CN107133378A - Become the oil-filled transformer fault early warning method of point estimation based on Higher Dimensional Linear Models - Google Patents

Become the oil-filled transformer fault early warning method of point estimation based on Higher Dimensional Linear Models Download PDF

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CN107133378A
CN107133378A CN201710193920.3A CN201710193920A CN107133378A CN 107133378 A CN107133378 A CN 107133378A CN 201710193920 A CN201710193920 A CN 201710193920A CN 107133378 A CN107133378 A CN 107133378A
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CN107133378B (en
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华中生
周健
徐晓燕
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Zhejiang University ZJU
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Zhejiang University ZJU
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/16Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Abstract

The invention discloses a kind of fault early warning method for the oil-filled transformer for becoming point estimation based on Higher Dimensional Linear Models, group's drag-line estimation that the Higher Dimensional Linear Models set up by several oil-filled transformer failure indexs of correlation to selection are adapted to, the height position in Higher Dimensional Linear Models is obtained, the position occurred using height realizes the early warning to transformer fault as the position of oil-filled transformer fault pre-alarming.Relative to other failure prediction methods, the present invention only needs to the characteristic gas concentration of dissolving in oil-filled transformer insulating oil, without other extra equipment.Meanwhile, applicability of the present invention extensively, goes for the various fault types produced inside oil-filled transformer.

Description

Become the oil-filled transformer fault early warning method of point estimation based on Higher Dimensional Linear Models
Technical field
The present invention relates to oil-filled transformer fault pre-alarming field, and in particular to one kind is estimated based on Higher Dimensional Linear Models height The oil-filled transformer fault early warning method of meter.
Background technology
The most failure of oil-filled transformer will not occur within the extremely short time, be a process slowly accumulated, When accumulation reaches a certain amount, the generation of failure will be caused.Therefore we need a kind of failure of oil-filled transformer pre- Alarm method so that we can be within the period that oil-filled transformer failure is accumulated, to the running status of oil-filled transformer Make early warning.So that we carry out necessary maintenance and repair to oil-filled transformer, the generation of failure is prevented, and can save Substantial amounts of manpower, financial resources and material resources loss.
Whether the failure predication of oil-filled transformer is the feature according to failure, be able to can be broken down progress for transformer Prediction.At present, there is following conventional method both at home and abroad:
1) dissolved gas analysis method in oil
The ratio method of dissolved gas analysis is one of transformer fault prediction most common method.Due in transformer The different failure in portion can produce different internal environments, so as to produce different gases.Therefore, we are by analyzing oil dissolved gas The index such as content, relative percentage, can reach the purpose that transformer fault diagnosis and prediction failure occur.
2) vibration analysis method
The failures such as short circuit, the insulation ag(e)ing of inside transformer are likely to make the winding of transformer be deformed or make to draw The structure of line produces skew or disturbed.Therefore, using these fault messages, early warning can also be carried out to the failure of transformer.Shake Dynamic analytic approach is exactly a kind of method for monitoring this transformer fault, and this method is by the vibration signal for transformer It is monitored and analyzes, reaches the purpose of monitoring running state of transformer.
3) IR thermometry
Infrared Thermography Technology refers to receiving the infrared radiation signal that measured target is given out by infrared detector, Then by the processing of amplification, the vision signal of standard is converted into, and then shows by monitor infrared thermography.Such as Fruit inside transformer exist the bad contact of lead, have rosin joint at the conductor tab of coil, overload a series of feelings such as operation During condition, it may all cause the loop hot-spot of inner conductive, meanwhile, if there is multipoint earthing of iron core situation, it is also possible to produce Pig iron core is overheated.Infrared temperature-test technology is exactly to utilize the infrared waves produced in these situations, carries out failure predication.At present, The temperature measurement accuracy of Infrared Thermography Technology is higher, can be analyzed in actual applications using infrared image, monitor transformer component In each several part temperature, temperature data is then carried out longitudinal direction and lateral comparison, running state of transformer judged and must The early warning wanted.
However, there are some defects in above-mentioned existing method.Dissolved gas analysis side in such as current existing oil In method, the static threshold that several characteristic gas indexs of fixation are in accordance with greatly is pre-warning signal, and the accuracy rate of prediction is relatively low.Shake Dynamic analytic approach is larger by external environment influence, and larger interference, Er Qiebian may be produced under relatively noisy working environment The failure of some types inside depressor can not well be showed by the form of mechanical oscillation.Infrared measurement of temperature rule must More accurate infrared monitoring equipment need additionally be bought, it is necessary to put into more financial resources, next there are some inside transformers Failures such as failure, such as shelf depreciation etc., can not be showed well by infrared temperature-test technology.Lacking based on the above method Fall into, a kind of fault early warning method of accurate quick of oil-filled transformer field exigence.
The content of the invention
In view of above-mentioned, the present invention proposes a kind of oil-filled transformer fault early warning method for becoming point estimation based on higher-dimension, This method is based on the various dissolving characteristic gas index in oil-filled transformer insulating oil, to various features gas index institute (height refers to a certain position or moment to the height of the Higher Dimensional Linear Models of composition, and front and rear observation or data follow two herein The point of individual different model) estimated, so as to obtain the fault pre-alarming moment.This method can be according to a variety of transformers Failure, chooses a variety of different characteristic gas indexs, carries out the prediction of transformer fault, accurate with stronger applicability and prediction Exactness.
A kind of oil-filled transformer fault early warning method for being become point estimation based on Higher Dimensional Linear Models of the present invention, is chosen first Several oil-filled transformer failure indexs of correlation, then using these Index Establishment Higher Dimensional Linear Models, pass through the group of adaptation Drag-line method of estimation, estimates the height position in Higher Dimensional Linear Models, and oil immersion is used as using the time location that height occurs The position of formula transformer fault early warning.The oil-filled transformer fault early warning method objective and fair, it is simple and easy to apply.
A kind of fault early warning method for the oil-filled transformer for becoming point estimation based on Higher Dimensional Linear Models, including following step Suddenly:
(1) p kind oil-filled transformer failure indexs of correlation are chosen, y is designated as respectively1,y2,...,yi,...,yp, wherein, yi =(yi,1,yi,2,..,yi,t,..,yi,n)T, yi,tRepresent value of i-th kind of oil-filled transformer failure index of correlation in t;
(2) according to the p kind oil-filled transformer failure indexs of correlation selected, the Higher Dimensional Linear Models of many heights are set up such as Under:
Wherein, vector xitIt is d dimension explanatory variables, vectorial βjIt is the d dimension unknown parameters of non-zero, eitIt is error term, snIt is not Know variable point numeral;aj, j=1,2 ..., snRepresent the position of unknown height;
yi,tRepresent the value in i-th kind of failure index of correlation of t, the common p of index of correlationtKind, ptRepresent the failure in moment t The number of index of correlation, because failure index of correlation there may be missing values, there are p kinds at the not necessarily all moment;
Do sign reversingY= (y(1),...,y(n))T, e=(e(1),...,e(n))T(1)1,J=1 ..., sn(Meaning Taste parameter betaj+1≠βj, i.e. ajFor the height position of model),
The Higher Dimensional Linear Models of many power transformations are converted into matrix form y=X θ+e;
(3) by adaptability group's drag-line estimation (Adaptive Group Lasso Estimator) to the higher-dimension of many heights Parameter θ in linear model y=X θ+e is estimated, it is possible to obtain the position of height in the Higher Dimensional Linear Models of many heights Put;θ group's drag-line estimator is:
Wherein,
| | | | the theorem in Euclid space norm of expression, d is explanatory variable xitDimension;Explanatory variable is transformer itself Endogenous variable, for explaining dependent variable yi,tλnIt is regulation parameter with v;Parameter v=1, parameter lambdanPass through bayesian information criterion (Bayesian information criterion) chooses, i.e.,
Wherein,
Described group's drag-line estimates that the method for parameter θ is:
A, note X=(X(1),...,X(n)), wherein
B, definitionT=1 ..., n;(ν is Greek alphabet)
C, initializes the value of parameter, and wherein s=0 is iteration count parameter, and r is iteration parameter,
D, for arbitrary t=1 ..., n, does following iteration:
(d-1) calculate
(d-2) update
(d-3) update
Until r convergences, otherwise update s=s+1, repeat step (d-1)~step (d-3) process;
E, after convergence, adaptability group's drag-line estimation parameter of parameter θBecome Point set is combined into
After height position is obtained, in sample data, to be not later than last height position of failure appearance as change Depressor fault pre-alarming position, the time between transformer fault early warning position and abort situation is the average pre-warning time of failure.
Compared with prior art, the present invention has advantages below:
Oil-filled transformer fault early warning method of the present invention is related by several oil-filled transformer failures to selection Group's drag-line estimation that the Higher Dimensional Linear Models that index is set up are adapted to, has obtained the height position in Higher Dimensional Linear Models, The position occurred using height realizes the early warning to transformer fault as the position of oil-filled transformer fault pre-alarming.Relatively In other failure prediction methods, the present invention only needs to the characteristic gas concentration of dissolving in oil-filled transformer insulating oil, without Want other extra equipment.Meanwhile, applicability of the present invention extensively, goes for the various events produced inside oil-filled transformer Hinder type.
Brief description of the drawings
Fig. 1 is transformer CH in embodiment 14And C2H6Concentration tendency and height and abort situation figure;
Fig. 2 is transformer CO/CO in embodiment 12、CH4/(CH4+C2H6+C2H4) and C2H4/(H2+C2H6+C2H4) tendency with Height and abort situation figure.
Embodiment
In order to more specifically describe the present invention, below in conjunction with the accompanying drawings and embodiment is to technical scheme It is described in detail.
Embodiment 1
The present embodiment have chosen 5 kinds of characteristic gas indexs by taking the failure transformer that Zhejiang power grid numbering is 895058 as an example, The CH4 concentration of dissolving respectively in oil-filled transformer insulating oil, C2H6 concentration, CO/CO2 ratio, CH4 relative to C2H6, Relative concentration values C2H4/ (H2+s of the C2H4 relative concentration values CH4/ (CH4+C2H6+C2H4) and C2H4 relative to H2, C2H6 C2H6+C2H4 value).
First, it regard the later moment in time of above-mentioned 5 kinds of indexs as failure phase relative to the absolute value of the growth rate of previous moment Close index.Assuming that λ12,...,λ5For above-mentioned five kinds of characteristic gas indexs, wherein λi=(λi,1i,2,..,λi,n)T, λi,tFor Value of the i kind characteristic gas indexs t-th of moment.Failure index of correlation is designated as y1,y2,...,y5, wherein yi=(yi,1, yi,2,..,yi,n)T, yi,tRepresent value of i-th kind of oil-filled transformer failure index of correlation t-th of moment.Order:
Then, according to 5 kinds of failure indexs of correlation obtained above, the Higher Dimensional Linear Models for setting up many heights are as follows:
Wherein yi,tRepresent the value in i-th kind of failure index of correlation of t (totally 5 kinds);Vector xitIt is d dimension explanatory variables, to Measure βjIt is the d dimension unknown parameters of non-zero, makes d=1, i.e. explanatory variable only comprising intercept here, so that xit=1.eitIt is error , snIt is unknown variable point numeral;aj, j=1,2 ..., snRepresent the position of unknown height.
Do sign reversingY= (y(1),...,y(n))T, e=(e(1),...,e(n))T(1)1,J=1 ..., sn(Meaning Taste parameter betaj+1≠βj, i.e. ajFor the height position of model),
Then the Higher Dimensional Linear Models of many heights can be converted into matrix form y=X θ+e.
Finally, the parameter θ in the Higher Dimensional Linear Models y=X θ+e of many heights is estimated by adaptability group's drag-line estimation Meter, it is possible to obtain the position of height in the Higher Dimensional Linear Models of many heights.θ group's drag-line estimator is:
Wherein,
| | | | the theorem in Euclid space norm of expression, λnIt is regulation parameter with v.Parameter v=1, parameter lambdanBelieved by Bayes Cease criterion to choose, i.e.,
Wherein
Parameter θ group drag-line estimation method be:
A, note X=(X(1),...,X(n)), wherein
B, definitionT=1 ..., n;(ν is Greek alphabet)
C, initializes the value of parameter, and wherein s=0 is iteration count parameter, and r is iteration parameter,
D, for arbitrary t=1 ..., n, does following iteration:
(d-1) calculate
(d-2) update
(d-3) update
Until r convergences, otherwise update s=s+1, repeat step (d-1)~step (d-3) process.
E, after convergence, adaptability group's drag-line estimation parameter of parameter θBecome Point set is combined into
And then the height position estimated can be regard as the fault pre-alarming position of oil-filled transformer.
Fig. 1,2 illustrate five kinds of failure indexs of correlation (every by taking the failure transformer that Zhejiang power grid numbering is 895058 as an example One curve is a kind of failure index of correlation, because CH4、C2H6Concentration and CO/CO2,CH4/(CH4+C2H6+C2H4) and C2H4/(H2 +C2H6+C2H4) ordinate ratio gap is excessive, therefore divide into two figures to represent) relation of variation tendency and height position. With the place of perpendicular solid marks it is the height position that model is estimated on axis of abscissas, the position with perpendicular dashed lines labeled is failure hair Raw position.If using be not later than failure appearance last height as fault pre-alarming position, four-headed arrow mark distance Exactly 895058 transformers are converted into the early warning duration of malfunction from fault pre-alarming, i.e., No. 895058 failure transformers The early warning duration is 119 days.
Embodiment 2
With reference to 14 high temperature overheating fault transformers of Zhejiang power grid and 24 normal transformer belt electro-detection data, use Same method in embodiment 1, the height situation to all 38 transformers is estimated.To be not later than the last of failure appearance One height is transformer fault early warning position, and estimated result is as shown in table 1.
Transformer fault early warning situation of the table 1 based on many height Higher Dimensional Linear Models
Failure transformer Normal transformer
Average variable point numeral 5.2 2.3
It is not later than the early warning rate of failure generation 78.6% /
Failure is to failure average time 193 days /
As can be seen from Table 1, the average variable point numeral of failure transformer is apparently higher than the average variable point numeral of normal transformer.In failure In transformer, failure transformer can be accounted in the transformer for being not later than failure appearance and carrying out fault pre-alarming effect by becoming point estimation Ratio is 78.6%.If to be not later than last height of failure appearance as fault pre-alarming position, from fault pre-alarming to former The average transformation time of barrier state, that is, the average pre-warning time of failure is 193 days.Therefore, by failure index of correlation Many height Higher Dimensional Linear Models in height position estimation, using model change point as malfunction early-warning point, it is possible to achieve to become The dynamic early-warning of depressor operation conditions.So as to can have certain lead, to that may break down, oil-filled transformer enters The necessary maintenance and repair of row, and then the generation of failure is prevented, save substantial amounts of manpower, financial resources, material resources consumption.
Technical scheme and beneficial effect are described in detail above-described embodiment, Ying Li Solution is to the foregoing is only presently most preferred embodiment of the invention, is not intended to limit the invention, all principle models in the present invention Interior done any modification, supplement and equivalent substitution etc. are enclosed, be should be included in the scope of the protection.

Claims (2)

1. a kind of fault early warning method for the oil-filled transformer for being become point estimation based on Higher Dimensional Linear Models, is comprised the following steps:
(1) p kind oil-filled transformer failure indexs of correlation are chosen, y is designated as respectively1,y2,...,yi,...,yp, wherein, yi= (yi,1,yi,2,..,yi,t,..,yi,n)T, yi,tRepresent value of i-th kind of oil-filled transformer failure index of correlation in t;
(2) according to the p kind oil-filled transformer failure indexs of correlation selected, the Higher Dimensional Linear Models for setting up many heights are as follows:
<mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mi>T</mi> </msup> <msub> <mi>&amp;beta;</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>e</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mn>1</mn> <mo>&amp;le;</mo> <mi>t</mi> <mo>&lt;</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mi>T</mi> </msup> <msub> <mi>&amp;beta;</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>e</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>&amp;le;</mo> <mi>t</mi> <mo>&lt;</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mi>T</mi> </msup> <msub> <mi>&amp;beta;</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>e</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>a</mi> <mi>j</mi> </msub> <mo>&amp;le;</mo> <mi>t</mi> <mo>&lt;</mo> <msub> <mi>a</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mi>T</mi> </msup> <msub> <mi>&amp;beta;</mi> <mrow> <msub> <mi>s</mi> <mi>n</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>e</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>a</mi> <msub> <mi>s</mi> <mi>n</mi> </msub> </msub> <mo>&amp;le;</mo> <mi>t</mi> <mo>&lt;</mo> <mi>n</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
Wherein, vector xitIt is d dimension explanatory variables, vectorial βjIt is the d dimension unknown parameters of non-zero, eitIt is error term, snIt is unknown change Points;aj, j=1,2 ..., snRepresent the position of unknown height;
Do sign reversingY= (y(1),...,y(n))T, e=(e(1),...,e(n))T,Meaning Taste parameter betaj+1≠βj, i.e. ajFor the height position of model),
<mrow> <mi>X</mi> <mo>=</mo> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <msub> <mi>X</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>X</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msub> </mtd> <mtd> <msub> <mi>X</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <msub> <mi>X</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </msub> </mtd> <mtd> <msub> <mi>X</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </msub> </mtd> <mtd> <msub> <mi>X</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </msub> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <msub> <mi>X</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>
Then the Higher Dimensional Linear Models of many power transformations are converted into matrix form y=X θ+e;
(3) parameter θ in the Higher Dimensional Linear Models y=X θ+e of many heights is estimated by adaptability group's drag-line estimation, obtained The height position into the Higher Dimensional Linear Models of many heights;θ group's drag-line estimator is:
<mrow> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>=</mo> <mi>arg</mi> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>&amp;theta;</mi> </munder> <mo>{</mo> <mo>|</mo> <mo>|</mo> <mi>y</mi> <mo>-</mo> <mi>X</mi> <mi>&amp;theta;</mi> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>&amp;lambda;</mi> <mi>n</mi> </msub> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <mfrac> <msqrt> <mi>d</mi> </msqrt> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mover> <mi>&amp;theta;</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </msub> <mo>|</mo> <msup> <mo>|</mo> <mi>v</mi> </msup> </mrow> </mfrac> <mo>|</mo> <mo>|</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </msub> <mo>|</mo> <mo>|</mo> <mo>}</mo> </mrow>
Wherein,
<mrow> <msub> <mover> <mi>&amp;theta;</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mi>d</mi> </msqrt> </mfrac> <msup> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>T</mi> </msubsup> <msub> <mi>X</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>X</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>T</mi> </msubsup> <msub> <mi>y</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msub> </mrow>
<mrow> <msub> <mover> <mi>&amp;theta;</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mi>d</mi> </msqrt> </mfrac> <msup> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>T</mi> </msubsup> <msub> <mi>X</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>X</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>T</mi> </msubsup> <msub> <mi>y</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <msqrt> <mi>d</mi> </msqrt> </mfrac> <msup> <mrow> <mo>(</mo> <msubsup> <mi>X</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>T</mi> </msubsup> <msub> <mi>X</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>X</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>T</mi> </msubsup> <msub> <mi>y</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </msub> </mrow>
| | | | the theorem in Euclid space norm of expression, d is explanatory variable xitDimension;λnIt is regulation parameter with v;Parameter v=1, Parameter lambdanChosen by bayesian information criterion:
<mrow> <mi>&amp;lambda;</mi> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>L</mi> <mi>L</mi> </msub> <mo>,</mo> <mn>..</mn> <mo>,</mo> <msub> <mi>&amp;lambda;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>arg</mi> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>&amp;lambda;</mi> </munder> <mrow> <mo>(</mo> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <mo>|</mo> <mo>|</mo> <mi>y</mi> <mo>-</mo> <mi>X</mi> <mover> <mi>&amp;theta;</mi> <mo>^</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <mo>)</mo> <mo>+</mo> <mfrac> <mrow> <mi>d</mi> <mi>f</mi> </mrow> <mi>N</mi> </mfrac> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mo>(</mo> <mi>N</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow>
Wherein,
(4) after height position is obtained, in sample data, to be not later than last height position of failure appearance as transformation Device fault pre-alarming position, the time between transformer fault early warning position and abort situation is the average pre-warning time of failure.
2. the fault early warning method of the oil-filled transformer as claimed in claim 1 for becoming point estimation based on Higher Dimensional Linear Models, Characterized in that, the process to parameter θ progress group's drag-line estimation is:
A, note X=(X(1),...,X(n)), wherein
B, definition
C, initializes the value of parameter, and wherein s=0 is iteration count parameter, and r is iteration parameter,
D, for arbitrary t=1 ..., n, does following iteration:
(d-1) calculate
(d-2) update
(d-3) update
Until r convergences, otherwise update s=s+1, repeat step (d-1)~step (d-3) process;
E, after convergence, adaptability group's drag-line estimation parameter of parameter θBecome point set For
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