CN102721941A - Method for fusing and diagnosing fault information of circuit of electric meter on basis of SOM (self-organized mapping) and D-S (Dempster-Shafer) theories - Google Patents

Abstract

A method for fusing and diagnosing fault information of a circuit of an electric meter on the basis of SOM (self-organized mapping) and D-S (Dempster-Shafer) theories includes firstly, creating a fault mode set for the faulty circuit according to circuit analysis of the faulty circuit of the electric energy meter and fault modes specified by GJB299C; secondly, selecting to-be-observed fault signal points corresponding to fault modes in the set according to the fault mode set created in the first step and using the to-be-observed fault signal points as test points for functions and states of the circuit; thirdly, preprocessing fault signals acquired at the fault signal points selected in the second step; fourthly, fusing fault information by the aid of the SOM theory, outputting fault conclusions, selecting 70% of data for training and selecting 30% of the data for testing; and fifthly, fusing the fault conclusions by the aid of the D-S theory and making a decision for faults. By the aid of the method, confidence degree of a fault diagnostic result is further increased, integral uncertainty caused by errors is reduced, accuracy of fault diagnosis is greatly improved, and the method is an extremely important means in the field of information fusion.

Description

A kind of based on SOM and theoretical fusion of meter circuit failure message and the diagnostic method of D-S

(1) technical field:

The present invention provides a kind of electric energy meter circuit failure message to merge and the faulty circuit diagnostic method; Relate in particular to that a kind of electric energy meter circuit failure message based on s self-organizing feature map network (promptly based on SOM) merges and theoretical (the D-S theory is at first to be proposed in 1967 by Dempster based on D-S; A kind of inexact reasoning by his student shafer further developed in 1976 is theoretical, is also referred to as evidence theory or D-S evidence theory) the method for electric energy meter circuit fault diagnosis.It belongs to fault information fusion and diagnostic field.

(2) background technology:

Over past ten years; As the typical application of system failure emulation technology in circuit design field---circuit performance, reliability and testability analysis-by-synthesis technology based on fault simulation have obtained very fast development; In this technical research, utilize eda tool that circuit is carried out malfunction emulation, obtain the fault quantitative analysis results of objective circuit; Utilize each node failure data of circuit of gained; Through given analytical algorithm, estimate circuit test property parameter, provide the predicted value of fault detect rate/isolation rate.This technology can realize the robotization and the intellectuality of performance evaluation, fail-safe analysis and testability analytic process, is the important technology development of electronic product comprehensive Design and analytical technology.

Yet should technology still exist not enough at present; This technical research also mainly concentrates on circuit board level at present with using; And for the research and the application of Circuits System level; Too many owing to the components and parts fault mode, simulation time is long and the model scale is excessive etc., and reason also can't can't be delivered to the upper strata circuit with the sorted generalization that influences of fault.On the other hand, in the circuit fault diagnosis field development of failure prediction technology that is that all right is ripe.Status informations such as the operation characteristic parameter of requirement acquisition real-time watch device, environmental parameter, thus the data of the current ruuning situation of institute's extraction equipment are carried out parameter analysis and failure prediction, and these parameters of electronic system are difficult to obtain.

Meanwhile, information fusion technology becomes the focus of current research, for pattern-recognition and failure prediction have been opened up new approach.Information fusion be meant to the information from single or a plurality of sensors (or information source) detect automatically with data, multi-level, many-sided processing such as related, relevant, estimation and combination; Accurate target location is estimated and complete target identities is estimated to obtain, and battlefield situation, threat and significance level thereof are carried out the estimation of appropriateness.It utilizes the redundancy of information and complementarity can enlarge the space-time hunting zone, improves the target detectivity, improves detection performance; The resolution in raising time or space, the dimension of increase target signature vector, the uncertainty of reduction information, the degree of confidence of improvement information; The fault-tolerant ability of enhanced system and adaptive ability; The thing followed is to reduce the fog-level of reasoning, has improved decision-making capability, thereby the performance of total system is improved greatly.

Characteristic layer merges through SOM the input data is classified in this patent, and calculates the trusting degree of classification results, yet, when evidence quantity increases or classification results when conflict is arranged, only rely on SOM just can not draw compellent diagnostic result.Therefore carrying out the D-S evidence in decision-making level and merge, make that the trusting degree to the result of fault diagnosis further increases, reduced because error is brought whole uncertainly, improved the accuracy of fault diagnosis greatly, is the very important means in information fusion field.

(3) summary of the invention:

1, purpose: the purpose of this invention is to provide that a kind of failure message based on the s self-organizing feature map network merges and based on the method for the electric energy meter circuit fault diagnosis of D-S evidence theory.

2, technical scheme: the present invention realizes through following technical scheme:

The present invention provides a kind of meter circuit failure message based on SOM and D-S evidence theory to merge and diagnostic method, and these method concrete steps are following:

Step 1:, and, faulty circuit is set up a fault mode set according to the fault mode that GJB299C stipulates according to circuit analysis to the electrical energy meter fault circuit;

Step 2: according to the fault mode of step 1 set choose with gather in fault mode fault-signal point (voltage of certain trouble spot, electric current etc.) corresponding to be observed, as the test point of circuit function and state;

Step 3: the fault-signal that the fault-signal point place that in step 2, chooses is obtained carries out pre-service;

Because the characteristic that the present invention adopts comprises temporal characteristics, frequecy characteristic and statistical nature,, be described below so in carrying out the Signal Pretreatment process, also adopt the processing mode of going forward one by one:

(1) the fault-signal interpolation of elder generation to obtaining, thus unified signal granularity obtains the change procedure curve of fault-signal, i.e. time characteristic;

(2) on the basis of (1), temporal characteristics is carried out normalization, carry out discrete Fourier transformation, picked up signal frequency spectrum and correlated characteristic;

(3) on the basis of (1), the statistical property of signal calculated comprises the second order distance, the quadravalence distance, and maximal values etc. are set up eigenvectors matrix;

According to the characteristics of circuit signal, the present invention adopts the time, and the information of frequency and three dimensions of statistical nature is carried out signal fused, and its synoptic diagram is as shown in Figure 2;

Step 4: use SOM to carry out failure message and merge, output fault conclusion; The data of selection 70% are trained, and the data of selection 30% are tested; In order to keep three set of feature data unified, SOM has identical basic setup; SOM is provided with 1 input layer; Only comprise 1 output layer in the network layer, no hidden layer is provided with 9 neurons, uses to connect distance function calculating input vector to neuronic distance, and transition function is made as state of conflict compet, and topological structure is hexagonal network etale topology function hextop; The initialization function of input weight vector (inputWeights) is a mid point value initialization just, and learning function is self-organization mapping weights learning functions (learnsom); Iterations is 80;

Step 5: use the D-S evidence theory that the fault conclusion is merged, do the decision-making of being out of order; Under certain fault mode; Failure message has comprised correct conclusion through the information fusion of characteristic layer SOM among the gained result, but the scope that the SOM recognition result floats is bigger; Also need dwindle its scope, obtain more accurate fault diagnosis conclusion through decision-making level's information fusion; According to the result of fault simulation, set up the identification framework of diagnosing information fusion fault;

Wherein, Described in the step 1 faulty circuit is being set up fault mode set according to GJB299C; The method of its foundation is following: according to the fault mode that GJB299C comprised, the fault mode of each trouble spot of circuit under test is numbered and tabulated, concrete form can be shown in form 1;

The set of form 1 fault mode

Sequence number	Fault mode	Sequence number	Fault mode
				M1	C1-parameter drift+5%	M8	R1-parameter drift-5%
M2	The Q1-open circuit c utmost point	M9	The R1-open circuit
				M3	The Q1-open circuit b utmost point	M10	C1-parameter drift-5%
M4	The Q1-open circuit e utmost point	M11	C2-parameter drift+5%
				M5	The Q1-short circuit cb utmost point	M12	C2-parameter drift-5%

M6	The Q1-short circuit be utmost point	M13	The C2-open circuit
				M7	R1-parameter drift+5%	M14	The C2-short circuit

Wherein, carrying out pre-service at the fault-signal to obtaining described in the step 3, is to adopt the mode of normalization and interpolation that signal is carried out pre-service; Normalization is that the data that amplitude range is bigger are mapped on another interval through certain rule change; Like ([0,1] or [1,1]); Usually the input data of model have different dimensions; Represent different significance, through normalization reaching the minimizing data volume, the purpose of computation complexity and unified dimension; To a series of data point (x on [a, b] interval ₀, y ₀) (x ₁, y ₁) (x ₂, y ₂) ... (x _n, y _n), main normalized mapping rule is as follows:

$y=\frac{(y_{\max }-y_{\min })(x-x_{\min })}{x_{\max }-x_{\min }}+y_{\min }---\left(1\right)$

$\stackrel{\‾}{x}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i$

${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00001790153300021.png"\; state="\{\{state\}\}">S</figure-callout>}}^2=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(x_i-\stackrel{\&OverBar;}{x})}^2$

$y_i=\frac{x_i-\stackrel{\&OverBar;}{x}}{S}---\left(2\right)$

In the formula, y _Min, y _MaxBe the minimum and maximum value of y, x _Min, x _MaxIt is the minimum and maximum value of x.

The data of handling according to formula (1) can limit the border of mapping, belong to a kind of linear mapping; And according to the processing of formula (2) standardization that is otherwise known as, resultant data mean value is 0, and variance is 1;

Interpolation has been generally the method that solves the functional value of middle unknown point between function region and adopt; The method of method of interpolation is:

If following data point is arranged on [a, b] interval:

(x ₀,y ₀)(x ₁,y ₁)(x ₂,y ₂)……(x _n,y _n)

Y wherein _i=f (x _i), i=0,1 ... N, x ₀, x ₁X _nBe called node; According to the value of f (x), construct an enough smooth and fairly simple function at node

Be called interpolating function,, calculate then as the approximate expression of f (x)

[a, b] (being called the interpolation interval), gone up the functional value of any 1 x in the interval, as the approximate value of original f (x) at this point; The general algebraic polynomial that adopts is as interpolating function;

When n=1, the algebraically interpolation problem becomes, through two point (x ₀, y ₀) and (x ₁, y ₁), ask 1 interpolation polynomial p of function y=f (x) ₁(x), according to cartesian geometry knowledge, can get

$p_1\left(x\right)=\frac{x-x_1}{x_0-x_1}{y}_0+\frac{x-x_0}{x_1-x_0}{y}_1=l_0\left(x\right)y_0+l_1\left(x\right)y_1---\left(4\right)$

Wherein, l ₀, l ₁Being called the interpolation basis function one time, all is an order polynomial, p ₁(x) be a lagrange polynomial; Can verify that they satisfy

l ₀(x)+l ₁(x)=1 （5）

l ₀(x)=1, l ₁Or l (x)=0 ₀(x)=0, l ₁(x)=1 (6)

At x, under the certain condition of y, the interior slotting moment point of given unification can be carried out interpolation successively according to above-mentioned formula, obtains granularity unified time sequence;

Wherein, at the statistical nature of the signal described in the step 3, computing method are following:

Suppose that resulting fault-signal is x after the pre-service ₁, x ₂..., x _n, sampling time interval is Δ t, the statistical property of employing has the secondary distance, and four squares, maximum value and maximum amplitude point, formula is following:

The second order distance $x_1={\left(\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{y}_i^2\right)}^{\frac{1}{2}}---\left(7\right)$

The quadravalence distance $x_2={\left(\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{y}_i^4\right)}^{\frac{1}{4}}---\left(8\right)$

Maximum value $x_3=\underset{i}{\mathrm{Max}}\left|y_i\right|---\left(9\right)$

Maximum amplitude point x ₄=k Δ t if $y_k=\underset{i=1}{\overset{m}{\mathrm{Max}}}{y}_i---\left(10\right)$

Wherein, carry out failure message at the use self-organized mapping network described in the step 4 and merge, the learning algorithm of the self-organized mapping network of use is following:

(1) initialization; Each weight vector of output layer is given little random number and carried out normalization processing, the manifold at random after obtaining handling

J=1,2 ..., m sets up initial winning neighborhood N _j. (0), learning rate is composed initial value;

(2) input learning sample; From training set, choose an input pattern and carry out the normalization processing; Obtain input vector the p ∈ { 1 after normalization is handled; 2;, p}

(3) seek the triumph node; Calculate

With

Dot product, j=1,2,, m therefrom selects the maximum triumph node j of dot product ^*If input pattern is handled without normalization, should according to Calculate Euclidean distance, find out the minimum triumph node of distance;

(4) the winning neighborhood N of definition _j. (t) with j ^*For confirming t weights adjustment territory constantly, general initial neighborhood N in the center _j. (0) is bigger, N in the training process _j. shrink in time gradually (0);

(5) adjustment weights are to winning neighborhood N _j. all the node adjustment weights in (0):

$W_{\mathrm{ij}}(t+1)=W_{\mathrm{ij}}\left(t\right)+\mathrm{\&eta;}(t,N)[x_i^p-W_{\mathrm{ij}}\left(t\right)];i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n,j\&Element;N_j.\left(0\right)$

Wherein, (t N) is the function of the topology distance N between interior j neuron of training time t and neighborhood and the triumph neuron to η;

(6) finish inspection, training finish be with learning rate whether decay to 0 or certain predetermined positive decimal be condition, do not satisfy condition and then get back to step 2,3,4;

Wherein, following at the use D-S evidence theory described in the step 5 to the step that the fault conclusion merges:

(1) the output p (Fi) with the characteristic layer information fusion is the basis, calculates the fault elementary probability according to following formula (16) and counts mT, mF and mS, and as the evidence group mass (F) of decision-making level's information fusion, wherein uncertain probability m (θ) is the error E n of SOM;

(2) adopt D-S evidence combined rule to carry out after decision-making level's information fusion, obtain the comprehensive evidence group of fault;

(3) reliability of calculating fault is interval; If the fault hypothesis set in the Fault Identification framework all is a singleton, belief function Bel (F)=mass (F) so, likelihood function Pls (F)=Bel (F)+m (θ);

(4), draw the fault diagnosis conclusion according to decision rule;

According to the network structure of SOM, following elementary probability partition function is proposed

$d_i=\sqrt{\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{(y\left(j\right)-P_{F_i}\left(j\right))}^2}---\left(11\right)$

$K_i=\frac{1}{d_i}---\left(12\right)$

${\mathrm{Nd}}_i=\sqrt{\underset{j}{\mathrm{\&Sigma;}}{(P_{F_0}\left(j\right)-P_{F_i}\left(j\right))}^2}---\left(13\right)$

$\mathrm{Err}=\frac{|{\mathrm{Nd}}_i-d_i|}{\mathrm{\&Sigma;}|{\mathrm{Nd}}_i-d_i|}---\left(14\right)$

$E_n=\sqrt{\frac{\mathrm{\&Sigma;}{\mathrm{Err}}^2}{L}}---\left(15\right)$

$m\left(F_i\right)=\frac{K_i}{\mathrm{\&Sigma;}{K}_i}(1-E_n)---\left(16\right)$

m(θ)=E _n (17)

Wherein, d _iFor desired output y arrives each neuronic Euclidean distance, the more little expression matching degree of distance is high more, and corresponding elementary probability assignment should be big more, therefore to d _iGet inverse and obtain K _tNd _iBe reality output

To each neuronic Euclidean distance, L is the length of weight vector, E _nExport the poor of distance for desired output distance and reality, carry out normalization again, also can represent the uncertain degree of evidence body; And basic probability function is exactly by K _iAnd E _nCalculate jointly;

By the elementary probability partition function, can calculate belief function Bel (F) and likelihood degree function Pls (F), criterion can be represented by the reliability interval that Bel (F) and Pls (F) form during the DS evidence merged; F (0,1): explanation can't confirm whether fault F takes place; Bel (F)=0 explains that it is 0 that fault F occurs as genuine degree of belief;

explains it is 0 also that fault F does not occur as genuine degree of belief, that is to say whether to take place by failure judgement F; F (0,0): explain that fault F does not take place one and is decided to be very; F (1,1): explain that fault F takes place one and is decided to be very;

In fault emulation, it is generally acknowledged that fault all is independent the generation, does not promptly exist common factor, each fault F between each fault _jOnly exist with indeterminate θ and occur simultaneously with self.

The present invention provides a kind of electric energy meter circuit failure message based on the s self-organizing feature map network to merge and based on the method for the electric energy meter circuit fault diagnosis of D-S evidence theory, its advantage and effect have:

The characteristic layer fusion is classified to the input data through the SOM network in this patent; And calculate the trusting degree of classification results; Yet,, only rely on SOM just can not draw compellent diagnostic result when evidence body quantity increases or classification results when conflict is arranged.Therefore carrying out the D-S evidence in decision-making level and merge, make that the trusting degree to the result of fault diagnosis further increases, reduced because error is brought whole uncertainly, improved the accuracy of fault diagnosis greatly, is the very important means in information fusion field.

(4) description of drawings:

The process flow diagram of Fig. 1 the method for the invention

Fig. 2 feature extraction and fusion process synoptic diagram

Fig. 3 (a) SOM neural network classification result

Fig. 3 (b) SOM neural network classification result

(5) embodiment:

The process chart of the method for the invention is as shown in Figure 1.The present invention provide a kind of based on the s self-organizing feature map network electric energy meter circuit failure message fusion method and based on the electric energy meter circuit method for diagnosing faults of D-S evidence theory, its step is following:

Step 1: the electrical energy meter fault circuit is carried out circuit analysis, and set up the fault mode set with reference to the fault mode that GJB299C comprises.

Step 2: according to the fault mode of step 1 set choose with gather in fault mode fault-signal point corresponding to be observed, as the test point of circuit function and state.

Step 3: the fault-signal that the fault-signal point place that in step 2, chooses is obtained carries out pre-service.This patent adopts the mode of normalization and interpolation that signal is carried out pre-service.Normalization is that the data that amplitude range is bigger are mapped on another interval through certain rule change; Like ([0,1] or [1,1]); Usually the input data of model have different dimensions; Represent different significance, through normalization reaching the minimizing data volume, the purpose of computation complexity and unified dimension.Main normalized mapping rule is as follows:

$y=\frac{(y_{\max }-y_{\min })(x-x_{\min })}{x_{\max }-x_{\min }}+y_{\min }---\left(18\right)$

$\stackrel{\&OverBar;}{x}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_i$

${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00001790153300021.png"\; state="\{\{state\}\}">S</figure-callout>}}^2=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(x_i-\stackrel{\&OverBar;}{x})}^2$

$y_i=\frac{x_i-\stackrel{\&OverBar;}{x}}{S}---\left(19\right)$

In the formula, ymin, ymax are the minimum and maximum value of y, and xmin, xmax are the minimum and maximum values of x.

The data of handling according to formula (1) can limit the border of mapping, belong to a kind of linear mapping.And according to the processing of formula (19) standardization that is otherwise known as, resultant data mean value is 0, and variance is 1.

Interpolation has been generally the method that solves the functional value of middle unknown point between function region and adopt.The method of method of interpolation is:

If following data point is arranged on [a, b] interval:

(x ₀,y ₀)(x ₁,y ₁)(x ₂,y ₂)……(x _n,y _n)

Y wherein _i=f (x _i), i=0,1 ... N, x ₀, x ₁X _nBe called node.According to the value of f (x) at node; Construct an enough smooth and fairly simple function

and be called interpolating function; Approximate expression as f (x); Calculate

then at interval [a; B] functional value of any 1 x on (being called the interpolation interval), as the approximate value of original f (x) at this point.The general algebraic polynomial that adopts is as interpolating function.

When n=1, the algebraically interpolation problem becomes, through two point (x ₀, y ₀) and (x ₁, y ₁), ask 1 interpolation polynomial p of function y=f (x) ₁(x), according to cartesian geometry knowledge, can get

$p_1\left(x\right)=\frac{x-x_1}{x_0-x_1}{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA00001790153300021.png"\; state="\{\{state\}\}">y</figure-callout>}}_0+\frac{x-x_0}{x_1-x_0}{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00001790153300021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1=l_0\left(x\right){\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA00001790153300021.png"\; state="\{\{state\}\}">y</figure-callout>}}_0+l_1\left(x\right)y_1---\left(21\right)$

Wherein, l ₀, l ₁Being called the interpolation basis function one time, all is an order polynomial, p ₁(x) be a lagrange polynomial.Can verify that they satisfy

l ₀(x)+l ₁(x)=1 （22）

l ₀(x)=1, l ₁Or l (x)=0 ₀(x)=0, l ₁(x)=1 (23)

At x, under the certain condition of y, the interior slotting moment point of given unification can be carried out interpolation successively according to above-mentioned formula, obtains granularity unified time sequence.

The characteristic that this patent adopts comprises temporal characteristics, frequecy characteristic and statistical nature, and in carrying out the Signal Pretreatment process, also adopt the processing mode of going forward one by one.

(1) the fault-signal interpolation of elder generation to obtaining, thus unified signal granularity obtains the change procedure curve of fault-signal, i.e. time characteristic;

(2) on the basis of (1), temporal characteristics is carried out normalization, carry out discrete Fourier transformation, picked up signal frequency spectrum and correlated characteristic;

(3) on the basis of (1), the statistical property of signal calculated comprises the second order distance, the quadravalence distance, and maximal values etc. are set up eigenvectors matrix;

Characteristics this patent according to circuit signal adopts the time, and the information of frequency and three dimensions of statistical nature is carried out signal fused, and its synoptic diagram is as shown in Figure 2.

1 temporal characteristics

The fault characteristic can be reflected on the procedure parameter correlation properties of circuit operation.The procedure parameter of circuit operation comprises magnitude of voltage, current value, and performance number etc., these procedure parameters are time dependent, therefore we can say fault also reaction to some extent on time coordinate, are the temporal characteristics of fault.

When being input as the data of different faults pattern; Its seasonal effect in time series length is all inconsistent with the sampling granularity; Therefore need step 3 that data are carried out pre-service, mainly reach stylistic unification, to satisfy of the requirement of intelligent classification device to the input data through interpolation and difference.

2 frequecy characteristics

Fault also is presented as the change of frequency in the simulation process except showing as certain temporal signatures.Different fault modes can produce different influences to the circuit signal frequency component.Aspect data processing; Particularly signal Processing field Fourier transform (Fourier) has vital role; See that theoretically many common computings have good character (for example, the difference quotient computing becomes multinomial operation, and convolution becomes common multiplication) under Fourier transform; See that from practice it all is this physical phenomenon of simple harmonic oscillation stack by simple frequency that Fourier expansion has been described each periodic vibration from the mathematics angle.Fourier transform has clearly disclosed the spectrum structure of data.This patent utilizes Fourier transform that time-domain signal is converted into frequency-region signal, thereby obtains its frequency domain character.Generally adopt Fast Fourier Transform (FFT) for discrete signal, its (contrary) transformation for mula is following

$X\left(k\right)=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}x\left(j\right){\mathrm{\&omega;}}_N^{(j-1)(k-1)}---\left(24\right)$

$x\left(j\right)=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}X\left(k\right){\mathrm{\&omega;}}_N^{-(j-1)(k-1)}---\left(25\right)$

ω wherein _N=e ^{(2 π i)/N}..Use unified SF when this patent carries out Fast Fourier Transform (FFT) to the fault-signal under the different faults pattern, thereby resulting frequency-region signal has identical dimension.

3 statistical natures

For accuracy and the reliability that improves fusion, should adopt a plurality of statistical natures to merge.The concrete source of statistical nature can be a single-sensor, also can be a plurality of sensors, and they are consistent on mathematical form.The meaning directly perceived that adopts a plurality of statistical natures is exactly from different sides more fault status information to be provided, and for the fusion of fault provides detailed as far as possible information, thereby improves syncretizing effect.

Suppose that resulting fault-signal is x after the pre-service ₁, x ₂..., x _n, sampling time interval is Δ t, the statistical property of employing has the secondary distance, and four squares, maximum value and maximum amplitude point, formula is following:

The second order distance $x_1={\left(\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{y}_i^2\right)}^{\frac{1}{2}}---\left(26\right)$

The quadravalence distance $x_2={\left(\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{y}_i^4\right)}^{\frac{1}{4}}---\left(27\right)$

Maximum value $x_3=\underset{i}{\mathrm{Max}}\left|y_i\right|---\left(28\right)$

Maximum amplitude point x ₄=k Δ t if $y_k=\underset{i=1}{\overset{m}{\mathrm{Max}}}{y}_i---\left(29\right)$

Fault-signal can be similar to the stack of regarding some simple harmonic waves as, is expressed as

$y=f\left(x\right)=a_0+\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{a}_n\cos \frac{\mathrm{n\&pi;x}}{L}+b_n\sin \frac{\mathrm{n\&pi;x}}{L}---\left(30\right)$

Its magnitude shift amount a often ₀Amplitude a much larger than vibration harmonics _n, b _n, thereby see the vibration of signal and not obvious from macroscopic view, its secondary distance is very little apart from difference with four times, causes the data field calibration not high.In order to address this problem, this patent carries out normalization earlier with the signal time sequence, is mapped to interval [0,1], counting statistics characteristic again, and its DATA DISTRIBUTION is more satisfactory, is easy to distinguish the different faults pattern.

Step 4: use self-organized mapping network to carry out failure message and merge, output fault conclusion.The data of selection 70% are trained, and the data of selection 30% are tested.In order to keep three set of feature data unified, the SOM network has identical basic setup.SOM is provided with 1 input layer; Only comprise 1 output layer in the network layer, no hidden layer is provided with 9 neurons, uses to connect distance function calculating input vector to neuronic distance, and transition function is made as state of conflict compet, and topological structure is hexagonal network etale topology function hextop; The initialization function of input weight vector (inputWeights) is a mid point value initialization just, and learning function is self-organization mapping weights learning functions (learnsom); Iterations is 80.

The learning algorithm of self-organized mapping network is following:

1 initialization; Each weight vector of output layer is given little random number and carried out normalization processing, the manifold at random after obtaining handling

J=1,2 ..., m sets up initial winning neighborhood N _j. (0), learning rate is composed initial value;

2 input learning samples; From training set, choose an input pattern and carry out the normalization processing; Obtain input vector

the p ∈ { 1 after normalization is handled; 2;, p}

3 seek the triumph node; Calculate

With

Dot product, j=1,2,, m therefrom selects the maximum triumph node j of dot product ^*If input pattern is handled without normalization, should according to

Calculate Euclidean distance, find out the minimum triumph node of distance;

The winning neighborhood N of 4 definition _j. (t) with j ^*For confirming t weights adjustment territory constantly, general initial neighborhood N in the center _j. (0) is bigger, N in the training process _j. shrink in time gradually (0);

5 adjustment weights are to winning neighborhood N _j. all the node adjustment weights in (0):

$W_{\mathrm{ij}}(t+1)=W_{\mathrm{ij}}\left(t\right)+\mathrm{\&eta;}(t,N)[x_i^p-W_{\mathrm{ij}}\left(t\right)];i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n,j\&Element;N_j.\left(0\right)$

Wherein, (t N) is the function of the topology distance N between interior j neuron of training time t and neighborhood and the triumph neuron to η;

6 finish inspection, training finish be with learning rate whether decay to 0 or certain predetermined positive decimal be condition, do not satisfy condition and then get back to step 2,3,4;

The training of self-organized mapping network is not stable, and when training repeatedly, even the network of the same group of identical setting of data substitution, its result also might not be identical.This and data self characteristics have relation, and be also relevant with neural network self initialization function.Therefore, in training process, can suitably artificially adjust, to obtain satisfied classification results.

Step 5: use the D-S evidence theory that the fault conclusion is merged, do the decision-making of being out of order.

Under certain fault mode; Failure message has comprised correct conclusion through the information fusion of characteristic layer SOM among the gained result, but the scope that the SOM recognition result floats is bigger; Also need dwindle its scope, obtain more accurate fault diagnosis conclusion through decision-making level's information fusion.According to the result of fault simulation, set up the identification framework of diagnosing information fusion fault.

This patent adopts the D-S evidence theory as information fusion method in decision-making level, and key step is following:

(1) the output p (Fi) with the characteristic layer information fusion is the basis, calculates the fault elementary probability according to formula (36) and counts mT, mF and mS, and as the evidence group mass (F) of decision-making level's information fusion, wherein uncertain probability m (θ) is the error E n of SOM;

(2) adopt D-S evidence combined rule to carry out after decision-making level's information fusion, obtain the comprehensive evidence group of fault;

(3) reliability of calculating fault is interval.If the fault hypothesis set in the Fault Identification framework all is a singleton, belief function Bel (F)=mass (F) so, likelihood function Pls (F)=Bel (F)+m (θ).

(4), draw the fault diagnosis conclusion according to decision rule.

According to the network structure of SOM, following elementary probability partition function is proposed

$d_i=\sqrt{\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{(y\left(j\right)-P_{F_i}\left(j\right))}^2}---\left(31\right)$

$K_i=\frac{1}{d_i}---\left(32\right)$

${\mathrm{Nd}}_i=\sqrt{\underset{j}{\mathrm{\&Sigma;}}{(P_{F_0}\left(j\right)-P_{F_i}\left(j\right))}^2}---\left(33\right)$

$\mathrm{Err}=\frac{|{\mathrm{Nd}}_i-d_i|}{\mathrm{\&Sigma;}|{\mathrm{Nd}}_i-d_i|}---\left(34\right)$

$E_n=\sqrt{\frac{\mathrm{\&Sigma;}{\mathrm{Err}}^2}{L}}---\left(35\right)$

$m\left(F_i\right)=\frac{K_i}{\mathrm{\&Sigma;}{K}_i}(1-E_n)---\left(36\right)$

m(θ)=E _n (37)

Wherein, d _iFor desired output y arrives each neuronic Euclidean distance, the more little expression matching degree of distance is high more, and corresponding elementary probability assignment should be big more, therefore to d _iGet inverse and obtain K _iNd _iBe reality output

To each neuronic Euclidean distance, L is the length of weight vector, E _nExport the poor of distance for desired output distance and reality, carry out normalization again, also can represent the uncertain degree of evidence body.And basic probability function is exactly by K _iAnd E _nCalculate jointly.

By above elementary probability partition function, can calculate belief function Bel (F) and likelihood degree function Pls (F), criterion can be represented by the reliability interval that Bel (F) and Pls (F) form during the DS evidence merged.F (0,1): explanation can't confirm whether fault F takes place.Bel (F)=0 explains that it is 0 that fault F occurs as genuine degree of belief;

explains that it also is 0 that fault F does not occur as genuine degree of belief.That is to say whether to take place by failure judgement F.F (0,0): explain that fault F does not take place one and is decided to be very.F (1,1): explain that fault F takes place one and is decided to be very.

In fault emulation, it is generally acknowledged that fault all is independent the generation, promptly there is not common factor between each fault, each fault Fj only exists with indeterminate θ with self and occurs simultaneously.According to the data after the training; Calculate elementary probability number and uncertain value according to above-mentioned formula; MT is for the temporal characteristics being the fault mode elementary probability number of input; MF is for the frequecy characteristic being the fault mode elementary probability number of input, and mS is for the statistical nature being the fault mode elementary probability number of importing.To mT, mF and mS merge between any two with D-S evidence combined rule, calculate the belief function Bel (F) and the likelihood function Pls (F) of fault.

According to expertise, formulate decision rule, draw diagnosis.

Case study on implementation 1

This paper chooses the metering circuit of certain model electric energy meter as case.The defective device of choosing has metalfilmresistor resistance R 1, solid tantalum electrochemical capacitor C1, and 1 type of Leaded Ceramic Disc Capacitor C2, common double bipolar transistor Q1 sets up fault mode set according to GJB299C, and typical fault pattern in totally 14 is like form 2.The voltage of selecting circuit output point is signaling point to be observed, with this test point as circuit function and state.

The definition of form 2 fault modes

Sequence number	Fault mode	Sequence number	Fault mode
				M1	C1-parameter drift+5%	M8	R1-parameter drift-5%
M2	The Q1-open circuit c utmost point	M9	The R1-open circuit
				M3	The Q1-open circuit b utmost point	M10	C1-parameter drift-5%
M4	The Q1-open circuit e utmost point	M11	C2-parameter drift+5%
				M5	The Q1-short circuit cb utmost point	M12	C2-parameter drift-5%
M6	The Q1-short circuit be utmost point	M13	The C2-open circuit
				M7	R1-parameter drift+5%	M14	The C2-short circuit

Select for use the SOM network as the intelligent classification device, carry out pattern classification.Always have the data of 14 kinds of fault modes, set up knowledge base through training.In order to keep three set of feature data system, the SOM network has identical basic setup, and the training result of temporal characteristics is shown in Fig. 3 (a) and (b).Wherein Fig. 3 (a) transverse axis is represented fault mode M1 ~ M14, and the longitudinal axis is represented the neuron sequence number of being hit, and the pattern representative that sequence number is identical is divided into same type; Fig. 3 (b) is neuronic classification situation, and from left to right, neuronic from top to bottom sequence number is 1 ~ 9, and is corresponding with the value of the longitudinal axis in the histogram.Can see that in the network topology structure of 3*3 14 groups of inputs have been divided into 5 types, blue neuron, the input vector number that numeral comprised wherein for the competition triumph.The classification results of frequecy characteristic and statistical nature is identical therewith, like form 3.

Form 3 neuron classification results

The neuron classification	Fault mode
		F1	M1，M7，M10，M11，M12
F2	M2，M3，M4
		F3	M5，M6，M9
F4	M8，M13

F5

M14

According to the data after the training; Calculate the elementary probability number and uncertain value is as shown in table 4 according to above-mentioned formula; MT is for the temporal characteristics being the fault mode elementary probability number of input; MF is for the frequecy characteristic being the fault mode elementary probability number of input, and mS is for the statistical nature being the fault mode elementary probability number of importing.Calculate belief function Bel (F) and likelihood degree function Pls (F) with formula again, shown in 1 ~ 3 row in the form 5.

Form 4 decision-making level's fusion results

	mT	mF	mS	mT&mF	mT&mS	mF&mS	(mT&mF)&mS
								K				0.4699	0.6224	0.5912	0.6657
m(θ)	0.0144	0.1482	0.2236	0.0046	0.0052	0.0561	0.0015
								m(F 1)	0.0400	0.0656	0.0231	0.0202	0.0164	0.0332	0.0076
m(F 2)	0.0235	0.1375	0.0143	0.0185	0.0093	0.0589	0.0067
								m(F 3)	0.6388	0.4004	0.5338	0.7582	0.7898	0.6468	0.8664
m(F 4)	0.0396	0.0627	0.0229	0.0197	0.0162	0.0319	0.0074
								m(F 5)	0.2437	0.1856	0.1823	0.1788	0.1631	0.1731	0.1103

Adopt D-S evidence combined rule to mT, mF and mS merge between any two, calculate the belief function Bel (F) and the likelihood function Pls (F) of fault; After merging; The elementary probability number of F5 is respectively 0.7582,0.7898 and 0.6468, before merging, is significantly increased.The value of uncertain probability m (θ) becomes 0.0046,0.0052 and 0.0561, before merging, significantly reduces.Experimental data shows that through information fusion, the confidence level that target faults takes place improves, and the uncertainty of judgement weakens.

Further adopt D-S evidence combined rule to mT, merge between mF and the mS three, fusion results is shown in the 7th row in the table 4.The belief function Bel (F) of fault and likelihood function Pls (F) are shown in the 7th row in the form 5.

Form 5 decision-making level's reliabilities are interval

	T	F	S	T&F	T&S	F&S	(T&F)&S
								m(θ)	0.0144	0.1482	0.2236	0.0046	0.0052	0.0561	0.0015

Pls(F1)	0.0544	0.2139	0.2467	0.0248	0.0216	0.0892	0.0092
								Bel(F1)	0.0400	0.0656	0.0231	0.0202	0.0164	0.0332	0.0076
Pls(F2)	0.0379	0.2857	0.2379	0.0231	0.0145	0.1150	0.0082
								Bel(F2)	0.0235	0.1375	0.0143	0.0185	0.0093	0.0589	0.0067
Pls(F3)	0.6533	0.5486	0.7574	0.7628	0.7950	0.7029	0.8679
								Bel(F3)	0.6388	0.4004	0.5338	0.7582	0.7898	0.6468	0.8664
Pls(F4)	0.0540	0.2109	0.2465	0.0243	0.0214	0.0879	0.0090

With reference to expertise, adopt following decision rule.

(1) the belief function value of target faults is the maximal value in all belief function values;

(2) the belief function value of target faults is at least 2 times of belief function value of other fault;

(3) belief function Bel (F)＞0.5;

(4) uncertain probability m (θ) < 0.01.

Rule (1) explains in all fault types of evidence group to have only the maximum fault of belief function value to be only target faults; Rule (2) explains that the belief function value of having only target faults and other fault type has enough difference, could confirm that target faults takes place; Rule (3) explains only to organize on evidence that fault is had enough supports, could confirm that fault takes place; Rule (4) explains that the judgement through the evidence body has enough determinacy, could confirm that target faults takes place.

Can find that through analyzing after the fusion, the elementary probability number of fault F3 further improves, and becomes 0.8664, to satisfy the decision-making judgment rule of " belief function Bel (F)>0.5 ".Simultaneously, the belief function value of F3 is the maximal value in all belief function values, and is 2 times of other fault belief function values at least.Explain that through information fusion, the confidence level of " F3 generation " improves, and has reached the decision rule requirement.The uncertain probability m (θ) that judges " F3 generation " continues to reduce, and becomes 0.0015.

This patent carries out through the SOM network in the fusion of characteristic layer, yet, when evidence body quantity increases or classification results when conflict is arranged, only rely on SOM just can not draw compellent diagnostic result.Therefore carrying out the D-S evidence in decision-making level and merge, make that the trusting degree to the result of fault diagnosis further increases, reduced because error is brought whole uncertainly, improved the accuracy of fault diagnosis greatly, is the very important means in information fusion field.

Claims (6)

1. the meter circuit failure message based on SOM and D-S evidence theory merges and diagnostic method, and it is characterized in that: these method concrete steps are following:

Step 1:, and, faulty circuit is set up a fault mode set according to the fault mode that GJB299C stipulates according to circuit analysis to the electrical energy meter fault circuit;

Step 2: based on the fault mode of step 1 set choose with gather in fault mode fault-signal point corresponding to be observed, as the test point of circuit function and state;

Step 3: the fault-signal that the fault-signal point place that in step 2, chooses is obtained carries out pre-service;

Because the characteristic that adopts comprises temporal characteristics, frequecy characteristic and statistical nature,, be described below so in carrying out the Signal Pretreatment process, adopt the processing mode of going forward one by one:

(1) the fault-signal interpolation of elder generation to obtaining, thus unified signal granularity obtains the change procedure curve of fault-signal, i.e. time characteristic;

(2) on the basis of (1), temporal characteristics is carried out normalization, carry out discrete Fourier transformation, picked up signal frequency spectrum and correlated characteristic;

(3) on the basis of (1), the statistical property of signal calculated comprises the second order distance, and quadravalence distance and maximal value are set up eigenvectors matrix;

According to the characteristics of circuit signal, the information of employing time, frequency and three dimensions of statistical nature is carried out signal fused;

Step 4: use SOM to carry out failure message and merge, output fault conclusion; The data of selection 70% are trained, and the data of selection 30% are tested; In order to keep three set of feature data unified, SOM has identical basic setup; SOM is provided with 1 input layer; Only comprise 1 output layer in the network layer, no hidden layer is provided with 9 neurons, uses to connect distance function calculating input vector to neuronic distance, and transition function is made as state of conflict compet, and topological structure is hexagonal network etale topology function hextop; The input weight vector is that the initialization function of inputWeights is a mid point value initialization just, and learning function is that self-organization mapping weights learning function is learnsom; Iterations is 80;

Step 5: use the D-S evidence theory that the fault conclusion is merged, do the decision-making of being out of order; Under certain fault mode; Failure message has comprised correct conclusion through the information fusion of characteristic layer SOM among the gained result, but the scope that the SOM recognition result floats is bigger; Also need dwindle its scope, obtain more accurate fault diagnosis conclusion through decision-making level's information fusion; According to the result of fault simulation, set up the identification framework of diagnosing information fusion fault.

2. a kind of meter circuit failure message based on SOM and D-S evidence theory according to claim 1 merges and diagnostic method; It is characterized in that: described in the step 1 faulty circuit is being set up fault mode set according to GJB299C; The method of its foundation is following: according to the fault mode that GJB299C comprised; The fault mode of each trouble spot of circuit under test is numbered and tabulated, and concrete form is shown in form 1.

The set of form 1 fault mode

Sequence number Fault mode Sequence number Fault mode M1 C1-parameter drift+5% M8 R1-parameter drift-5% M2 The Q1-open circuit c utmost point M9 The R1-open circuit M3 The Q1-open circuit b utmost point M10 C1-parameter drift-5% M4 The Q1-open circuit e utmost point M11 C2-parameter drift+5% M5 The Q1-short circuit cb utmost point M12 C2-parameter drift-5% M6 The Q1-short circuit be utmost point M13 The C2-open circuit M7 R1-parameter drift+5% M14 The C2-short circuit

3. a kind of meter circuit failure message based on SOM and D-S evidence theory according to claim 1 merges and diagnostic method; It is characterized in that: the fault-signal to obtaining described in the step 3 carries out pre-service, is to adopt the mode of normalization and interpolation that signal is carried out pre-service; Normalization is that the data that amplitude range is bigger are mapped on another interval through certain rule change; Usually the input data of model have different dimensions; Represent different significance, through normalization reaching the minimizing data volume, the purpose of computation complexity and unified dimension; To a series of data point (x on [a, b] interval ₀, y ₀) (x ₁, y ₁) (x ₂, y ₂) ... (x _n, y _n), main normalized mapping rule is as follows:

$y=\frac{(y_{\max }-y_{\min })(x-x_{\min })}{x_{\max }-x_{\min }}+y_{\min }---\left(1\right)$

$\stackrel{\&OverBar;}{x}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_i$

$S^2=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(x_i-\stackrel{\&OverBar;}{x})}^2$

$y_i=\frac{x_i-\stackrel{\&OverBar;}{x}}{S}---\left(2\right)$

In the formula, y _Min, y _MaxBe the minimum and maximum value of y, x _Min, x _MaxIt is the minimum and maximum value of x;

The data of handling according to formula (1) limit the border of shining upon, and belong to a kind of linear mapping; And according to the processing of formula (2) standardization that is otherwise known as, resultant data mean value is 0, and variance is 1;

Interpolation has been generally the method that solves the functional value of middle unknown point between function region and adopt; The method of method of interpolation is:

If following data point is arranged on [a, b] interval:

(x ₀,y ₀)(x ₁,y ₁)(x ₂,y ₂)……(x _n,y _n)

Y wherein _i=f (x _i), i=0,1 ... N, x ₀, x ₁X _nBe called node; According to the value of f (x), construct an enough smooth and fairly simple function at node

Be called interpolating function,, calculate then as the approximate expression of f (x)

The functional value that promptly is called any 1 x on the interpolation interval in interval [a, b] is as the approximate value of original f (x) at this point; The general algebraic polynomial that adopts is as interpolating function;

When n=1, the algebraically interpolation problem becomes, through two point (x ₀, y ₀) and (x ₁, y ₁), ask 1 interpolation polynomial p of function y=f (x) ₁(x), according to cartesian geometry knowledge, obtain;

$p_1\left(x\right)=\frac{x-x_1}{x_0-x_1}{y}_0+\frac{x-x_0}{x_1-x_0}{y}_1=l_0\left(x\right)y_0+l_1\left(x\right)y_1---\left(4\right)$

Wherein, l ₀, l ₁Being called the interpolation basis function one time, all is an order polynomial, p ₁(x) be a lagrange polynomial; Empirical tests, they satisfy

l ₀(x)+l ₁(x)=1 （5）

l ₀(x)=1, l ₁Or l (x)=0 ₀(x)=0, l ₁(x)=1 (6)

At x, under the certain condition of y, the interior slotting moment point of given unification is promptly carried out interpolation according to above-mentioned formula successively, obtains granularity unified time sequence.

4. a kind of meter circuit failure message based on SOM and D-S evidence theory according to claim 1 merges and diagnostic method, and it is characterized in that: at the statistical nature of the signal described in the step 3, computing method are following:

Suppose that resulting fault-signal is x after the pre-service ₁, x ₂..., x _n, sampling time interval is Δ t, the statistical property of employing has the secondary distance, and four squares, maximum value and maximum amplitude point, formula is following:

The second order distance $x_1={\left(\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{y}_i^2\right)}^{\frac{1}{2}}---\left(7\right)$

The quadravalence distance $x_2={\left(\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{y}_i^4\right)}^{\frac{1}{4}}---\left(8\right)$

Maximum value $x_3=\underset{i}{\mathrm{Max}}\left|y_i\right|---\left(9\right)$

Maximum amplitude point x ₄=k Δ t if $y_k=\underset{i=1}{\overset{m}{\mathrm{Max}}}{y}_i.---\left(10\right)$

5. a kind of meter circuit failure message based on SOM and D-S evidence theory according to claim 1 merges and diagnostic method; It is characterized in that: carry out failure message at the use self-organized mapping network described in the step 4 and merge, the learning algorithm of the self-organized mapping network of use is following:

(1) initialization; Each weight vector of output layer is given little random number and carried out normalization processing, the manifold at random after obtaining handling

J=1,2 ..., m sets up initial winning neighborhood N _j. (0), learning rate is composed initial value;

(2) input learning sample; From training set, choose an input pattern and carry out the normalization processing; Obtain input vector the p ∈ { 1 after normalization is handled; 2;, p};

(3) seek the triumph node; Calculate With

Dot product, j=1,2,, m therefrom selects the maximum triumph node j of dot product ^*If input pattern is handled without normalization, should according to

Calculate Euclidean distance, find out the minimum triumph node of distance;

(4) the winning neighborhood N of definition _j. (t) with j ^*For confirming t weights adjustment territory constantly, general initial neighborhood N in the center _j. (0) is bigger, N in the training process _j. shrink in time gradually (0);

(5) adjustment weights are to winning neighborhood N _j. all the node adjustment weights in (0):

$W_{\mathrm{ij}}(t+1)=W_{\mathrm{ij}}\left(t\right)+\mathrm{\&eta;}(t,N)[x_i^p-W_{\mathrm{ij}}\left(t\right)];i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n,j\&Element;N_j.\left(0\right)$

Wherein, (t N) is the function of the topology distance N between interior j neuron of training time t and neighborhood and the triumph neuron to η;

(6) finish inspection, training finish be with learning rate whether decay to 0 or certain predetermined positive decimal be condition, do not satisfy condition and then get back to step 2,3,4.

6. a kind of meter circuit failure message based on SOM and D-S evidence theory according to claim 1 merges and diagnostic method, and it is characterized in that: the use D-S evidence theory described in the step 5 is following to the step that the fault conclusion merges:

(1) the output p (Fi) with the characteristic layer information fusion is the basis, calculates the fault elementary probability according to following formula (16) and counts mT, mF and mS, and as the evidence group mass (F) of decision-making level's information fusion, wherein uncertain probability m (θ) is the error E n of SOM;

(2) adopt D-S evidence combined rule to carry out after decision-making level's information fusion, obtain the comprehensive evidence group of fault;

(3) reliability of calculating fault is interval; If the fault hypothesis set in the Fault Identification framework all is a singleton, belief function Bel (F)=mass (F) so, likelihood function Pls (F)=Bel (F)+m (θ);

(4), draw the fault diagnosis conclusion according to decision rule;

According to the network structure of SOM, following elementary probability partition function is proposed

$d_i=\sqrt{\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{(y\left(j\right)-P_{F_i}\left(j\right))}^2}---\left(11\right)$

$K_i=\frac{1}{d_i}---\left(12\right)$

${\mathrm{Nd}}_i=\sqrt{\underset{j}{\mathrm{\&Sigma;}}{(P_{F_0}\left(j\right)-P_{F_i}\left(j\right))}^2}---\left(13\right)$

$\mathrm{Err}=\frac{|{\mathrm{Nd}}_i-d_i|}{\mathrm{\&Sigma;}|{\mathrm{Nd}}_i-d_i|}---\left(14\right)$

$E_n=\sqrt{\frac{\mathrm{\&Sigma;}{\mathrm{Err}}^2}{L}}---\left(15\right)$

$m\left(F_i\right)=\frac{K_i}{\mathrm{\&Sigma;}{K}_i}(1-E_n)---\left(16\right)$

m(θ)=E _n (17)

Wherein, d _iFor desired output y arrives each neuronic Euclidean distance, the more little expression matching degree of distance is high more, and corresponding elementary probability assignment is big more, therefore to d _iGet inverse and obtain K _iNd _iBe reality output

To each neuronic Euclidean distance, L is the length of weight vector, E _nExport the poor of distance for desired output distance and reality, carry out normalization again, also represent the uncertain degree of evidence body; And basic probability function is exactly by K _iAnd E _nCalculate jointly;

By the elementary probability partition function, calculate belief function Bel (F) and likelihood degree function Pls (F), criterion was represented by the reliability interval that Bel (F) and Pls (F) form during the DS evidence merged; F (0,1): explanation can't confirm whether fault F takes place; Bel (F)=0 explains that it is 0 that fault F occurs as genuine degree of belief; explains it is 0 also that fault F does not occur as genuine degree of belief, that is to say whether to take place by failure judgement F; F (0,0): explain that fault F does not take place one and is decided to be very; F (1,1): explain that fault F takes place one and is decided to be very;

In fault emulation, it is generally acknowledged that fault all is independent the generation, does not promptly exist common factor, each fault F between each fault _jOnly exist with indeterminate θ and occur simultaneously with self.

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