CN109543769A - A kind of transformer station high-voltage side bus shortage of data mending method based on function type principal component analysis and wavelet transformation - Google Patents
A kind of transformer station high-voltage side bus shortage of data mending method based on function type principal component analysis and wavelet transformation Download PDFInfo
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Abstract
The invention discloses a kind of transformer station high-voltage side bus shortage of data mending method based on function type principal component analysis and wavelet transformation, the following steps are included: analyzing using FPCA method the operation data point acquired, the operation data function x in entire time series is fittedi(t)；It is made the difference to former data point and by the data point that FPCA is obtained, obtains residual error function ε (t)；Residual error function ε (t) is converted using small echo and is denoised, ε ' (t) is obtained；Estimation functionBy the time t at missing point0It substitutes intoIt obtains
Description
Technical field
The present invention relates to power equipment data cleansing fields, especially a kind of to be become based on function type principal component analysis and small echo
The transformer station high-voltage side bus shortage of data mending method changed.
Background technique
Transformer is one of most important equipment in power grid, and operation data is most important to subsequent big data analysis.
However in data acquisition and transportational process, shortage of data may be led to due to some failures and human factor, after this is unfavorable for
Continuous data analysis and data mining, it is therefore necessary to which missing data is filled up.
Currently used missing data complementing method has: artificial filling, interpolation, recurrence etc..But manually fill time-consuming expense
Power, it is also unpractical that artificial filling is carried out to the mass data generated daily；The confidence level of interpolation method is not high, and inserts
Value method is difficult to adapt to the case where a large amount of continuous datas missing；Homing method is very high to the accuracy requirement of function model, still
Determine that a reasonable function model is difficult, and the applicability very little of model.It is a kind of new it is therefore desirable to establish
Method, by data feature, missing data is filled up.
Summary of the invention
The transformer station high-voltage side bus data based on function type principal component analysis and wavelet transformation that the object of the present invention is to provide a kind of
Lack mending method, known data point need to only be learnt, so that it may find in data feature, fit entire
Function in time series can make repairing to the value of missing point by value of this function on corresponding time point.
To achieve the above object, the present invention adopts the following technical solutions:
A kind of transformer station high-voltage side bus shortage of data mending method based on function type principal component analysis and wavelet transformation, including
Following steps:
The operation data point acquired is analyzed using FPCA method, fits the operation number in entire time series
According to function xi(t)；
It is made the difference to former data point and by the data point that FPCA is obtained, obtains residual error function ε (t)；
Residual error function ε (t) is converted using small echo and is denoised, ε ' (t) is obtained；
Estimation functionBy the time t at missing point0It substitutes intoIt obtains
As the repairing value at missing point.
Further, described that the operation data point acquired is analyzed using FPCA method, fit the entire time
Operation data function x in sequencei(t) before step, further includes:
All efficiently sampling times and corresponding efficiently sampling value in the transformer n days are taken, a time record square is obtained
Battle array T and sampled value record matrix Y, the i-th row jth column element T of TijIndicate the time of i-th day j-th sampled point, the i-th row of Y the
J column element YijIndicate the numerical value of i-th day j-th sampled point.
Further, described that the operation data point acquired is analyzed using FPCA method, fit the entire time
Operation data function x in sequencei(t), it specifically includes:
The transformer station high-voltage side bus data of acquisition are sequentially arranged, ten day datas are analyzed as one group；
According to KL theorem, the daily operation data of transformer can be expressed as, xi
(t) function of the operation data of i-th day transformer about the time is indicated, μ (t) is the mean value letter in transformer ten days under sample
Number, αikIt is one group of coefficient for depending on number of days,It is one group of basic function under ten days samples, estimates mean function μ (t),
Estimate basic functionEstimation coefficient αik, preceding K characteristic function is chosen to indicate xi(t), x is obtainedi(t) according to a preliminary estimate,
I.e.
Further, the estimation mean function μ (t), specifically includes: estimating mean function using weighted least-squares method
μ (t):
Majorized functionRespectively to β0And β1Local derviation is sought,
niIndicate i-th day effective sampling points number, k () uses gaussian kernel function, hμIt is bandwidth, passes through the method choice band of GCV
It is wide；
Enabling two partial derivatives is zero, is obtainedWherein Estimation to μ (t) are as follows:
Further, the estimation basic functionIt specifically includes:
Sample estimates covariance function G (s, t)；
According toCharacteristic function is obtained by the method for scatter estimation or Numerical valueAnd eigenvalue λk, wherein Γ indicates xi(t) domain,It is the estimation function of sample covariance function G (s, t), G
The expression formula of (s, t) are as follows: G (s, t)=cov (x (s), x (t)).
Further, the sample estimates covariance function G (s, t) specifically includes:
A. at s ≠ t, G (s, t) estimated value, i.e. majorized function are obtained by weighted least-squares method:Respectively to β0、β11And β12Ask inclined
Derivative, and three partial derivatives is enabled to be equal to zero, it obtains,
Wherein
Here k2() is a binary kernel function, and expression formula ishGFor
Bandwidth, by the method choice bandwidth of GCV,
B. at s=t, 45 ° first is rotated clockwise to reference axis, that is, is had
Following majorized function is minimized again:
It obtains
Further, the determining factor alphaikIt specifically includes:
By design conditions expectation come estimation coefficient αik:
Wherein
Here δjlIt is 0 when being 1, j ≠ l in j=l,It is given by
WhereinIt is the value of the estimation function as obtained in step a on the diagonal,It is by being obtained in step b
Estimation function value on the diagonal.
Further, K characteristic function indicates x before the selectioni(t), it specifically includes:
The mode of cross validation is selected to select K, i.e., by keeping the value of following formula minimum:
WhereinIt indicates after all removing i-th day data, i-th day obtained estimation function, i.e.,
Wherein,It indicates after all removing the 1st day data, the 1st day obtained estimation function,
It indicates after all removing the 1st day data, the 1st day obtained characteristic value,
It indicates after all removing the 1st day data, the 1st day obtained characteristic function.
Further, described to be made the difference to former data point and by the data point that FPCA is obtained, residual error function ε (t) is obtained, is had
Body includes:
By i-th day t of transformerjThe measurement data Y at momentijWithIt makes the difference to obtain residual error function εi(t) in tjThe value at moment
According to service logic, missing point can be divided into two classes, one kind is the missing of fritter, i.e., consecutive miss data when
Between interval be less than or equal to ten minutes；One kind is the missing of bulk, i.e., the time interval of consecutive miss data is greater than ten minutes, to residual
The processing method of difference function missing point is as follows:
A. to the missing of fritter, the value of missing point residual error function is predicted with the mode of rolling average: if the point of kth minute
Missing, thenPreceding ten minutes missings can not be calculated with this formula, therefore in boundary, rightEstimation are as follows:
B. to the missing of bulk, the value of the residual error function at the missing of bulk is set as zero.
Further, described converted using small echo to residual error function ε (t) is denoised, and is obtained ε ' (t), is specifically included:
Wavelet transformation is done to residual error function ε (t) with MATLAB, remove noise: wavelet type takes db4 small echo, Decomposition order
It is 3, threshold method selects the fixed threshold estimation technique, and noise structure selects Unscaled white noise, after being denoised
Residual error function εi′(t)。
The effect provided in summary of the invention is only the effect of embodiment, rather than invents all whole effects, above-mentioned
A technical solution in technical solution have the following advantages that or the utility model has the advantages that
1, the present invention establishes function model without the service logic previously according to data, as long as providing enough measurements
Point can fit function curve according to the internal characteristics of data.
2, the distribution of missing point is not required, can be both made prediction to single missing values, it can also be to continuous
Missing values are made prediction.
3, the present invention can hold the feature of data set in such a way that FPCA and wavelet transformation are combined on the whole,
It can improve local degree of fitting again, more traditional fitting means, predicted value confidence level of the invention is higher.
Specific embodiment
In order to clarify the technical characteristics of the invention, being explained in detail below by specific embodiment the present invention
It states.In addition, the present invention can in different examples repeat reference numerals and/or letter.This repetition is in order to simplified and clear
Purpose, itself do not indicate discussed various embodiments and/or setting between relationship.Present invention omits to known assemblies
Description with treatment technology and process is to avoid being unnecessarily limiting the present invention.
Transformer station high-voltage side bus shortage of data mending method based on function type principal component analysis and wavelet transformation, specific steps
It is as follows:
1) collected data may include the information of multiple transformers simultaneously, and arrangement is also likely to be mixed and disorderly unordered.Cause
This is arranged firstly the need of to these data.All data of wherein some transformer are chosen first, it is then suitable according to the time
Sequence arrangement.For the good data of the transformer arrangement under normal circumstances by the data different comprising 12 classes, they are high pressure respectively at this time
Side-U, medium voltage side-U, low-pressure side-U, high-pressure side-I, medium voltage side-I, low-pressure side-I, high-pressure side-P, medium voltage side-P, low-pressure side-P,
High-pressure side-Q, medium voltage side-Q, low-pressure side-Q.Any one data chosen in this 12 class data are analyzed, with high-pressure side-U
For, all efficiently sampling times of high-pressure side-U and corresponding efficiently sampling value in the transformer n days are taken, a time is obtained
It records matrix T and sampled value records matrix Y.The i-th row jth column element T of TijIndicate the time of i-th day j-th sampled point, Y's
I-th row jth column element YijIndicate the numerical value of i-th day j-th sampled point.
2) FPCA method (Functional Principal Component Analysis) and KL theorem are used
High-pressure side-U data modeling (Karhunen-Loeve theorem) daily to transformer.
Assuming that the daily high-pressure side-U data of transformer can be expressed as function xi(t), then being indicated according to KL, function can
To indicate are as follows:
Here xi(t) function of the high-pressure side-U data of i-th day transformer about the time is indicated, μ (t) is transformer n days
In all high-pressure side-U data mean function, αikIt is one group of coefficient for depending on number of days,It is one group under n days samples
Basic function.There may be certain errors when in view of measurement, it is believed that true transformer data cases are as follows:
It is 0 that wherein ε, which is mean value, variance σ2Stochastic error.Daily high-pressure side-U data correspond to yi(t) on not
With the sampling at time point:
3) mean function μ (t) is estimated with the method for weighted least-squares.Utilize majorized function:
Wherein k () is a kernel function, the linear kernel function of common kernel function, Polynomial kernel function etc..The present invention
Using gaussian kernel function, expression formula are as follows:
hμIt is bandwidth, the selection of bandwidth influences whether the quality of mean function estimation, and use generalized crossover to examine here
Method (Generalized Cross-Validation, GCV) the selection bandwidth tested, generally can also rule of thumb determine with roomy
It is small.
niIndicate i-th day effective sampling points number, TijAnd YijMeaning with described in first point, β0And β1It is two passes
In the function of t, then our estimations to μ (t) are as follows:
Specific calculation method is, by majorized function respectively to β0And β1Local derviation is sought, enabling two partial derivatives is zero, is obtained
Wherein
4) then we need estimation function baseAccording to Karhunen-Loeve theorem,It is sample covariance function
Characteristic function, that is, meet
Wherein Γ indicates xi(t) domain, Γ is [1,1440] in the narration of here.It is sample association
The estimation function of variance function G (s, t), the expression formula of G (s, t) are as follows:
G (s, t)=cov (x (s), x (t))
Therefore in estimation function baseBefore, we are firstly the need of sample estimates covariance function G (s, t).
A. at s ≠ t, the estimation of G (s, t) is obtained by weighted least-squares, that is, minimizes following majorized function:
Here k2() is a binary kernel function, and expression formula ishGFor
Bandwidth, still can by the method choice bandwidth of GCV,Accordingly, we are estimated
MeterSpecific calculation method, still can be by respectively to β with (3)0、β11And β12Partial derivative is sought, and enables three
A partial derivative is equal to zero and obtains.Have,
Wherein
B. at s=t, due to the local secondary fitting association side more closer than local once fitting on Vertical Diagonal line direction
The shape of poor curved surface, therefore we need to modify majorized function.Specifically, we first rotate clockwise 45 ° to reference axis,
Have
We minimize following majorized function again:
It obtains
We have just obtained the estimation of sample covariance function G (s, t) in this way
5) by obtainingEstimate characteristic function baseWe obtain characteristic function according to following equationAnd spy
Value indicative λk:
Wherein the meaning of Γ is the same as described in (4).Specifically calculating us can be by scatter estimation or Numerical value
Method acquire.
6) factor alpha is determinedik。
We are by design conditions expectation come estimation coefficient αik:
Wherein
Here δjlBe when being 1, j ≠ l in j=l 0. we also need pairEstimation is made,It is given by
WhereinIt is the value of estimation function on the diagonal as obtained in (4) .a,It is by being obtained in (4) .b
Estimation function value on the diagonal.
7) preceding K characteristic function is chosen to indicate xi(t), it would be desirable to determine the quantity of K.It can choose cross validation
Mode selects K, specifically, keeping the value of following formula minimum:
WhereinIt indicates after all removing i-th day data, repeats i-th day estimation letter that (1)-(6) step obtains
Number, i.e.,
WhereinMeaning andMeaning it is identical.
In conjunction with (1)-(7), we just pass through FPCA and have obtained xi(t) according to a preliminary estimate, i.e.,
Next we will be with wavelet transformation to xi(t) estimation is done further perfect.
8) estimate residual error function.
By i-th day t of transformerjThe measurement data Y at momentijWithIt makes the difference to obtain residual error function εi(t) in tjThe value at momentBut since the measurement data of transformer has missing, residual error function ε cannot be obtainedi(t) in all tjWhen
The value at quarter.For convenience followed by Noise Elimination from Wavelet Transform, need to carry out missing point to residual error function to supply.To residual error function
The processing method of missing point is as follows:
A. according to service logic, missing point can be divided into two classes, one kind is the missing of fritter, i.e. consecutive miss data
Time interval is less than or equal to ten minutes；One kind is the missing of bulk, i.e., the time interval of consecutive miss data is greater than ten minutes.
B. to the missing of fritter, the value of missing point residual error function is predicted with the mode of rolling average.Specifically, if kth
The point missing of minute, thenIt should be noted that preceding ten minutes missings can not be carried out with this formula
It calculates, therefore in boundary, we are rightEstimation are as follows:
C. to the missing of bulk, since the absolute value of residual error function is inherently smaller, and functional value is done by noise
It disturbs, therefore little to big section of residual error function of missing progress prediction significance, result can be made more insincere instead.Therefore by bulk
Missing at the value of residual error function be set as zero.
9) wavelet transformation is done to residual error function with MATLAB, removes noise.
According to orthogonal experiments, optimal parameter combination is selected are as follows: wavelet type takes db4 small echo, Decomposition order 3,
Threshold method selects the fixed threshold estimation technique, and noise structure selects Unscaled white noise, the residual error after being denoised
Function of ε 'i(t)。
10) by the residual error function ε ' after denoisingi(t) it is added toOn, final estimation function is obtained, i.e.,
To sum up, we obtain final prediction, i.e., the high voltage side of transformer-U data predicted value of i-th day kth minute isIt is filled up with the numerical value that the predicted value carries out missing point.
Above-mentioned, although specific embodiments of the present invention have been described, not to the limit of the scope of the present invention
System, those skilled in the art should understand that, based on the technical solutions of the present invention, those skilled in the art do not need to pay
The various modifications or changes that creative work can be made out are still within protection scope of the present invention.
Claims (10)
1. a kind of transformer station high-voltage side bus shortage of data mending method based on function type principal component analysis and wavelet transformation, feature
It is, comprising the following steps:
The operation data point acquired is analyzed using FPCA method, fits the operation data letter in entire time series
Number xi(t)；
It is made the difference to former data point and by the data point that FPCA is obtained, obtains residual error function ε (t)；
Residual error function ε (t) is converted using small echo and is denoised, ε ' (t) is obtained；
Estimation functionBy the time t at missing point0It substitutes intoIt obtainsAs
Repairing value at missing point.
2. the method as described in claim 1, characterized in that described to be carried out using FPCA method to the operation data point acquired
Analysis, fits the operation data function x in entire time seriesi(t) before step, further includes:
Take all efficiently sampling times and corresponding efficiently sampling value in the transformer n days, obtain time record matrix T and
Sampled value records matrix Y, the i-th row jth column element T of TijIndicate the time of i-th day j-th sampled point, the i-th row jth of Y arranges member
Plain YijIndicate the numerical value of i-th day j-th sampled point.
3. method according to claim 2, characterized in that described to be carried out using FPCA method to the operation data point acquired
Analysis, fits the operation data function x in entire time seriesi(t), it specifically includes:
The transformer station high-voltage side bus data of acquisition are sequentially arranged, ten day datas are analyzed as one group；
According to KL theorem, the daily operation data of transformer can be expressed as, xi(t) table
Show that function of the operation data about the time of i-th day transformer, μ (t) are the mean function in transformer ten days under sample, αikIt is
One group of coefficient dependent on number of days,It is one group of basic function under ten days samples, estimates mean function μ (t), estimates base letter
NumberEstimation coefficient αik, preceding K characteristic function is chosen to indicate xi(t), x is obtainedi(t) according to a preliminary estimate, i.e.,
4. method as claimed in claim 3, characterized in that the estimation mean function μ (t) specifically includes: most using weighting
Small square law estimates mean function μ (t):
Majorized functionRespectively to β0And β1Ask local derviation, niTable
Show i-th day effective sampling points number, k () uses gaussian kernel function, hμIt is bandwidth, passes through the method choice bandwidth of GCV；
Enabling two partial derivatives is zero, is obtainedWherein Estimation to μ (t) are as follows:
5. method as claimed in claim 3, characterized in that the estimation basic functionIt specifically includes:
Sample estimates covariance function G (s, t)；
According toCharacteristic function is obtained by the method for scatter estimation or Numerical valueWith
Eigenvalue λk, wherein Γ indicates xi(t) domain,It is the estimation function of sample covariance function G (s, t), G (s,
T) expression formula are as follows: G (s, t)=cov (x (s), x (t)).
6. method as claimed in claim 5, characterized in that the sample estimates covariance function G (s, t) specifically includes:
A. at s ≠ t, G (s, t) estimated value, i.e. majorized function are obtained by weighted least-squares method:Respectively to β0、β11And β12Ask inclined
Derivative, and three partial derivatives is enabled to be equal to zero, it obtains,
Wherein
Here k2() is a binary kernel function, and expression formula ishGFor bandwidth,
By the method choice bandwidth of GCV,
B. at s=t, 45 ° first is rotated clockwise to reference axis, that is, is had
Following majorized function is minimized again:
It obtains
7. method as claimed in claim 6, characterized in that the determining factor alphaikIt specifically includes:
By design conditions expectation come estimation coefficient αik:
Wherein
Here δjlIt is 0 when being 1, j ≠ l in j=l,It is given by
WhereinIt is the value of the estimation function as obtained in step a on the diagonal,It is to estimate as obtained in step b
Count the value of function on the diagonal.
8. the method as described in any one of claim 4 to 7 claim, characterized in that K characteristic function comes before the selection
Indicate xi(t), it specifically includes:
The mode of cross validation is selected to select K, i.e., by keeping the value of following formula minimum:
WhereinIt indicates after all removing i-th day data, i-th day obtained estimation function, i.e.,
Wherein,It indicates after all removing the 1st day data, the 1st day obtained estimation function,
It indicates after all removing the 1st day data, the 1st day obtained characteristic value,
It indicates after all removing the 1st day data, the 1st day obtained characteristic function.
9. method according to claim 2, characterized in that described to be done to former data point and by the data point that FPCA is obtained
Difference obtains residual error function ε (t), specifically includes:
By i-th day t of transformerjThe measurement data Y at momentijWithIt makes the difference to obtain residual error function εi(t) in tjThe value at moment
According to service logic, missing point can be divided into two classes, one kind is the missing of fritter, i.e., between the time of consecutive miss data
Every less than or equal to ten minutes；One kind is the missing of bulk, i.e., the time interval of consecutive miss data is greater than ten minutes, to residual error letter
The processing method of number missing point is as follows:
A. to the missing of fritter, the value of missing point residual error function is predicted with the mode of rolling average: if the point of kth minute lacks
It loses, thenPreceding ten minutes missings can not be calculated with this formula, therefore in boundary, rightEstimation are as follows:
B. to the missing of bulk, the value of the residual error function at the missing of bulk is set as zero.
10. method as claimed in claim 9, characterized in that described converted using small echo to residual error function ε (t) is denoised, and is obtained
ε ' (t) is specifically included:
Do wavelet transformation to residual error function ε (t) with MATLAB, remove noise: wavelet type takes db4 small echo, Decomposition order 3,
Threshold method selects the fixed threshold estimation technique, and noise structure selects Unscaled white noise, the residual error after being denoised
Function of ε 'i(t)。
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| CN112287562A (en) * | 2020-11-18 | 2021-01-29 | 国网新疆电力有限公司经济技术研究院 | Power equipment retired data completion method and system |
| CN113806967A (en) * | 2021-10-18 | 2021-12-17 | 广东英达思迅智能制造有限公司 | Missing equipment data simulation method and system based on Internet of things and storage medium |
| CN114691666A (en) * | 2022-04-18 | 2022-07-01 | 西安电子科技大学 | Flight test data missing value filling method based on wavelet denoising optimization |
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