CN106384298B - A kind of intelligent power missing data modification method based on two stages interpolation model - Google Patents
A kind of intelligent power missing data modification method based on two stages interpolation model Download PDFInfo
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Abstract
The invention discloses a kind of intelligent power missing data modification method based on two stages interpolation model, its feature includes: to select the power consumer of at most only one missing item in the first stage first, use the PMM regression model based on the multiple interpolation of chain type equation, multiple candidate interpolation values are calculated for each missing item of power consumer, linear regression model (LRM) is recycled to calculate unique final interpolation value;Then in second stage, interpolation value is calculated using linear interpolation method to the missing data of dump power user;Finally, comprehensive two stages as a result, obtaining the complete intelligent power data of all power consumers.The present invention can be realized more accurate intelligent power missing data amendment, and computation complexity is effectively reduced, and the interpolation of the sparse data set to multivariable missing can be rapidly completed, with good stability.
Description
Technical field
The present invention relates to electric system missing data correction technique fields, specifically a kind of to be based on two stages interpolation mould
The intelligent power missing data modification method of type.
Background technique
Currently, China's power industry has tentatively built up domestically leading, world-class information integrated platform, fundamental form
At the strong smart grid characterized by interactivity, integration, digitlization and intelligence.Smart grid be one can be real-time
The automation of the links such as power generation, transmission of electricity, distribution, power transformation and electricity consumption is monitored for power utilization network, can be realized from power generation end to electricity consumption
Hold the two-way flow of electric current and information flow.Magnanimity, real time data in smart grid more highlight the characteristic of big data, big number
It is also applied more and more widely in power industry according to analysis mining.
With the widespread deployment and intelligence of advanced measurement system (Advanced Metering Infrastructure, AMI)
The rapid proliferation of energy ammeter, the extensive dynamic realtime electricity consumption data of power consumer have been able to collected and store.However, by
It is influenced in by system inside and outside complicated factor, these intelligent power data can not be kept away during acquisition, transimission and storage
That exempts from will appear missing.Missing data often means that the loss of useful information, is easy to fall into electric power big data mining process
Confusion causes insecure result to export.In addition, a large amount of presence of missing data increase the complexity of electric power big data analysis
Property, so that the uncertainty of intelligent power service and management dramatically increases.Intelligent power how is quickly and efficiently handled to lack
Mistake data have become a critical issue in the excavation of electric power big data analysis.
Common missing data processing method has elimination method and interpolation in electric system.Elimination method will lead to useful information
Loss, be particularly unsuitable for the situation of large amount of complex missing data.And mean value interpolation, regression imputation, calorie interpolation, last
Observation (LOCF) etc. traditional simple interpolating method accuracy of carrying down is not high, to intelligent power missing data correction effect compared with
Difference.In addition, there is only Stable Defects for multiple interpolating method, the multivariable missing data concentrated to sparse data can not be complete
Interpolation, and when facing the intelligent power data of magnanimity, computation complexity is higher, and treatment effeciency is lower.Therefore, it is badly in need of intelligence
The modified efficient stable method of electricity consumption missing data.
Summary of the invention
The present invention is to provide a kind of intelligence based on two stages interpolation model to overcome the shortcomings of the prior art place
Calculating is effectively reduced to can be realized more accurate intelligent power missing data amendment in energy electricity consumption missing data modification method
Complexity, and the interpolation of the sparse data set to multivariable missing can be rapidly completed, have good stability, so as to fast
Speed effectively corrects intelligent power missing data.
The present invention to achieve the above object of the invention, adopts the following technical scheme that
A kind of the characteristics of intelligent power missing data modification method based on two stages interpolation model of the invention, is:
Power consumer number in the intelligent power data of collection is denoted as N, N number of power consumer is denoted as U={ U1,
U2,...,Ui,...,UN, 1≤i≤N, UiIndicate i-th of power consumer;
Time point number in the intelligent power data of collection is denoted as M, the interval between each time point is uniform, and M
The time zone that time point is constituted is denoted as T={ T1,T2,...,Tj,...,TM, 1≤j≤M, TjIndicate j-th of time point;
By i-th of power consumer UiIn j-th of time point TjOn intelligent power data be denoted as eij, i-th of the electric power
User UiIntelligent power data on time zone T are denoted asJ-th of time point TjOn
The intelligent power data of N number of power consumer U are denoted asN number of power consumer U is in time zone
Intelligent power data on the T of domain constitute the matrix of N × M, are denoted as
The intelligent power missing data modification method based on two stages interpolation model is to carry out as follows:
Step 1: i-th of power consumer UiIntelligent power data when being lacked on certain time point, by the intelligence of missing
Energy electricity consumption data is denoted as missing item;N power consumer of at most only one missing item, note are selected from N number of power consumer U
For U '={ U '1,U′2,...,U′p,...,U′n, U 'pThe power consumer of p-th of expression only one most missing item, 1≤p≤
N, 1≤n≤N;Calculate p-th of power consumer U 'pIntelligent power statistical average on time zone T, is denoted asThe pth
A power consumer U 'pIf there is missing item on time zone T, ignores missing item and calculate p power consumer U 'pIn remaining time
Intelligent power statistical average on point, thus obtain the intelligent power statistical average composition of the n power consumer U '
Column vector is denoted as
Step 2: the power consumer number without missing item in n power consumer is denoted as n1;By the n-n1A electric power is used
The time zone that time point where the missing item at family is constituted is denoted as T '={ T '1, T '2,...,T′q,...,T′t, T 'qIndicate the
Time point where q missing item, 1≤q≤t, 1≤t≤n-n1;By p-th of power consumer U 'pIn q-th of time point T 'qOn
Intelligent power data be denoted as e 'pq, p-th of power consumer U 'pIntelligent power data on time zone T ' are denoted asThe time point T 'qThe intelligent power data of upper n power consumer are denoted asIntelligent power data of the n power consumer on time zone T ' constitute n × t square
Battle array, is denoted as
Step 3: the PMM regression model based on the multiple interpolation of chain type equation being used to the matrix E ' in the step 2, is every
A missing item calculates m candidate interpolation value, m > 1;
Step 4: utilizing linear regression model (LRM), and according to described m candidate interpolation value and column vectorFor each missing item
Unique final interpolation value is calculated, to obtain n-n1A final interpolation value;By the n-n1A final interpolation value inserts matrix
E ' obtains the matrix E without missing item1 *;
Step 5: (N-n) × M square that intelligent power data of the remaining N-n power consumer on time zone T are constituted
Battle array is denoted as E ", calculates interpolation value to all missing items in matrix E " using linear interpolation method, and by the interpolation value of the calculating
Matrix E " is inserted, the matrix E without missing item is obtained2 *;
Step 6: by matrix E1 *With matrix E2 *Merge, obtains whole N number of power consumer U on time zone T without any
Lack the full matrix E that the intelligent power data of item are constituted*。
The characteristics of intelligent power missing data modification method of the present invention, lies also in, and the step 4 is by following mistake
Cheng Jinhang:
Step 4.1: utilizing the linear regression model (LRM) as shown in formula (1), obtain the least-squares estimation of kth group regression coefficient
Measure λqkWith λ 'qk, to obtain m group least squares estimator;
In formula (1),Indicate n power consumer in q-th of time point T 'qIt is upper candidate for k-th of substitution of corresponding missing item
The column vector that intelligent power data after interpolation value are constituted, 1≤k≤m;
Step 4.2: average least squares estimator is obtained after being averaged respectively to m group least squares estimatorWithTo obtain n-n using formula (2)1A power consumer is in q-th of time point T 'qThe final interpolation value of upper corresponding missing item
To obtain n-n1A power consumer accordingly lacks the final interpolation value of item on t time point:
Compared with the prior art, the invention has the advantages that:
1, the present invention is a kind of antihunt means that can quickly, effectively correct intelligent power missing data, is inserted based on two stages
Complementary modulus type, which carries out the amendment of intelligent power missing data, can obtain precision more compared to the conventional methods such as linear interpolation are directlyed adopt
High interpolation effect;Compared to multiple interpolating method is directlyed adopt, computation complexity can be effectively reduced and overcome stability lack
It falls into.
2, the present invention is based on two stages interpolation models to carry out the amendment of intelligent power missing data, by selecting in the first phase
Particular power user is selected, and candidate interpolation value is calculated using multiple interpolating method to selected power consumer, is overcome entire
The Stable Defects being subject to when using multiple interpolation on data set, and effectively reduce computation complexity.
3, the present invention is based on two stages interpolation models to carry out the amendment of intelligent power missing data, comprehensive using linear regression model (LRM)
Multiple groups candidate's interpolation value that multiple interpolating method calculates is closed, unique final interpolation value is obtained, compared with conventional one group of random selection
Method of the candidate interpolation value as final interpolation value reduces the accidental sexual deviation in interpolation value calculating.
Detailed description of the invention
Fig. 1 is the method for the present invention flow chart;
Fig. 2 is the result of implementation figure of the method for the present invention and linear interpolation method.
Specific embodiment
In the present embodiment, as shown in Figure 1, the power consumer number in the intelligent power data of collection is denoted as N, N number of electricity
Power user is denoted as U={ U1,U2,...,Ui,...,UN, 1≤i≤N, UiIndicate i-th of power consumer;
Time point number in the intelligent power data of collection is denoted as M, the interval between each time point is uniform, M time
The time zone that point is constituted is denoted as T={ T1,T2,...,Tj,...,TM, 1≤j≤M, TjIndicate j-th of time point;
By i-th of power consumer UiIn j-th of time point TjOn intelligent power data be denoted as eij, i-th of power consumer Ui
Intelligent power data on time zone T are denoted asJ-th of time point TjUpper N number of electric power is used
The intelligent power data of family U are denoted asIntelligence of N number of power consumer U on time zone T is used
Electric data constitute N × Metzler matrix, are denoted as
In the present embodiment, a kind of intelligent power missing data modification method based on two stages interpolation model, including it is following
Step:
Step 1: as i-th of power consumer UiIntelligent power data when being lacked on certain time point, by the intelligence of missing
Electricity consumption data is denoted as missing item;The n power consumer that at most only one missing item is selected from N number of power consumer U, is denoted as
U '={ U '1,U′2,...,U′p,...,U′n, U 'pIndicate the power consumer of p-th of only one most missing item, 1≤p≤n;
Calculate p-th of power consumer U 'pIntelligent power statistical average on time zone T, is denoted asIf p-th of power consumer
U′pThere is missing item on time zone T, then ignores missing item and calculate p power consumer U 'pIntelligence on remaining time point is used
Electric statistical average is denoted as to obtain the column vector of the intelligent power statistical average composition of the n power consumer U '
Step 2: the power consumer number without missing item in n power consumer is denoted as n1;By n-n1A power consumer
The time zone that time point where missing item is constituted is denoted as T '={ T '1,T′2,...,T′q..., T 't, T 'qIt indicates q-th
Lack the time point where item, 1≤q≤t, 1≤t≤n-n1;By p-th of power consumer U 'pIn q-th of time point T 'qOn intelligence
Energy electricity consumption data is denoted as e 'pq, p-th of power consumer U 'pIntelligent power data on time zone T ' are denoted asBy time point T 'qThe intelligent power data of upper n power consumer are denoted asThen intelligent power data of the n power consumer on time zone T ' constitute n × t matrix,
It is denoted as
Step 3: the PMM regression model based on the multiple interpolation of chain type equation being used to the matrix E ' in step 2, is lacked to be each
It loses item and calculates m candidate interpolation value, m > 1, m takes 5 under normal conditions;
The process for calculating m candidate interpolation value using PMM regression model is as follows:
Firstly, for time point T '1, determine linear regression model (LRM):
From n1A be free of in missing item sample obtains the least squares estimator of regression coefficientWith residual error side
Poor estimated valueIt is time point T ' by following 3 steps Repeated m time1In each intelligent power missing data calculate m group
Candidate interpolation value:
Step 3.1: being n from freedom degree1In the chi square distribution of-t extract random number g [k], k=1,2 ..., m, obtain with
Machine observation
Step 3.2: being from mean valueVariance isNormal distribution in extract random numberWhereinI is the n that value is 11Dimensional vector;
Step 3.3: byThe estimated value Y of computational intelligence electricity consumption missing datak, selection
Closest to estimated value Y in intelligent power datakValue as k-th of the candidate interpolation value calculated;
It then, is time point T '2In each intelligent power missing data calculate the candidate interpolation value of m group, determine linear time
Return model:
According to the step 3.1, step 3.2, step 3.3 acquisition time point T '2In each intelligent power missing data m
The candidate interpolation value of group;
Continue as time point T '2In intelligent power missing data calculate the candidate interpolation value of m group, it is a until completing all t
The calculating of missing data candidate interpolation value on time point.
Step 4: utilizing linear regression model (LRM), and according to m candidate interpolation value and column vectorFor the calculating of each missing item
Unique final interpolation value out, to obtain n-n1A final interpolation value;By n-n1A final interpolation value inserts matrix E ', obtains
Matrix E without missing item1 *;
Specifically, the process that step 4 calculates final interpolation value is performed as follows:
Step 4.1: utilizing the linear regression model (LRM) as shown in formula (1), obtain the least-squares estimation of kth group regression coefficient
Measure λqkWith λ 'qk, to obtain m group least squares estimator;
In formula (3),Indicate n power consumer in q-th of time point T 'qIt is upper candidate for k-th of substitution of corresponding missing item
The column vector that intelligent power data after interpolation value are constituted, 1≤k≤m;
Step 4.2: average least squares estimator is obtained after being averaged respectively to m group least squares estimatorWithTo obtain n power consumer in q-th of time point T ' using formula (4)qThe final interpolation value of upper corresponding missing itemFrom
And obtain the final interpolation value that n power consumer accordingly lacks item on t time point:
Step 5: (N-n) × M square that intelligent power data of the remaining N-n power consumer on time zone T are constituted
Battle array is denoted as E ", calculates interpolation value to all missing items in matrix E " using linear interpolation method, and by the interpolation value of the calculating
Matrix E " is inserted, the matrix E without missing item is obtained2 *;
If intelligent power data eijIt lacks, calculates the intelligent power missing data interpolation using linear interpolation method in step 5
The formula of value, such as formula (5):
In formula (5), eiaAnd eibIt respectively indicates near intelligent power missing data eijObservation, a and b are respectively represented
A-th and b-th of time point.
Step 6: by matrix E1 *With matrix E2 *, obtain all N number of power consumer U and be free of any missing on time zone T
The full matrix E that the intelligent power data of item are constituted*。
Specific application example:
Missing data is simulated in intelligent power data sample using R language, this sample is 100 power consumers 2014
The true electricity consumption data in July in year, thus N=100, M=31.Interpolation is calculated using the method for the present invention and linear interpolation method respectively
Value, and the accuracy of mean absolute deviation MAD the comparison linear interpolation method and the method for the present invention defined using formula (6):
In formula (6), Q indicates missing item number,Represent the interpolation value calculated v-th of missing values, yvIt represents and is simulated
The true value of v-th of missing values.It can easily be seen that MAD value is smaller, illustrate that the interpolation value calculated is more approximate with true value, method
Precision it is also better.In Fig. 2, is represented with abscissa and test the number for simulating missing, the MAD value that ordinate representative calculates, two
Broken line respectively represents the MAD value situation of the method for the present invention and linear interpolation method, the results showed that the method for the present invention can be realized more
Accurate intelligent power missing data amendment.
Claims (2)
1. a kind of intelligent power missing data modification method based on two stages interpolation model, it is characterised in that:
Power consumer number in the intelligent power data of collection is denoted as N, N number of power consumer is denoted as U={ U1,
U2,...,Ui,...,UN, 1≤i≤N, UiIndicate i-th of power consumer;
Time point number in the intelligent power data of collection is denoted as M, the interval between each time point is uniform, M time
The time zone that point is constituted is denoted as T={ T1,T2,...,Tj,...,TM, 1≤j≤M, TjIndicate j-th of time point;
By i-th of power consumer UiIn j-th of time point TjOn intelligent power data be denoted as eij, i-th of power consumer Ui
Intelligent power data on time zone T are denoted asJ-th of time point TjUpper N number of electricity
The intelligent power data of power user U are denoted asN number of power consumer U is on time zone T
Intelligent power data constitute N × M matrix, be denoted as
The intelligent power missing data modification method based on two stages interpolation model is to carry out as follows:
Step 1: i-th of power consumer UiIntelligent power data when being lacked on certain time point, by the intelligent power of missing
Data are denoted as missing item;Selected from N number of power consumer U at most only one missing items n power consumer, be denoted as U '=
{U′1,U′2,...,U′p,...,U′n, U 'pIndicate the power consumer of p-th of only one most missing item, 1≤p≤n, 1≤n
≤N;Calculate p-th of power consumer U 'pIntelligent power statistical average on time zone T, is denoted asP-th of electricity
Power user U 'pIf there is missing item on time zone T, ignores missing item and calculate p power consumer U 'pOn remaining time point
Intelligent power statistical average, thus obtain the n power consumer U ' intelligent power statistical average composition column to
Amount, is denoted as
Step 2: the power consumer number without missing item in n power consumer is denoted as n1;By n-n1The missing of a power consumer
The time zone that time point where is constituted is denoted as T '={ T1′,T2′,...,Tq′,...,Tt', Tq' indicate q-th of missing
Time point where, 1≤q≤t, 1≤t≤n-n1;By p-th of power consumer Up' in q-th of time point Tq' on intelligence use
Electric data are denoted as e 'pq, p-th of power consumer U 'pIntelligent power data on time zone T ' are denoted asThe time point TqThe intelligent power data of ' upper n power consumer are denoted asIntelligent power data of the n power consumer on time zone T ' constitute n × t square
Battle array, is denoted as
Step 3: the PMM regression model based on the multiple interpolation of chain type equation being used to the matrix E ' in the step 2, is lacked to be each
It loses item and calculates m candidate interpolation value, m > 1;
Step 4: utilizing linear regression model (LRM), and according to described m candidate interpolation value and column vectorFor the calculating of each missing item
Unique final interpolation value out, to obtain n-n1A final interpolation value;By the n-n1A final interpolation value inserts matrix E ',
Obtain the matrix E without missing item1 *;
Step 5: (N-n) × Metzler matrix that intelligent power data of the remaining N-n power consumer on time zone T are constituted is remembered
For E ", interpolation value is calculated to all missing items in matrix E " using linear interpolation method, and the interpolation value of the calculating is inserted
Matrix E " obtains the matrix E without missing item2 *;
Step 6: by matrix E1 *With matrix E2 *Merge, obtains all N number of power consumer U and be free of any missing on time zone T
The full matrix E that the intelligent power data of item are constituted*。
2. intelligent power missing data modification method according to claim 1, characterized in that the step 4 is by as follows
Process carries out:
Step 4.1: utilizing the linear regression model (LRM) as shown in formula (1), obtain the least squares estimator λ of kth group regression coefficientqk
With λ 'qk, to obtain m group least squares estimator;
In formula (1),Indicate n power consumer in q-th of time point Tq' upper for k-th of the substitution candidate interpolation of corresponding missing item
The column vector that intelligent power data after value are constituted, 1≤k≤m;
Step 4.2: average least squares estimator is obtained after being averaged respectively to m group least squares estimatorWithTo
N-n is obtained using formula (2)1A power consumer is in q-th of time point Tq' go up the corresponding final interpolation value for lacking itemTo obtain
Obtain n-n1A power consumer accordingly lacks the final interpolation value of item on t time point:
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