R_i={\left(r_{\mathrm{ijl}}\right)}_{J\×L}=\left[\begin{array}{cccccc}{r}_{i11}& r_{i12}& \·\·\·& r_{i1l}& \·\·\·& r_{i1L}\\ r_{i21}& r_{i22}& \·\·\·& r_{i2l}& \·\·\·& r_{i2L}\\ \·& \·& \·& & \·& \\ \·& \·& \·& & \·& \\ \·& \·& \·& & \·& \\ r_{\mathrm{iJ}1}& r_{\mathrm{iJ}2}& \·\·\·& r_{\mathrm{iJl}}& \·\·\·& r_{\mathrm{iJL}}\end{array}\right]$

In formula, r _ijlrepresent index u _ijto l level comment V _ldegree of membership, r _ijl=s _ijl/ s, s are the expert's sum participating in Fuzzy comprehensive evaluation, s _ijlfor thinking index u in the expert that participates in evaluation and electing _ijbelong to evaluation approach V _lexpert's number, know

4th step, determines each risk indicator weight based on the group decision analytical hierarchy process improved;

According to the significance level of railway heavy snow calamity source factor, utilize group decision analytical hierarchy process to ask the corresponding weight of each Railway Disaster risk factors, represent one-level weight with W, W _irepresent secondary weight vectors, concrete steps are as follows:

(4.1) hierarchical structure model is set up;

By carrying out labor to railway heavy snow calamity source factor, draw all influence factors, then according to the different attribute of each influence factor, they are summed up in the point that in the middle of different levels, the recursive hierarchy structure that formation one of successively going forward one by one is orderly, element in upper strata has dominating role to all elements of adjacent lower floor or Partial Elements, and namely all or part of element of lower floor is a segmentation of upper strata element, so just can be configured to an orderly hierarchical structure model.Here model is mainly divided into 3 parts: destination layer, rule layer, operation layer.

(4.2) pairwise comparison matrix is constructed: the Scale Method structure pairwise comparison matrix adopting 1 ~ 9 scale and inverse thereof;

If the unit of lower floor that element M is arranged altogether have n, i.e. a ₁, a ₂..., a _n, then the pairwise comparison matrix A=(a adopting 1 ~ 9 scale to draw _pq) _{n × n}there is following form:

Element a in the pairwise comparison matrix of above-mentioned form _pqrepresent: take element M as criterion, element a _pto element a _qthe comparison of significance level, determine each element value according to following scale implication:

The implication of table 1 proportion quotiety 1 ~ 9 scale

(4.3) pairwise comparison matrix consistency check method improves

Professor Saaty proposes a kind of method of pairwise comparison matrix consistency check, first obtains the consistency ration C compared in pairs _sif, C _s< 0.1, then meet consistance.

(1) the coincident indicator C of pairwise comparison matrix is determined _o:

$C_O=\frac{{\mathrm{\&lambda;}}_{\max }-n}{n-1}$

Wherein, λ _maxfor the eigenvalue of maximum of pairwise comparison matrix, n is the dimension of pairwise comparison matrix;

(2) consistency ration C is determined _s:

$C_S=\frac{C_O}{S_O}$

Wherein, S _ofor random index, relevant with matrix dimension n, 2 to try to achieve by tabling look-up;

Table 2 Aver-age Random Consistency Index S _o

Work as C _swhen being greater than 0.1, if the weight drawn by this pairwise comparison matrix is to calculate final assessment result, the uncertainty of assessment result being increased, therefore needing the pairwise comparison matrix to not meeting consistency check to revise, below provide a kind of inconsistent pairwise comparison matrix optimization method.

(3) inconsistent pairwise comparison matrix D regards a crash consistency comparator matrix A as and has added a disturbance quantity δ _pqif the eigenvalue of maximum of A is λ _max, proper vector is x=(x ₁, x ₂..., x _n), then the element in matrix A meets a _pq=x _p/ x _q, in so inconsistent pairwise comparison matrix D, element is:

d _pq＝a _pq·δ _pq

As consistency ration C _sduring > 0.1, determine inconsistent pairwise comparison matrix D disturbance quantity δ _pq:

${\mathrm{\&delta;}}_{\mathrm{pq}}=d_{\mathrm{pq}}\&CenterDot;\frac{x_q}{x_p}$

In formula, p, q=1,2,3 ..., n;

(4) regard respective element in a crash consistency comparator matrix A as due to inconsistent each element of pairwise comparison matrix D and add the result after disturbance, so first set about revising from that element that disturbance is maximum, obtain maximum perturbation amount δ _rs, determine the value of r and s, and revise d _rsand d _sr, by d _rsitem subtracts 1, d _sritem revises accordingly, and obtains new pairwise comparison matrix δ _rssolve according to the following formula:

${\mathrm{\&delta;}}_{\mathrm{rs}}=\underset{p,q}{\max }\left\{{\mathrm{\&delta;}}_{\mathrm{pq}}\right\}=\underset{p,q}{\max }\left\{d_{\mathrm{pq}}\frac{x_q}{x_p}\right\}p,q=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n$

(5) right ask consistency ration, if meet coherence request, then stop optimizing, otherwise continue to ask maximum perturbation amount, and right maximum perturbation amount corresponding in element modify, construct new pairwise comparison matrix, then consistency ration recalculated to the matrix after having revised, repeat step (1) ~ (4), until new pairwise comparison matrix has satisfied consistance;

$C_S=\frac{C_O}{S_O}---\left(2\right)$

In formula, C _sfor consistency ration; S _ofor random index, relevant with matrix dimension n, try to achieve by tabling look-up; C _ofor coincident indicator, try to achieve according to formula (3):

$C_O=\frac{{\mathrm{\&lambda;}}_{\max }-n}{n-1}---\left(3\right)$

In formula, λ _maxfor the eigenvalue of maximum of pairwise comparison matrix, n is the dimension of pairwise comparison matrix.

Work as C _swhen being greater than 0.1, if the weight drawn by this pairwise comparison matrix is to calculate final assessment result, the uncertainty of assessment result being increased, therefore needing the pairwise comparison matrix to not meeting consistency check to revise, below provide a kind of inconsistent pairwise comparison matrix optimization method.

Inconsistent pairwise comparison matrix D regards a crash consistency comparator matrix A as and has added a disturbance quantity δ _pq.If the eigenvalue of maximum of A is λ _max, proper vector is x=(x ₁, x ₂..., x _n), then the element in matrix A meets a _pq=x _p/ x _q, in so inconsistent pairwise comparison matrix D, element is:

d _pq＝a _pq·δ _pq

In formula, p, q=1,2,3 ..., n.

Work as δ _pqwhen=1, matrix D is the same with matrix A, meets coherence request.Then disturbance quantity δ _pq:

${\mathrm{\&delta;}}_{\mathrm{pq}}=d_{\mathrm{pq}}\&CenterDot;\frac{x_q}{x_p}$

In formula, p, q=1,2,3 ..., n.

Regard respective element in a crash consistency comparator matrix A as due to inconsistent each element of pairwise comparison matrix D and add the result after disturbance, so first set about revising from that element that disturbance is maximum, obtain maximum perturbation amount δ _rs, determine the value of r and s, and revise d _rsand d _sr, by d _rsitem subtracts 1, d _sritem revises accordingly, and obtains new pairwise comparison matrix δ _rssolve according to the following formula:

${\mathrm{\&delta;}}_{\mathrm{rs}}=\underset{p,q}{\max }\left\{{\mathrm{\&delta;}}_{\mathrm{pq}}\right\}=\underset{p,q}{\max }\left\{d_{\mathrm{pq}}\frac{x_q}{x_p}\right\}p,q=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n$

Right ask consistency ration, if meet coherence request, then stop optimizing, otherwise continue to ask maximum perturbation amount, and right maximum perturbation amount corresponding in element modify, then consistency ration is recalculated to the matrix after having revised, repeats above-mentioned steps until pairwise comparison matrix has satisfied consistance.

(4.4) assemble the determination of expert opinion and each index weights, try to achieve one-level weight and secondary weight vectors;

Adopt a kind of method of scales transforming,-8 ~ 8 scales are become by 1 ~ 9 scales transforming, then the data after conversion are assembled, and in the process of assembling, consider the weight of decision maker individual, because be all the same to the cognition of decision problem not reaching all decision maker, the corresponding relation of scales transforming is as follows

During assembly, first convert the data that decision maker inputs to-8 ~ 8 scales, the individual weight then with decision maker is weighted on average, and simply rounds up to the result after assembling, then is transformed into 1 ~ 9 scale, obtains final aggregate matrix.The proper vector of aggregate matrix is corresponding weight vectors, and construct pairwise comparison matrix respectively according to an expert view, trying to achieve one-level weight is W, and secondary weight vectors is Wi.

5th step, determines secondary fuzzy evaluation vector B _i; That is:

$B_i=W_i\&CenterDot;R_i=(w_{i1},w_{i2},\&CenterDot;\&CenterDot;\&CenterDot;w_{\mathrm{iJ}})\left[\begin{array}{cccccc}{r}_{i11}& r_{i12}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{i1l}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{i1L}\\ r_{i21}& r_{i22}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{i2l}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{i2L}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& & \&CenterDot;& \\ \&CenterDot;& \&CenterDot;& \&CenterDot;& & \&CenterDot;& \\ \&CenterDot;& \&CenterDot;& \&CenterDot;& & \&CenterDot;& \\ r_{\mathrm{iJ}1}& r_{\mathrm{iJ}2}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{\mathrm{iJl}}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{\mathrm{iJL}}\end{array}\right]=(b_{i1},b_{i2},\&CenterDot;\&CenterDot;\&CenterDot;,b_{\mathrm{iL}})$

In formula, W _ifor secondary weight vectors, R _ifor fuzzy expert Judgement Matrix, ω _ijfor W _icomponent, j=1,2 ... J.

6th step, determines the Membership Vestor b of Railway Disaster risk revulsion U to Comment gathers V; Be specially:

Fuzzy comprehensive evoluation matrix:

$B=\left[\begin{array}{c}{B}_1\\ B_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ B_I\end{array}\right]=\left[\begin{array}{cccc}{b}_{11}& b_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& b_{1L}\\ b_{21}& b_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& b_{2L}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ b_{I1}& b_{I2}& \&CenterDot;\&CenterDot;\&CenterDot;& b_{\mathrm{IL}}\end{array}\right]$

Railway Disaster risk revulsion U is to the Membership Vestor b of Comment gathers V:

b＝W·B＝(b ₁，b ₂，…b _L)

In formula: W represents one-level weight, B fuzzy comprehensive evoluation matrix.

7th step, traditional Field Using Fuzzy Comprehensive Assessment generally judges disaster rank according to maximum membership grade principle, and even Membership Vestor is b=(b ₁, b ₂... b _m), b _ψ=max (b ₁, b ₂... b _m), disaster rank to be evaluated is ψ level.When the largest component in fuzzy comprehensive evoluation matrix and the 2nd large component are more or less the same, show that evaluation conclusion is slightly reluctantly aobvious according to maximum membership grade principle, the present invention comprehensively adopts Reliability Code and rank feature values formula determination railway heavy snow calamity source level of evaluation, and concrete steps are:

(7.1) according to Membership Vestor b, the availability α of maximum membership grade principle is calculated:

$\mathrm{\&alpha;}=\frac{\mathrm{m\&beta;}-1}{2\mathrm{\&gamma;}(m-1)}$

In formula: m is the element number of Membership Vestor b, β is maximum membership degree, and γ is the 2nd large degree of membership;

(7.2) adaptability of maximum membership grade principle is judged:

As 0.5≤α < 1, maximum membership grade principle is effective, adopts maximum membership grade principle assessment railway heavy snow calamity source rank; As 0≤α < 0.5, maximum membership grade principle poor efficiency; When α=0, maximum membership grade principle complete failure;

(7.3) as availability α <0.5, the following two kinds of method determination railway heavy snow calamity source ranks of comprehensive employing:

(1) application level eigenwert formulae discovery railway heavy snow calamity source rank:

$H=\underset{u=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{ub}}_u$

In formula: b _ufor the component of Membership Vestor b, m is the element number of Membership Vestor b;

(2) (V is established ₁, V ₂..., V _l) be an orderly railway heavy snow Hazard Risk Assessment collection, λ is degree of confidence, and monitoring railway risk class belongs to V _lthe degree of membership of class is b _l, note monitoring railway risk class is V _k, then there is following formula:

$k=\min \{k:\underset{l=1}{\overset{k}{\mathrm{\&Sigma;}}}{b}_l\&GreaterEqual;\mathrm{\&lambda;},1\&le;k\&le;L\}$

In formula: b _lthe component of Membership Vestor b, m is the element number of Membership Vestor b.

Reliability Code considers from the angle of " by force ", artificially more strong better, and the large percentage that the classification of " by force " should account for.Degree of confidence λ generally gets 0.6 ~ 0.7, gets 0.6 herein.

Embodiment 1

Railway heavy snow Hazard Risk Assessment grade classification is 5 grade: V by comprehensive expert opinion ₁=high, V ₂=higher, V ₃=general, V ₄=lower, V ₅=low, choose 10 experts in industry, railway operation and relevant historical data are provided, the judge of expert to the railway heavy snow calamity source level status of certain Railway Bureau " Feng Le ~ peace " section is solicited by sending a letter, data craft's suggestion, obtain the risk class probability distribution of each risk indicator, as shown in table 3:

Table 3 risk class probability distribution

Then can obtain each fuzzy expert Judgement Matrix is:

$R_1=\left[\begin{array}{ccccc}0.1& 0.1& 0.2& 0.4& 0.2\\ 0.1& 0.2& 0.3& 0.3& 0.1\\ 0.2& 0.2& 0.4& 0.1& 0.1\\ 0.2& 0.3& 0.3& 0.1& 0.1\end{array}\right],R_2=\left[\begin{array}{ccccc}0.1& 0.1& 0.4& 0.3& 0.1\\ 0.2& 0.3& 0.1& 0.2& 0.2\\ 0.3& 0.3& 0.2& 0.1& 0.1\end{array}\right]$

$R_3=\left[\begin{array}{ccccc}0.1& 0.2& 0.3& 0.2& 0.1\\ 0.1& 0.3& 0.2& 0.2& 0.2\\ 0.2& 0.2& 0.3& 0.2& 0.1\end{array}\right],R_4=\left[\begin{array}{ccccc}0.1& 0.4& 0.2& 0.2& 0.1\\ 0.1& 0.3& 0.2& 0.2& 0.2\\ 0.2& 0.3& 0.3& 0.1& 0.1\end{array}\right]$

According to the judgement of expert A to one-level judging quota importance between two, multilevel iudge matrix can be obtained:

$A^{\left(1\right)}=\left[\begin{array}{cccc}1& 2& 3& 5\\ 1/2& 1& 1/2& 7\\ 1/3& 2& 1& 4\\ 1/5& 1/7& 1/4& 1\end{array}\right]$

First try to achieve the eigenvalue of maximum of matrix, and all proper vectors are normalized, obtain eigenvalue of maximum and normalized vector is respectively λ _max=4.2950, ω ⁽¹⁾=(0.4582,0.2296,0.2551,0.0571), then obtains A according to formula (2), (3) ⁽¹⁾coincident indicator be C _o=0.0983, C _s=0.1105 > 0.1, this matrix does not meet conforming requirement as seen.According to formula (4), obtain A ⁽¹⁾all disturbance quantities and maximum perturbation amount:

${\mathrm{\&delta;}}_{\mathrm{rs}}=\left[\begin{array}{cccc}1.0000& 1.0020& 1.6697& 0.6232\\ 0.9980& 1.0000& 0.5555& 1.7416\\ 0.5989& 1.8003& 1.0000& 0.8958\\ 1.6045& 0.5742& 1.1163& 1.0000\end{array}\right]$

δ _max＝1.8003

To A ⁽¹⁾in a ₃₂revise, by a ₃₂scale subtracts 1, then can obtain multilevel iudge matrix newly:

$A^{\&prime;}=\left[\begin{array}{cccc}1& 2& 3& 5\\ 1/2& 1& 1& 7\\ 1/3& 1& 1& 4\\ 1/5& 1/7& 1/4& 1\end{array}\right]$

Try to achieve matrix A ' eigenvalue of maximum, and all proper vectors to be normalized, to obtain eigenvalue of maximum and normalized vector is respectively λ ' _max=4.1664, ω '=(0.4632,0.2697,0.2089,0.0583) is then C according to the coincident indicator that A ' is obtained in formula (2), (3) _o=0.0488, C _s=0.0548 < 0.1, visible revised matrix meets conforming requirement.

In like manner can obtain expert B to one-level judging quota multilevel iudge matrix:

$B^{\&prime;}=\left[\begin{array}{cccc}1& 1/3& 3& 5\\ 3& 1& 2& 8\\ 1/3& 1/2& 1& 2\\ 1/5& 1/8& 1/2& 1\end{array}\right]$

According to Mode of Level Simple Sequence scales transforming used, assemble expert A, B viewpoint, multilevel iudge Matrix C newly can be obtained, with C ₁₂element is example, and Mode of Level Simple Sequence assembling process is described.Elements A ' ₁₂being 2, is-1 after scales transforming, element B ' ₁₂being 1/3, is 2 after scales transforming, 0.5 (-1)+0.52=1/2 after weighted mean, then is transformed into 1 ~ 9 scale, the multilevel iudge Matrix C after can assembling ₁₂=1.

Adopt same procedure all 10 expert view are assembled, obtain primary risk index between two relatively after multilevel iudge matrix:

$M=\left[\begin{array}{cccc}1& 3& 2& 7\\ 1/3& 1& 3& 3\\ 1/2& 1/3& 1& 2\\ 1/7& 1/3& 1/2& 1\end{array}\right]$

Try to achieve the eigenvalue of maximum of matrix M and corresponding normalized vector, be respectively λ _max=4.2020, ω=(0.5069,0.2658,0.1532,0.0742) is then C according to the coincident indicator that M is obtained in formula (2), (3) _o=0.0673, C _s=0.0757 < 0.1, assembles the multilevel iudge matrix after all experts and meets coherence request.

In sum, one-level weight is ω=(0.5069,0.2658,0.1532,0.0742).

In like manner can obtain, with the two-level index Judgment Matrix According as Consistent Rule of snow depth, accumulated snow duration, temperature and topographic relief amplitude be:

$U_1=\left[\begin{array}{cccc}1& 2& 6& 2\\ 1/2& 1& 2& 2\\ 1/6& 1/2& 1& 1/4\\ 1/2& 1/2& 4& 1\end{array}\right]$

With the two-level index Judgment Matrix According as Consistent Rule of line conditions, bridge tunnel situation and communication facilities be:

$U_2=\left[\begin{array}{ccc}1& 2& 4\\ 1/2& 1& 3\\ 1/4& 1/3& 1\end{array}\right]$

With the two-level index Judgment Matrix According as Consistent Rule of Employee Security sense of risk, ' professional and personnel's labor discipline idea be:

$U_3=\left[\begin{array}{ccc}1& 1/3& 2\\ 3& 1& 4\\ 1/2& 1/4& 1\end{array}\right]$

To prevent the two-level index Judgment Matrix According as Consistent Rule of recovery capability after emergency relief ability and calamity in ability, calamity before calamity be:

$U_4=\left[\begin{array}{ccc}1& 1/3& 1/2\\ 3& 1& 3\\ 2& 1/3& 1\end{array}\right]$

Try to achieve matrix U ₁eigenvalue of maximum and corresponding normalized vector, be respectively λ _max=4.1707, ω ₁=(0.4494,0.2564,0.0809,0.2133) is then C according to the coincident indicator that M is obtained in formula (2), (3) _o=0.0569, C _s=0.0639 < 0.1, so this matrix has consistance.

The weight in like manner can trying to achieve each evaluation index in other each factors is as follows:

ω ₂＝(0.5584，0.3196，0.1220)

ω ₃＝(0.2385，0.6250，0.1365)

ω ₄＝(0.1571，0.5936，0.2493)

According to formula (5), obtaining each secondary fuzzy evaluation vector is:

B ₁＝ω ₁·R ₁＝(0.1294，0.1764，0.2632，0.2861，0.1449)

B ₂＝ω ₂·R ₂＝(0.1564，0.1883，0.2919，0.2436，0.1320)

B ₃＝ω ₃·R ₃＝(0.1137，0.2625，0.2375，0.2000，0.1625)

B ₄＝ω ₄·R ₄＝(0.1249，0.3157，0.2563，0.2065，0.1594)

According to formula (6), the risk probability obtaining each two-level index is:

$B=\left[\begin{array}{ccccc}0.1294& 0.1764& 0.2632& 0.2861& 0.1449\\ 0.1564& 0.1883& 0.2919& 0.2436& 0.1320\\ 0.1137& 0.2625& 0.2375& 0.2000& 0.1625\\ 0.1249& 0.3157& 0.2563& 0.2065& 0.1594\end{array}\right]$

According to formula (7), obtaining this railway section heavy snow calamity source is:

b＝(0.1338，0.2031，0.2664，0.2557，0.1453)

The availability α of maximum membership grade principle is calculated according to formula (8), α=0.1662<0.5, visible maximum membership grade principle lost efficacy, and judged this section heavy snow calamity source rank according to formula (9), formula (10).

According to formula (9), then railway heavy snow disaster rank is between 3,4 grades and is partial to 3 grades, need be determined further by Reliability Code;

According to formula (10), because the first two component sum of b is 0.369, first three component sum is 0.6033, and degree of confidence is herein 0.6, and therefore the minimum value of k is 3, and namely railway heavy snow disaster rank is V ₃, this section heavy snow calamity source rank is in " generally ".

According to rank feature values formula, this section heavy snow calamity source rank deflection V ₃, judged further by Reliability Code, can judge that this section railway heavy snow calamity source is in V ₃rank.

In sum, the present invention compared with prior art, can judge railway heavy snow calamity source rank rationally, reliably, formulate preparedness measure of taking precautions against natural calamities exactly, reduce all kinds of loss for science, guarantees that circuit is unimpeded, train running on scheduled time runs very necessary.

Claims (8)

1. a railway heavy snow calamity source Fuzzy Synthetic Evaluation, is characterized in that: comprise the following steps:

1st step, sets up the set of factors U of tolerance railway heavy snow calamity source;

2nd step, setting railway heavy snow calamity source evaluation grade V;

3rd step, data craft's suggestion, carries out the assessment of secondary risk Judgement Matrix, sets up railway heavy snow disaster fuzzy expert Judgement Matrix R _i;

4th step, determines each risk indicator weight based on the group decision analytical hierarchy process improved;

5th step, determines secondary fuzzy evaluation vector B _i;

6th step, determines the Membership Vestor b of Railway Disaster risk revulsion U to Comment gathers V;

7th step, comprehensive employing Reliability Code and rank feature values formula determination railway heavy snow calamity source level of evaluation.

2. railway heavy snow calamity source Fuzzy Synthetic Evaluation according to claim 1, is characterized in that: the set of factors U setting up tolerance railway heavy snow calamity source described in the 1st step, specific as follows:

Determine railway heavy snow calamity source set of factors U={u _i, i=1,2 ... I, I are the u of one-level evaluation index _inumber, u _i={ u _ij, j=1,2 ... J, J are one-level evaluation index u _iunder secondary evaluation index u _ijnumber.

3. railway heavy snow calamity source Fuzzy Synthetic Evaluation according to claim 1, is characterized in that: set railway heavy snow calamity source evaluation grade V described in the 2nd step, be specially:

According to the needs that actual conditions and railway heavy snow calamity source are assessed, be L grade: V={V by railway heavy snow Hazard Risk Assessment grade classification _l, l=1,2 ..., L.

4. railway heavy snow calamity source Fuzzy Synthetic Evaluation according to claim 1, is characterized in that: set up railway heavy snow disaster fuzzy expert Judgement Matrix R described in the 3rd step _i:

$R_i={\left(r_{\mathrm{ijl}}\right)}_{J\&times;L}=\left[\begin{array}{cccc}{r}_{i11}& r_{i12}& ...& r_{i1l}...r_{i1L}\\ r_{i21}& r_{i22}& ...& r_{i2l}...r_{i2L}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ r_{\mathrm{iJ}1}& r_{\mathrm{iJ}2}& ...& r_{\mathrm{iJl}}...r_{\mathrm{iJL}}\end{array}\right]$

In formula, r _ijlrepresent index u _ijto l level comment V _ldegree of membership, r _ijl=s _ijl/ s, s are the expert's sum participating in Fuzzy comprehensive evaluation, s _ijlfor thinking index u in the expert that participates in evaluation and electing _ijbelong to evaluation approach V _lexpert's number, know

5. railway heavy snow calamity source Fuzzy Synthetic Evaluation according to claim 1, is characterized in that: determine each risk indicator weight based on the group decision analytical hierarchy process improved described in the 4th step, concrete steps are:

(4.1) hierarchical structure model is set up;

(4.2) pairwise comparison matrix is constructed: the Scale Method structure pairwise comparison matrix adopting 1 ~ 9 scale and inverse thereof;

If the unit of lower floor that element M is arranged altogether have n, i.e. a ₁, a ₂..., a _n, then the pairwise comparison matrix A=(a adopting 1 ~ 9 scale to draw _pq) _{n × n}there is following form:

M a ₁a ₂… a _n

Wherein, a _pqrepresent with element M to be criterion, element a _pto element a _qthe comparison of significance level;

(4.3) pairwise comparison matrix consistency check method improves;

(1) the coincident indicator C of pairwise comparison matrix is determined _o:

$C_O=\frac{{\mathrm{\&lambda;}}_{\max }-n}{n-1}$

Wherein, λ _maxfor the eigenvalue of maximum of pairwise comparison matrix, n is the dimension of pairwise comparison matrix;

(2) consistency ration C is determined _s:

$C_S=\frac{C_O}{S_O}$

Wherein, S _ofor random index;

(3) inconsistent pairwise comparison matrix D regards a crash consistency comparator matrix A as and has added a disturbance quantity δ _pqif the eigenvalue of maximum of A is λ _max, proper vector is x=(x ₁, x ₂..., x _n), then the element in matrix A meets a _pq=x _p/ x _q, in so inconsistent pairwise comparison matrix D, element is:

d _pq＝a _pq·δ _pq

As consistency ration C _sduring > 0.1, determine inconsistent pairwise comparison matrix D disturbance quantity δ _pq:

${\mathrm{\&delta;}}_{\mathrm{pq}}=d_{\mathrm{pq}}\&CenterDot;\frac{x_q}{x_p}$

In formula, p, q=1,2,3 ..., n;

(4) maximum perturbation amount δ is obtained _rs, determine the value of r and s, and revise d _rsand d _sr, by d _rsitem subtracts 1, d _sritem revises accordingly:

${\mathrm{\&delta;}}_{\mathrm{rs}}=\underset{p,q}{\max }\left\{{\mathrm{\&delta;}}_{\mathrm{pq}}\right\}=\underset{p,q}{\max }\left\{d_{\mathrm{pq}}\frac{x_q}{x_p}\right\}$

(5) construct new pairwise comparison matrix, repeat step (1) ~ (4), until new pairwise comparison matrix has satisfied consistance;

(4.4) assemble the determination of expert opinion and each index weights, try to achieve one-level weight and secondary weight vectors.

6. railway heavy snow calamity source Fuzzy Synthetic Evaluation according to claim 1, is characterized in that: determine secondary fuzzy evaluation vector B described in the 5th step _i, that is:

$B_i=W_i\&CenterDot;R_i=(w_{i1},w_{i2},...w_{\mathrm{iJ}})\left[\begin{array}{cccc}{r}_{i11}& r_{i12}& ...& r_{i1l}...r_{i1L}\\ r_{i21}& r_{i22}& ...& r_{i2l}...r_{i2L}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ r_{\mathrm{iJ}1}& r_{\mathrm{iJ}2}& ...& r_{\mathrm{iJl}}...r_{\mathrm{iJL}}\end{array}\right]=(b_{i1},b_{i2},...,b_{\mathrm{iL}})$

In formula, W _ifor secondary weight vectors, R _ifor fuzzy expert Judgement Matrix, ω _ijfor W _icomponent, j=1,2 ... J.

7. railway heavy snow calamity source Fuzzy Synthetic Evaluation according to claim 1, is characterized in that: determine the Membership Vestor b of Railway Disaster risk revulsion U to Comment gathers V described in the 6th step, be specially:

Fuzzy comprehensive evoluation matrix:

$B=\left[\begin{array}{c}{B}_1\\ B_2\\ .\\ .\\ .\\ B_I\end{array}\right]=\left[\begin{array}{cccc}{b}_{11}& b_{12}& ...& b_{1L}\\ b_{21}& b_{22}& ...& b_{2L}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ b_{I1}& b_{I2}& ...& b_{\mathrm{IL}}\end{array}\right]$

Railway Disaster risk revulsion U is to the Membership Vestor b of Comment gathers V:

b＝W·B＝(b ₁，b ₂，…b _L)

In formula: W represents one-level weight, B fuzzy comprehensive evoluation matrix.

8. railway heavy snow calamity source Fuzzy Synthetic Evaluation according to claim 1, is characterized in that: comprehensive employing Reliability Code and rank feature values formula determination railway heavy snow calamity source level of evaluation described in the 7th step, and concrete steps are:

(7.1) according to Membership Vestor b, the availability α of maximum membership grade principle is calculated:

$\mathrm{\&alpha;}=\frac{\mathrm{m\&beta;}-1}{2\mathrm{\&gamma;}(m-1)}$

In formula: m is the element number of Membership Vestor b, β is maximum membership degree, and γ is the 2nd large degree of membership;

(7.2) adaptability of maximum membership grade principle is judged:

As 0.5≤α < 1, maximum membership grade principle is effective, adopts maximum membership grade principle assessment railway heavy snow calamity source rank; As 0≤α < 0.5, maximum membership grade principle poor efficiency; When α=0, maximum membership grade principle complete failure;

(7.3) as availability α <0.5, the following two kinds of method determination railway heavy snow calamity source ranks of comprehensive employing:

(1) application level eigenwert formulae discovery railway heavy snow calamity source rank:

$H=\underset{u=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{ub}}_u$

In formula: b _ufor the component of Membership Vestor b, m is the element number of Membership Vestor b;

(2) (V is established ₁, V ₂..., V _l) be an orderly railway heavy snow Hazard Risk Assessment collection, λ is degree of confidence, and monitoring railway risk class belongs to V _lthe degree of membership of class is b _l, note monitoring railway risk class is V _k, then there is following formula:

$k=\min \{k:\underset{l=1}{\overset{k}{\mathrm{\&Sigma;}}}{b}_l\&GreaterEqual;\mathrm{\&lambda;},1\&le;k\&le;L\}$

In formula: b _lthe component of Membership Vestor b, m is the element number of Membership Vestor b.