CN104240154A - Distribution switch state quantity weight determination method based on extension hierarchy and critic - Google Patents

Abstract

The invention relates to a distribution switch equipment state evaluation technique, in particular to a distribution switch state quantity weight determination method based on extension hierarchy and critic. The method comprises the following steps of gathering distribution switch equipment state quantity data information; establishing a distribution switch equipment state quantity evaluation system; constructing an extension judgment matrix according to the state quantity evaluation system; calculating a comprehensive extension judgment matrix and a weight vector to obtain a static weight; obtaining a dynamic weight by using a critic method; and obtaining a comprehensive weight of a distribution switch equipment state quantity by using the obtained static weight and the obtained dynamic weight. The distribution switch state quantity weight is determined by using the method, and the objectivity and the subjectivity are improved. A weight evaluation result is objective, fair and accurate.

Description

A kind of panel switches quantity of state Weight Determination based on level and critic can be opened up

Technical field

The present invention relates to distribution switchgear state evaluation technology, especially relate to a kind of panel switches quantity of state Weight Determination based on level and critic can be opened up.

Background technology

Power distribution network is the electric power networks connecting power transmission network and user, it is the basis of electric system, its safe and stable operation and the interests of user have indivisible relation, in order to ensure the safe and stable operation of power distribution network, need to carry out state evaluation to distribution switches equipment.

Carrying out in state evaluation to distribution switchgear, the determination of evaluation index (quantity of state) weight is its key problem.At present two classes are mainly divided into the method that distribution switchgear quantity of state weight is determined: subjectivity and objectivity enabling legislation.Subjective weighting method compares according to the importance of judgement to each state of decision maker's subjectivity the power of tax, mainly contains analytical hierarchy process and expert point rating method etc.; Objective weighted model is a kind of method according to actual conditions, mutual relationship and degree of variation between each quantity of state being determined to weight, mainly contains entropy assessment, principal component analysis (PCA), critic method etc.The present invention adopt the subjective and objective enabling legislation combined of Extension AHP and critic method can rationally, exactly weight is carried out to distribution switchgear and determines.

Summary of the invention

The present invention mainly solves the technical matters existing for prior art; Provide and a kind ofly overcome deficiency that is main, objective weighted model, effectively can carry out weight to distribution switchgear quantity of state and determine, make result objective, just based on the panel switches quantity of state Weight Determination can opening up level and critic.

Above-mentioned technical matters of the present invention is mainly solved by following technical proposals:

Based on the panel switches quantity of state Weight Determination can opening up level and critic, it is characterized in that, comprise the following steps:

Step 1: collect distribution switchgear state quantity data information, builds distribution switchgear quantity of state rating database; Wherein, described panel switches state quantity data information comprises: the panel switches state quantity data of on-line monitoring, the state quantity data of operational inspection, the state quantity data of electrical test gained, by the quantity of state rating database of the data construct distribution switchgear of enough panel switches.

Step 2: can judgment matrix be opened up according to the quantity of state rating database structure that step 1 is set up, calculate and comprehensively can open up judgment matrix and weight vectors, draw static weight; Specifically comprise following sub-step:

Step 2.1, constructs preliminary multilevel iudge matrix, and multilevel iudge matrix gets by mutually comparing the relative Link Importance between two quantity of states.Definition a _ijrepresent the relative importance of i-th quantity of state and a jth quantity of state.Quantity of state i and quantity of state j no less important, then a _ii=1; If quantity of state i is more important a little than quantity of state j, then a _ij=3; If quantity of state i is obviously more important than quantity of state j, then a _ij=5; If quantity of state i is stronger than quantity of state important, then a _ij=7; If quantity of state i is extremely more important than quantity of state j, then a _ij=9; Wherein a _iirepresent that i-th factor of influence compares with the importance degree of self, therefore a _ii=1, what finally formed is the multilevel iudge matrix of a n × n.

Step 2.2, use the preliminary multilevel iudge matrix that extension science principle obtains based on step 2.1, acquisition can open up judgment matrix; Namely in extension science principle, for each element value a in preliminary multilevel iudge matrix _ij, all have an interval number

$K\left(a_{\mathrm{ij}}\right)=[\underset{\‾}{K}\left(a_{\mathrm{ij}}\right),\stackrel{\‾}{K}\left(a_{\mathrm{ij}}\right)]\∈I,\underset{\‾}{K}\left(a_{\mathrm{ij}}\right),\stackrel{\‾}{K}\left(a_{\mathrm{ij}}\right)\∈R$

Corresponding with it, multilevel iudge matrix is changed to one by single integer and can opens up interval.Final formation be one by the multilevel iudge the opened up matrix A can opening up the interval n × n formed.

Step 2.3, calculates and comprehensively can open up judgment matrix and weight vectors, draw static weight; Definition can open up comparator matrix A=< A ^-, A ⁺>, obtains matrix A ⁺, A ^-the normalization characteristic vector x of what eigenvalue of maximum was corresponding have positive component ⁺, x ^-, X=<kx ^-, mx ⁺> is all proper vectors that A corresponds to, w=(w ₁, w ₂... w _n) ^tfor weight vectors, then w=(w ₁, w ₂... w _n) ^t=[kx ^-, mx ⁺], sufficient and necessary condition be

$\frac{k}{m}=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{{\mathrm{\&Sigma;}}_{i=1}^n{a_{\mathrm{ij}}}^{+}}=\frac{1}{{\mathrm{\&Sigma;}}_{j=1}^n\frac{1}{{\mathrm{\&Sigma;}}_{i=1}^n{a_{\mathrm{ij}}}^{-}}}$

Therefore, can obtain

$\begin{array}{cc}k=\sqrt{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{{\mathrm{\&Sigma;}}_{i=1}^n{a_{\mathrm{ij}}}^{+}}}& m=\sqrt{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{{\mathrm{\&Sigma;}}_{i=1}^n{a_{\mathrm{ij}}}^{-1}}}\end{array}.$

Wherein proper vector S=< kx ^-, mx ⁺>.Static weight is established according to interval number relative importance can be opened up.For the element on K layer, their weight is all with interval number represent.According to extension science knowledge, interval number ratio importance degree can calculate by following expression formula,

$V(S_i^k\&GreaterEqual;S_j^k)=\frac{2(S_i^{k^{+}}-S_j^{k^{-}})}{(S_j^{k^{+}}+S_j^{k^{-}})+(S_i^{k^{+}}+S_i^{k^{-}})}$

For arbitrary i=1,2,3..., n _k; I ≠ j, has then get

$W_j^k=1,W_i^k=V(S_i^k\&GreaterEqual;S_j^k)i=\mathrm{1,2,3}\&CenterDot;\&CenterDot;\&CenterDot;,n_k;i\&NotEqual;j$

Therefore single orderweight vector of each element of K layer and the quantity of state appraisement system of distribution switchgear is multi-level structure, each quantity of state S of the definition bottom _i(n-th layer) is to each Elements C of N-1 layer _jsingle orderweight vector $q_i^N={(q_{1j}^N,q_{2j}^N,\&CenterDot;\&CenterDot;\&CenterDot;,q_{N_{n}j}^N)}^T(i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N_n),$ Make N _n× (N-1) _nrank matrix

$q^N=(q_1^N,q_2^N,\&CenterDot;\&CenterDot;\&CenterDot;,q_{N-1_n}^N)=\left[\begin{array}{cccc}{q}_{11}^N& q_{12}^N& \&CenterDot;\&CenterDot;\&CenterDot;& q_{1{(N-1)}_n}^N\\ q_{21}^N& q_{22}^N& \&CenterDot;\&CenterDot;\&CenterDot;& q_{2{(N-1)}_n}^N\\ M& M& & M\\ q_{N1}^N& q_{N2}^N& \&CenterDot;\&CenterDot;\&CenterDot;& q_{N{(N-1)}_n}^N\end{array}\right]$

Each Elements C of K layer _jcombination weight order for general objective layer is:

$W^K={(w_1^K,w_2^K,\&CenterDot;\&CenterDot;\&CenterDot;,W_{K_n}^K)}^{T}j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;K_n$

Therefore each quantity of state of the bottom is W for the static weight of general objective ⁿ=q ⁿw ^n-1.

Step 3: use critic method to draw changeable weight, specifically comprise following sub-step:

Step 3.1, structure Evaluations matrix, and ask the correlation matrix of Evaluations matrix.

For N number of distribution switchgear sample, for M quantity of state situation, structure Evaluations matrix T.

$T=\left[\begin{array}{cccc}{t}_{11}& t_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& t_{1M}\\ t_{21}& t_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& t_{2M}\\ M& M& & M\\ T_{N1}& t_{N2}& \&CenterDot;\&CenterDot;\&CenterDot;& t_{\mathrm{NM}}\end{array}\right]$

Each quantity of state S _i(i=1,2 ..., M), its standard deviation is

${\mathrm{\&sigma;}}_i=\sqrt{\frac{{(t_{1i}-{\stackrel{\&OverBar;}{t}}_i)}^2+{(t_{2i}-{\stackrel{\&OverBar;}{t}}_i)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(t_{\mathrm{Ni}}-{\stackrel{\&OverBar;}{t}}_i)}^2}{N}}$

Wherein for mean value.

The related coefficient of the quantity of state in this Evaluations matrix T can solve with following formula

$r_{i,j}=\frac{\mathrm{cov}(t_i,t_j)}{{\mathrm{\&sigma;}}_i{\mathrm{\&sigma;}}_j}=\frac{E(t_i-{\stackrel{\&OverBar;}{t}}_i)(t_j-{\stackrel{\&OverBar;}{t}}_j)}{{\mathrm{\&sigma;}}_i{\mathrm{\&sigma;}}_j}$

Wherein cov (t _i, t _j) be covariance between two parameters, be respectively the sample average of parameter.Defined by the related coefficient between parameter, can obtain the related coefficient of each row of Evaluations matrix T, the correlation matrix of Evaluations matrix T is:

$R=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{1M}\\ r_{21}& r_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{2M}\\ M& M& & M\\ r_{M1}& r_{M2}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{\mathrm{MM}}\end{array}\right]$

From the symmetry of correlation matrix, r _ij=r _ji

Step 3.2, determines changeable weight.

Critic method be by evaluation index between conflicting and specific strength is carried out to the objective weight of agriculture products.Then the conflicting quantizating index of i-th quantity of state and other quantity of states is used

$c_i={\mathrm{\&sigma;}}_i\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}(1-r_{\mathrm{ij}})j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,M$

C _irepresent the quantity of information that i-th quantity of state comprises.C _ilarger, then containing much information contained by this quantity of state, the weight of this quantity of state is larger.Therefore, the changeable weight of i-th quantity of state is

$W_i=\frac{c_i}{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{c}_i}i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,M$

Step 4: by static weight and changeable weight, draws the comprehensive weight of distribution switchgear quantity of state.

According to the static weight W obtained _jwith changeable weight W _d, adopt multiplicative synthesis normalization method to obtain comprehensive weight W _{comprehensively}.

So far, complete the weight of a distribution switchgear M quantity of state is determined.

Therefore, tool of the present invention has the following advantages: overcome deficiency that is main, objective weighted model, effectively can carry out weight to distribution switchgear quantity of state and determine, make result objective, just.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of the panel switches appraisement system Weight Determination based on Extension AHP and critic method of the present invention.

Embodiment

Below by embodiment, and by reference to the accompanying drawings, technical scheme of the present invention is described in further detail.In figure.

Embodiment:

The schematic diagram of the panel switches appraisement system Weight Determination embodiment based on Extension AHP and critic method of the present invention is shown in Fig. 1.

As shown in Figure 1, the panel switches appraisement system Weight Determination based on Extension AHP and critic method in the present embodiment comprises step:

Step S101: collect distribution switchgear state quantity data information, builds distribution switchgear quantity of state appraisement system;

Collect panel switches state quantity data information, comprising: the panel switches state quantity data of on-line monitoring, the state quantity data of operational inspection, the state quantity data of electrical test gained, and expert is to the evaluation result of panel switches.By the quantity of state appraisement system of the data construct distribution switchgear of enough panel switches.This appraisement system is mainly divided into three levels, i.e. destination layer, rule layer, factor layer.

Step S102: can judgment matrix be opened up according to quantity of state appraisement system structure, calculate and comprehensively can open up judgment matrix and weight vectors, draw static weight;

Step 2.1, constructs preliminary multilevel iudge matrix

Multilevel iudge matrix gets by mutually comparing the relative Link Importance between two quantity of states.If a _ijrepresent the relative importance of i-th quantity of state and a jth quantity of state.Quantity of state i and quantity of state j no less important, then a _ii=1; If quantity of state i is more important a little than quantity of state j, then a _ij=3; If quantity of state i is obviously more important than quantity of state j, then a _ij=5; If quantity of state i is stronger than quantity of state important, then a _ij=7; If quantity of state i is extremely more important than quantity of state j, then a _ij=9; Wherein a _iirepresent that i-th factor of influence compares with the importance degree of self, therefore a _ii=1, what finally formed is the multilevel iudge matrix of a n × n.

Step 2.2, extension science principle

Define 1 interval extension set

If there is any one element x, i.e. x ∈ X on domain X, there is an interval number

$K\left(x\right)=[\underset{\&OverBar;}{K}\left(x\right),\stackrel{\&OverBar;}{K}\left(x\right)]\&Element;I,\underset{\&OverBar;}{K}\left(x\right),\stackrel{\&OverBar;}{K}\left(x\right)\&Element;R$

Corresponding with it, then claim

A＝{(x,y)|x∈X,y＝K(x)＝[K(x),K(x)]∈I}

For the interval extension set of on domain X closes, be called for short XI extendible set.The positive territory of A and negative domain can be expressed as:

$\begin{array}{c}A=\left\{x\right|x\&Element;X,\underset{\&OverBar;}{K}\left(x\right)\&GreaterEqual;0\}\\ A=\left\{x\right|x\&Element;X,\stackrel{\&OverBar;}{K}\left(x\right)\&le;0\}\end{array}$

Definition 2 can open up interval arithmetic

If a=< is a ^-, a ⁺>, b=< b ^-, b ⁺> is two can open up interval, and the possibility degree that we define a|b is

$V(a\&GreaterEqual;b)=\frac{2(a^{+}-b^{-})}{(b^{+}+b^{-})+(a^{+}+a^{-})}$

Theorem 1 establishes A=[A ^-, A ⁺], λ ^-, λ ⁺it is left and right matrix A ^-, A ⁺eigenvalue of maximum, then

(1) λ=[λ ^-, λ ⁺] be the interval number eigenwert of A;

(2) x=[kx ^-, mx ⁺] be the proper vector about λ of A, wherein x ^-, x ⁺a respectively ^-, A ⁺be λ corresponding to eigenwert ^-, λ ⁺proper vector, k, m are arithmetic numbers, and meet mx ⁺>=kx ^->=0.

Theorem 2x ^-, x ⁺a respectively ^-, A ⁺corresponding to eigenvalue of maximum λ ^-, λ ⁺normalization characteristic vector, w=(w ₁, w ₂... w _n) ^tfor weight vectors, then w=(w ₁, w ₂... w _n) ^t=[kx ^-, mx ⁺], sufficient and necessary condition be

$\frac{k}{m}=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{{\mathrm{\&Sigma;}}_{i=1}^n{a_{\mathrm{ij}}}^{+}}=\frac{1}{{\mathrm{\&Sigma;}}_{j=1}^n\frac{1}{{\mathrm{\&Sigma;}}_{i=1}^n{a_{\mathrm{ij}}}^{-}}}$

Step 2.3, uses extension science principle, obtains opening up judgment matrix.

Use extension science principle, multilevel iudge matrix is changed to one by single integer and can opens up interval.Final formation be one by the multilevel iudge the opened up matrix A can opening up the interval n × n formed.

Step 2.4, calculates and comprehensively can open up judgment matrix and weight vectors, draw static weight.

If comparator matrix A=< A can be opened up ^-, A ⁺>, obtains matrix A ⁺, A ^-the normalization characteristic vector x of what eigenvalue of maximum was corresponding have positive component ⁺, x ^-, X=<kx ^-, mx ⁺> is all proper vectors that A corresponds to, and according to extension science theorem 2, can obtain

$K=\sqrt{\underset{J=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{1}{{\mathrm{\&Sigma;}}_{i=1}^n{a_{\mathrm{ij}}}^{+}}}$

$m=\sqrt{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{{\mathrm{\&Sigma;}}_{i=1}^n{a_{\mathrm{ij}}}^{-}}}.$

Wherein proper vector S=< kx ^-, mx ⁺>.Static weight is established according to interval number relative importance can be opened up.For the element on K layer, their weight is all with interval number represent.According to definition 2, interval number ratio importance degree can calculate by following expression formula,

$V(S_i^k\&GreaterEqual;S_j^k)=\frac{2(S_i^{k^{+}}-S_j^{k^{-}})}{(S_j^{k^{+}}+S_j^{k^{-}})+(S_i^{k^{+}}+S_i^{k^{-}})}$

For arbitrary i=1,2,3..., n _k; I ≠ j, has then get

$W_j^k=1,W_i^k=V(S_i^k\&GreaterEqual;S_j^k)i=\mathrm{1,2,3}\&CenterDot;\&CenterDot;\&CenterDot;,n_k;i\&NotEqual;j$

Therefore single orderweight vector of each element of K layer and the quantity of state appraisement system of distribution switchgear is multi-level structure, assuming that each quantity of state S of the bottom _i(n-th layer) is to each Elements C of N-1 layer _jsingle orderweight vector $q_i^N={(q_{1j}^N,q_{2j}^N,\&CenterDot;\&CenterDot;\&CenterDot;,q_{N_{n}j}^N)}^T(i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N_n),$ Make N _n× (N-1) _nrank matrix

$q^N=(q_1^N,q_2^N,\&CenterDot;\&CenterDot;\&CenterDot;,q_{N-1_n}^N)=\left[\begin{array}{cccc}{q}_{11}^N& q_{12}^N& \&CenterDot;\&CenterDot;\&CenterDot;& q_{1{(N-1)}_n}^N\\ q_{21}^N& q_{22}^N& \&CenterDot;\&CenterDot;\&CenterDot;& q_{2{(N-1)}_n}^N\\ M& M& & M\\ q_{N1}^N& q_{N2}^N& \&CenterDot;\&CenterDot;\&CenterDot;& q_{N{(N-1)}_n}^N\end{array}\right]$

Each Elements C of K layer _jcombination weight order for general objective layer is:

$W^K={(w_1^K,w_2^K,\&CenterDot;\&CenterDot;\&CenterDot;,W_{K_n}^K)}^{T}j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;K_n$

Therefore each quantity of state of the bottom is W for the static weight of general objective ⁿ=q ⁿw ^n-1.

Step S103: use critic method to draw changeable weight.

Step 3.1, structure Evaluations matrix, and ask the correlation matrix of Evaluations matrix.

For N number of distribution switchgear sample, for M quantity of state situation, structure Evaluations matrix T.

$T=\left[\begin{array}{cccc}{t}_{11}& t_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& t_{1M}\\ t_{21}& t_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& t_{2M}\\ M& M& & M\\ T_{N1}& t_{N2}& \&CenterDot;\&CenterDot;\&CenterDot;& t_{\mathrm{NM}}\end{array}\right]$

Each quantity of state S _i(i=1,2 ..., M), its standard deviation is

${\mathrm{\&sigma;}}_i=\sqrt{\frac{{(t_{1i}-{\stackrel{\&OverBar;}{t}}_i)}^2+{(t_{2i}-{\stackrel{\&OverBar;}{t}}_i)}^2+\&CenterDot;\&CenterDot;\&CenterDot;+{(t_{\mathrm{Ni}}-{\stackrel{\&OverBar;}{t}}_i)}^2}{N}}$

Wherein for mean value.

The related coefficient of the quantity of state in this Evaluations matrix T can solve with following formula

$r_{i,j}=\frac{\mathrm{cov}(t_i,t_j)}{{\mathrm{\&sigma;}}_i{\mathrm{\&sigma;}}_j}=\frac{E(t_i-{\stackrel{\&OverBar;}{t}}_i)(t_j-{\stackrel{\&OverBar;}{t}}_j)}{{\mathrm{\&sigma;}}_i{\mathrm{\&sigma;}}_j}$

Wherein cov (t _i, t _j) be covariance between two parameters, be respectively the sample average of parameter.Defined by the related coefficient between parameter, can obtain the related coefficient of each row of Evaluations matrix T, the correlation matrix of Evaluations matrix T is:

$R=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{1M}\\ r_{21}& r_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{2M}\\ M& M& & M\\ r_{M1}& r_{M2}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{\mathrm{MM}}\end{array}\right]$

From the symmetry of correlation matrix, r _ij=r _ji

Step 3.2, determines changeable weight.

Critic method be by evaluation index between conflicting and specific strength is carried out to the objective weight of agriculture products.Then the conflicting quantizating index of i-th quantity of state and other quantity of states is used

$c_i={\mathrm{\&sigma;}}_i\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}(1-r_{\mathrm{ij}})j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,M$

C _irepresent the quantity of information that i-th quantity of state comprises.C _ilarger, then containing much information contained by this quantity of state, the weight of this quantity of state is larger.Therefore, the changeable weight of i-th quantity of state is

$W_i=\frac{c_i}{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{c}_i}i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,M$

Step S104: by static weight and changeable weight, draws the comprehensive weight of distribution switchgear quantity of state.

According to the static weight W obtained _jwith changeable weight W _d, adopt multiplicative synthesis normalization method to obtain comprehensive weight W _{comprehensively}.

So far, complete the weight of a distribution switchgear M quantity of state is determined.

Specific embodiment described herein is only to the explanation for example of the present invention's spirit.Those skilled in the art can make various amendment or supplement or adopt similar mode to substitute to described specific embodiment, but can't depart from spirit of the present invention or surmount the scope that appended claims defines.

Claims (1)

1., based on the panel switches quantity of state Weight Determination can opening up level and critic, it is characterized in that, comprise the following steps:

Step 1: collect distribution switchgear state quantity data information, builds distribution switchgear quantity of state rating database; Wherein, described panel switches state quantity data information comprises: the panel switches state quantity data of on-line monitoring, the state quantity data of operational inspection, the state quantity data of electrical test gained, by the quantity of state rating database of the data construct distribution switchgear of enough panel switches;

Step 2: can judgment matrix be opened up according to the quantity of state rating database structure that step 1 is set up, calculate and comprehensively can open up judgment matrix and weight vectors, draw static weight; Specifically comprise following sub-step:

Step 2.1, constructs preliminary multilevel iudge matrix, and multilevel iudge matrix gets by mutually comparing the relative Link Importance between two quantity of states; Definition a _ijrepresent the relative importance of i-th quantity of state and i-th quantity of state; Quantity of state i and quantity of state j no less important, then a _ii=1; If quantity of state i is more important a little than quantity of state j, then a _ij=3; If quantity of state i is obviously more important than quantity of state j, then a _ij=5; If quantity of state i is stronger than quantity of state important, then a _ij=7; If quantity of state i is extremely more important than quantity of state j, then a _ij=9; Wherein a _iirepresent that i-th factor of influence compares with the importance degree of self, therefore a _ii=1, what finally formed is the multilevel iudge matrix of a n × n;

Step 2.2, use the preliminary multilevel iudge matrix that extension science principle obtains based on step 2.1, acquisition can open up judgment matrix; Namely in extension science principle, for each element value a in preliminary multilevel iudge matrix _ij, all have an interval number

$K\left(a_{\mathrm{ij}}\right)=[\underset{\&OverBar;}{K}\left(a_{\mathrm{ij}}\right),\stackrel{\&OverBar;}{K}\left(a_{\mathrm{ij}}\right)]\&Element;I,\underset{\&OverBar;}{K}\left(a_{\mathrm{ij}}\right),\stackrel{\&OverBar;}{K}\left(a_{\mathrm{ij}}\right)\&Element;R$

Corresponding with it, multilevel iudge matrix is changed to one by single integer and can opens up interval; Final formation be one by the multilevel iudge the opened up matrix A can opening up the interval n × n formed;

Step 2.3, calculates and comprehensively can open up judgment matrix and weight vectors, draw static weight; Definition can open up comparator matrix A=<A ^-, A ⁺>, obtains matrix A ⁺, A ^-the normalization characteristic vector x of what eigenvalue of maximum was corresponding have positive component ⁺, x ^-, X=<kx ^-, mx ⁺> is all proper vectors that A corresponds to, w=(w ₁, w ₂... w _n) ^tfor weight vectors, then w=(w ₁, w ₂... w _n) ^t=[kx ^-, mx ⁺], sufficient and necessary condition be

$\frac{k}{m}=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{{\mathrm{\&Sigma;}}_{i=1}^n{a_{\mathrm{ij}}}^{+}}=\frac{1}{{\mathrm{\&Sigma;}}_{j=1}^n\frac{1}{{\mathrm{\&Sigma;}}_{i=1}^n{a_{\mathrm{ij}}}^{-}}}$

Therefore, can obtain

$k=\sqrt{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{{\mathrm{\&Sigma;}}_{i=1}^n{a_{\mathrm{ij}}}^{+}}}$ $m=\sqrt{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{{\mathrm{\&Sigma;}}_{i=1}^n{a_{\mathrm{ij}}}^{-}}};$

Wherein proper vector S=<kx ^-, mx ⁺>; Static weight is established according to interval number relative importance can be opened up; For the element on K layer, their weight is all with interval number $S_i^k=<S_i^{k^{-}},S_i^{k^{+}}>=<{\mathrm{kx}}^{-},{\mathrm{mx}}^{+}>,(i=\mathrm{1,2,3}...n_k)$ Represent; According to extension science knowledge, interval number ratio importance degree can calculate by following expression formula,

$V(S_i^k\&GreaterEqual;S_j^k)=\frac{2(S_i^{k^{+}}-S_j^{k^{-}})}{(S_j^{k^{+}}+S_j^{k^{-}})+(S_i^{k^{+}}+S_i^{k^{-}})}$

For arbitrary i=1,2,3..., n _k; I ≠ j, has then get

$W_j^k=1,W_i^k=V(S_i^k\&GreaterEqual;S_j^k)i=\mathrm{1,2,3}...,n_k;i\&NotEqual;j$

Therefore single orderweight vector of each element of K layer and the quantity of state appraisement system of distribution switchgear is multi-level structure, each quantity of state S of the definition bottom _i(n-th layer) is to each Elements C of N-1 layer _jsingle orderweight vector

$q_i^N={(q_{1j}^N,q_{2j}^N,...,q_{N_{n}j}^N)}^T,(i=\mathrm{1,2},...,N_n),$ Make N _n× (N-1) _nrank matrix

$q^N=(q_1^N,q_2^N,...,q_{{N-1}_n}^N)=\begin{array}{}\left[\begin{array}{cccc}{q}_{11}^n& q_{12}^n& ...& q_{1{(N-1)}_n}^N\\ q_{21}^N& q_{22}^N& ...& q_{2{(N-1)}_n}^N\\ M& M& & M\\ q_{N1}^N& q_{N2}^N& ...& q_{N{(N-1)}_n}^N\end{array}\right]\end{array}$

Each Elements C of K layer _jcombination weight order for general objective layer is:

$W^K={(w_1^K,w_2^k,...,W_{K_n}^K)}^T,j=\mathrm{1,2},...K_n$

Therefore each quantity of state of the bottom is W for the static weight of general objective ⁿ=q ⁿw ^n-1;

Step 3: use critic method to draw changeable weight, specifically comprise following sub-step:

Step 3.1, structure Evaluations matrix, and ask the correlation matrix of Evaluations matrix;

For N number of distribution switchgear sample, for M quantity of state situation, structure Evaluations matrix T;

$T=\left[\begin{array}{cccc}{t}_{11}& t_{12}& ...& t_{1M}\\ t_{21}& t_{22}& ...& t_{2M}\\ M& M& ...& M\\ t_{N1}& t_{N2}& ...& t_{\mathrm{NM}}\end{array}\right]$

Each quantity of state S _i(i=1,2 ..., M), its standard deviation is

${\mathrm{\&sigma;}}_i=\sqrt{\frac{{(t_{1i}-{\stackrel{\&OverBar;}{t}}_i)}^2+{(t_{2i}-{\stackrel{\&OverBar;}{t}}_i)}^2+...+{(t_{\mathrm{Ni}}-{\stackrel{\&OverBar;}{t}}_i)}^2}{N}}$

Wherein for mean value;

The related coefficient of the quantity of state in this Evaluations matrix T can solve with following formula

$r_{i,j}=\frac{\mathrm{cov}(t_i,t_j)}{{\mathrm{\&sigma;}}_i{\mathrm{\&sigma;}}_j}=\frac{E(t_i-{\stackrel{\&OverBar;}{t}}_i)(t_j-{\stackrel{\&OverBar;}{t}}_j)}{{\mathrm{\&sigma;}}_i{\mathrm{\&sigma;}}_i}$

Wherein cov (t _i, t _j) be covariance between two parameters, be respectively the sample average of parameter; Defined by the related coefficient between parameter, can obtain the related coefficient of each row of Evaluations matrix T, the correlation matrix of Evaluations matrix T is:

$R=\left[\begin{array}{cccc}{r}_{11}& r_{12}& ...& r_{1M}\\ r_{21}& r_{22}& ...& r_{2m}\\ M& M& & M\\ r_{M1}& r_{M2}& ...& r_{\mathrm{MM}}\end{array}\right]$

From the symmetry of correlation matrix, r _ij=r _ji

Step 3.2, determines changeable weight;

Critic method be by evaluation index between conflicting and specific strength is carried out to the objective weight of agriculture products; Then the conflicting quantizating index of i-th quantity of state and other quantity of states is used

$c_i={\mathrm{\&sigma;}}_i\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}(1-r_{\mathrm{ij}}),j=\mathrm{1,2},...,M$

C _irepresent the quantity of information that i-th quantity of state comprises; c _ilarger, then containing much information contained by this quantity of state, the weight of this quantity of state is larger; Therefore, the changeable weight of i-th quantity of state is

$W_i=\frac{c_i}{\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{c}_i},i=\mathrm{1,2},...,M$

Step 4: by static weight and changeable weight, draws the comprehensive weight of distribution switchgear quantity of state;

According to the static weight W obtained _jwith changeable weight W _d, adopt multiplicative synthesis normalization method to obtain comprehensive weight W _{comprehensively};

So far, complete the weight of a distribution switchgear M quantity of state is determined.