CN106971240A - The short-term load forecasting method that a kind of variables choice is returned with Gaussian process - Google Patents
The short-term load forecasting method that a kind of variables choice is returned with Gaussian process Download PDFInfo
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Abstract
The present invention discloses a kind of short-term load forecasting method returned based on variables choice and Gaussian process, comprises the following steps:1) bad data rejecting, supplement and normalization is carried out to sample data to pre-process;2) candidate's input variable is angularly chosen from historical load, temperature and humidity, prediction day date type, calculating each variable importance by random forests algorithm scores and sort;3) Gaussian process regression model is combined, optimal variables collection is determined using sequence sweep forward strategy;4) the optimal variables collection training Gaussian process regression model based on determination, and utilization improves particle cluster algorithm Optimized model parameter;5) estimated performance of model is verified in test set.The method that the present invention is provided is effectively improved precision of prediction, can preferably solve the problems, such as Load Prediction In Power Systems.
Description
Technical field
The present invention relates to a kind of power-system short-term load forecasting method, power system load is predicted, belongs to electricity
Force system technical field.
Background technology
Improve Load Prediction In Power Systems precision be effective guarantee power system security, stably, the technology of economical operation arranges
One of apply, the load prediction of different time scales is to arranging power generation scheduling, Plant maintenance plan and medium-term and long-term Electric Power Network Planning
All it is extremely important.The data such as historical load, the meteorology of real system operation accumulation magnanimity, fully excavate these numbers
According to the information contained, new approach is provided to improve load forecast precision.
Gaussian process is returned (Gaussian process regression, GPR) and managed with bayesian theory and statistical learning
Based on, when handling the complicated regression problem such as high dimension, non-linear there is easy programming to realize, hyper parameter adaptively obtain with
And output has the advantages that probability distribution, in multi-field acquisitions such as time series analysis, dynamic system model identification, system controls
Extensive use.Based on above advantage, the present invention is returned using Gaussian process and sets up Short-term Load Forecasting Model.Conventional conjugation ladder
Spend (conjugate gradient, CG) method and solve Gaussian process regression model hyper parameter, but this method presence is easily absorbed in office
Portion's optimal solution, optimization performance by initial value selections influenceed greatly, iterations be difficult to determination the shortcomings of.Therefore, Gaussian process is being set up
, it is necessary to take measures to optimize model parameter processing during recurrence Short-term Load Forecasting Model.
In short-term load forecasting modeling process, the selection of input variable has a significant impact to model prediction result.Usually through
Experience chooses input variable, but the way relies on technical staff's subjective experience, is theoretically unsound.Meanwhile, artificial selection it is defeated
Enter dimension too high, be readily incorporated redundant variables, increase model training complexity, reduce estimated performance.Selection is a small amount of defeated
When entering variable, it is difficult to obtain enough information representation output characteristics again.Therefore, need to set up optimal variables set before training pattern
Close to overcome the shortcomings of that artificial experience is chosen.
The content of the invention
Goal of the invention:The present invention such as applies Gauss mistake for problem present in existing Load Prediction In Power Systems technology
When Cheng Huigui sets up load forecasting model, traditional conjugate gradient method solving model hyper parameter, which exists, is easily absorbed in local optimum
Solution, optimization performance by initial value selections influenceed greatly, iterations be difficult to determination the shortcomings of, not high scarce of the degree of accuracy that causes to predict the outcome
It is sunken that there is provided a kind of short-term load forecasting method returned based on Modified particle swarm optimization Gaussian process, i.e. PSO-GPR load predictions
Method.Meanwhile, input variable prominence score is provided using random forests algorithm, selects optimal with reference to Gaussian process regression model
Variables collection, improves precision of prediction.
Technical scheme:A kind of short-term load forecasting method returned based on variables choice and Gaussian process, including following step
Suddenly:
1) master data needed for power-system short-term load forecasting is obtained:Historical load data and original meteorological data;
Wherein historical load data is integral point moment load data of the history day per day interval 1h, and original meteorological data includes the integral point moment
The influence factors such as environment temperature, humidity, prediction day date type;
2) data prediction:Bad data in training and test sample collection data is rejected and supplemented, and data are entered
Row normalized, by sample data change of scale to interval [0,1];
3) consider the influence of historical load value, temperature, humidity factor and its cumulative effect to prediction daily load size, choose
A number of alternative input variable, calculates each input variable prominence score using random forests algorithm and is ranked up;
4) it is empty set to set initial optimal variables collection, and prominence score is added one by one most using sequence sweep forward strategy
High input variable simultaneously calculates its predictablity rate using Gaussian process regression model, until all input variables are traveled through, by pre-
Survey error minimum and can determine that optimal variables collection.
5) the optimal variables collection training Gaussian process regression model based on determination, and being optimized using particle cluster algorithm is improved
Model parameter;
6) estimated performance of model is verified in test set.
Beneficial effect:The power-system short-term load forecasting method of the present invention provides each input using random forest method and become
Amount prominence score is simultaneously sorted, and optimal variables collection is determined using sequence sweep forward strategy combination Gaussian process regression model,
Avoid artificial experience from choosing the deficiency of input variable, improve model prediction performance.Meanwhile, optimized using particle cluster algorithm is improved
Gaussian process Parameters in Regression Model, and then improve the precision and generalization ability of forecast model.
Brief description of the drawings
Fig. 1 is to choose optimal variables collection flow chart using random forests algorithm;
Fig. 2 is that variable importance scores and its predicated error curve;
Fig. 3 is Gaussian process regression model log-likelihood function iterativecurve;
Fig. 4 is the continuous 7 daily load prediction curve of PSO-GPR forecast models and actual curve of test.
Embodiment
With reference to specific embodiment, the present invention is furture elucidated, it should be understood that these embodiments are merely to illustrate the present invention
Rather than limitation the scope of the present invention, after the present invention has been read, various equivalences of the those skilled in the art to the present invention
The modification of form falls within the application appended claims limited range.
The thinking of the present invention is that random forests algorithm is used into power-system short-term load forecasting to model Input variable selection
In, provide each input variable prominence score using random forests algorithm and sort, thus with reference to Gaussian process regression model simultaneously
Optimal input variable set is determined based on sequence sweep forward strategy, its predicated error minimum correspond to optimal variables collection.
Meanwhile, using improvement population (particle swarm optimization, PSO) algorithm optimization Gaussian process regression model
Parameter, further enhancing model prediction performance, it is to avoid traditional conjugate gradient method is easily absorbed in the shortcoming of locally optimal solution.
In short-term load forecasting modeling process, the selection of input variable has a significant impact to model prediction result.The present invention
Optimal variables set merging is chosen using random forests algorithm and sets up Gaussian process recurrence Short-term Load Forecasting Model.Random forest
(random forest, RF) builds multiple subsample data sets using random resampling technique bootstrap, in each increment
This concentration randomly selects part input variable and chooses best splitting point by branch's Criterion of goodness, and robust is built by each regression tree
The strong integrated model of performance.
It is assumed that (X, y) containing n observation, input variable dimension is M to Power system load data training set, utilizes bootstrap
Method has that puts back to repeat b sub- sample sets of extraction from original training data set, and each subset sample number is n, thus may be used
Build b regression tree;Extract biDuring individual subset, non-selected observation constitutes the outer data (out-of-bag, OOB) of bag;
Construct biDuring regression tree, fixed qty is randomly selected for m from M dimension input variablestry(desirable mtry=M/3) input become
Quantity set as this regression tree feature space.For regression problem, fission process is minimum accurate as branch's goodness using variance
Then choose division variable, i.e.,
In formula, n is number of training, XkFor variable k sample value,For variable k sample average, I is this time most
Optimal sorting fission amount.
Every regression tree is used without Pruning strategy from the top-down recursive branch of root node, and setting leaf node minimum dimension is made
End condition is grown for regression tree.After the completion of b regression tree growth, you can build complete RF regression models.Finally, bag is passed through
The estimated performance of outer data prediction accuracy estimating model, i.e.,
In formula, nOOBFor data sample quantity, y outside bagiFor true load value,For RF model prediction results.
RF models evaluate each input variable to the influence degree of load with variable importance scoring, are reduced by mean square sesidual
Each input variable prominence score of gauge amount simultaneously sorts.B regression tree is tested using data outside bag, mean square sesidual is obtained
Respectively:MSE1,MSE2,L,MSEb.Variable XkData are concentrated use in randomized method displacement outside b bag, are formed outside new bag
Test set.Test is re-started to b regression tree using data outside new bag, constituting the Square Error matrix after random permutation is
K-th of input variable prominence score be:By MSE1,MSE2,L,MSEbIt is corresponding with Square Error matrix row k
Subtract each other and take b regression tree average value, last divided by b regression tree standard error SE, obtain variable XkMean square sesidual averagely subtract
In a small amount.Thus obtaining each input variable prominence score formula is
When GPR is used for short-term load forecasting modeling, training set is combined into D={ (xi, yi) | i=1,2,3 ..., n }=(X, y),
Wherein:xi∈RmFor m dimensional input vectors, m × n dimension input matrixes are then represented by X=[x1,x2,…,xn], n represents training sample
Point quantity, yi∈ R are corresponding to xiOutput scalar.
GPR load prediction processes are described with mathematical linguistics is:Defined function space f (x)=Φ (x)Tω, f (x(1))、f(x(2))、…、f(x(n)) set of stochastic variable is constituted, and Joint Gaussian distribution is obeyed, Gaussian process model can just be represented
For
In formula:It is 0 that independent white Gaussian noise, which obeys average, and variance isGaussian Profile, be denoted as ε:δijFor
Kronecker delta functions, as i=j, function δij=1;M (x) is the mean value function of family of finite-dimensional distribution, describes load
Average output result;K (x, x ') is covariance function, portrays load variance size.
To simplify derivation, load average m (x) carries out data prediction and is allowed to as 0.GPR forecast models are in n dimension training sets D
Prior distribution is inside set up, in n* dimension test set D*={ (xi, yi) | i=n+1, L, n+n* }=(X*, f*) under be changed into posteriority point
Cloth, then constitute Joint Gaussian distribution between training sample observation y and the output vector f* of test data
Wherein, K (X, X)=KnRepresent n × n nuclear matrix, its element Kij=k (xi,xj);K (X, X*)=K (X*, X)TFor
Covariance matrix between test data X* and the input X of training set;K (X*, X*) is X* itself covariance, and I is unit square
Battle array.
Thus show that predicted value f* Posterior distrbutionps are
Wherein
Mean vectorFor GPR model load prediction averages, exported corresponding to point prediction,For corresponding to
Variance, thus can obtain the load setting uncertainty with probability distribution meaning and predict the outcome.
Present invention selection square index covariance function (squared exponential covariance function,
SE nuclear matrix element) is calculated, its formula is
Unknown hyper parameter is included in above formula:M=diag (l-2), l is variance measure;For kernel function signal variance,For
Noise variance.Orderθ is the vector for including all hyper parameters.The log-likelihood function of training sample can be represented
For
Wherein:
GPR models adaptively obtain the optimal hyper parameter in covariance function by the likelihood function that maximizes, and obtain super ginseng
After number optimal value, you can to obtain the prediction average and variance of future position with the covariance function of determination.The present invention is using improvement
PSO Algorithm hyper parameter, effectively prevent the shortcoming of conjugate gradient method.
Particle swarm optimization algorithm is derived from simulating the heuristic value of flock of birds foraging behavior, is widely used in non-linear
Optimization problem.Standard PSO evolutionary equations are as follows
In formula:W is inertia weight;c1, c2For accelerated factor;r1,r2∈Rand[0,1];Respectively
Speed, position, individual extreme value optimal location and the colony's extreme value optimal location of hyper parameter i jth dimension variable in kth time iteration.
Inertia weight w and accelerated factor c in PSO algorithm1, c2For constant, colony is easily caused in search procedure various
Property lose, it is precocious, the problems such as be absorbed in local optimum.Particle cluster algorithm is improved to cause to strengthen local in later stage of evolution using formula (14)
Optimizing ability, formula (15) can play particle itself search capability and all particle group cognition abilities.
W=wmax-(wmax-wmin)kT (14)
In formula:wmax、wminRespectively initial inertia weight maximum and minimum value;Cmax、CminRespectively initial acceleration because
Sub- maximum, minimum value, w, C1、C2The respectively inertia weight of kth time iteration, accelerated factor value;T is iterations.
Using improving, particle cluster algorithm optimization GPR hyper parameter flows are as follows:
1) initialization algorithm parameter.Including particle scale, iterations, inertia weight, accelerated factor initial value.
2) hyper parameter is initialized.To each parameter initialization in hyper parameter vector, and determine each parameter variation range.
3) inertia weight and accelerated factor value are updated.
4) fitness is calculated.Each particle position correspond to a hyper parameter solution, calculate the training sample pair during this position
Number likelihood function is fitness value, and determines individual extreme point and global extremum point.
5) optimal solution updates.If particle current position is better than the optimal location of itself memory, replaced with current location;If
This time iteration global optimum position is better than the global optimum position up to the present searched, then with the global optimum of this iteration
Replace position.
6) particle state updates and mutation operation.Particle rapidity and position are updated by formula (14), (15).If particle position surpasses
Go out parameter variation range, then replaced with the corresponding boundary value of parameter.Setting particle variations probability go forward side by side row variation operation.
7) cycle calculations.Return to step 3) cycle calculations, until meeting the condition of convergence or reaching maximum iteration.
The present invention is on the basis of optimal variables collection is chosen, and the Gaussian process that foundation improvement particle cluster algorithm optimizes returns short
Phase load forecasting model, i.e. PSO-GPR models.First according to load characteristic, mould is angularly chosen from historical load, meteorologic factor
Type input variable simultaneously builds training set and checking collection, and each input variable importance is provided in training focus utilization random forests algorithm
Score and be ranked up.It is empty set to set optimal variables collection, based on sequence sweep forward strategy by prominence score highest
Input variable sequentially adds optimal variables collection, is tested, obtained using the Gaussian process regression model of optimization on checking collection
To the predicated error of now input variable set.After all input variables are traveled through, optimal variables collection is that correspond to prediction to miss
The minimum variables collection of difference.
Electric load is the coefficient result of many factors, and the present invention is main from meteorologic factor, historical load value and pre-
Short-term load forecasting models the selection of input variable from the aspect of survey day date type three.Electric load is daily, load weekly
The shape of curve, which discloses load, has obvious periodicity, while yearly load curve also has certain similitude.It is negative from history
Charge values can be found that the variation tendency of load, are the important influence factors of short-term load forecasting.Meanwhile, temperature, humidity factor pair
Daily load size, which has, to be directly affected, and the cumulative effect of meteorologic factor, such as the previous day temperature also can produce work to prediction daily load
With.Working day and day off are accustomed to difference due to work, the rest of people causes electricity consumption behavior to occur very big change, load value tool
There is notable difference.In summary analyze, the input variable that the present invention chooses is as shown in table 1.
The variable symbol of table 1 and its physical significance
To eliminate the difference of physics dimension, need that data are normalized before model is trained, normalize
Formula is
In formula:Data value after being normalized for a certain input variable;X (i) is input variable initial data;xmax、xmin
The respectively maximum and minimum value of initial data.
It is quantitative prediction value close to the degree of actual value, present invention selection mean absolute percentage error (Mean
Absolute Percentage Error, MAPE) and root-mean-square error (Root Mean Square Error, RMSE) conduct
Forecast result of model evaluation index, calculation formula is respectively:
In formula:N is future position number, yiPoint load actual value is predicted for i-th,For i-th of future position predicted value.
To verify the validity of the inventive method, following test is carried out:During using certain network load 15 days 4 June in 2015
To totally 1700 actual measurement load values are as training sample sequence during August 24 days 23, data sampling time sets up PSO- at intervals of 1h
168 load values of August 25 days 0 when August 31 days 23 are proposed the prediction of the previous day by GPR load forecasting models.
24 input variable importance are ranked up in training set using Random Forest model, random forest parameter is set
For:Regression tree number is 500, and node minimum dimension is 5, mtry=8.Variable importance sequence is as shown in Fig. 2 prominence score
Sequence is followed successively by from high to low:Predict day previous daily load, prediction degree/day, the first seven daily load, preceding 14 daily load, proxima luce (prox. luc)
It is temperature, preceding two daily load, first three daily load, forecast date type, prediction day humidity, the first eight daily load, preceding two degree/day, previous
Day humidity, same period last year humidity, the first eight day humidity, the first eight degree/day, preceding humidity on the 14th, same period last year load, first three day temperature
Degree, first three day humidity, the first seven degree/day, preceding humidity on the two, the first seven day humidity, preceding 14 degree/day, same period last year temperature.Can be with
Find out, recent history load value has a significant impact to prediction daily load tool, determines load variations trend, while predicting day temperature
Degree, humidity, date type also there is higher significant to score.Gaussian process regression model is combined by variable importance scoring, obtained
It is as shown in Figure 2 to load prediction error during different input variable numbers.It can be seen that less input variable is difficult to obtain
Enough information characterizes load characteristic, and precision of prediction is relatively low.With the increase of input variable number, information is further enriched, in advance
Precision is surveyed to increase.When input variable number reaches 16, it can be seen that now predicated error is minimum by error curve.But with
The further increase of input variable so that redundancy has been mixed into optimal input variable set, increase model training is complicated
Degree, reduces generalization ability, therefore downward trend can be presented in precision of prediction again.Thus, 16 before selection variable importance sequence
Variable constitutes optimal input variable set.In addition, under variable same case, improving particle cluster algorithm and entering with respect to conjugate gradient method
There is more preferable prediction effect during row Gaussian process regression forecasting.
Fig. 3 is input variable number when being 16, and improvement particle cluster algorithm and conjugate gradient algorithms solving model is respectively adopted
The fitness curve of hyper parameter.With respect to conjugate gradient algorithms, improve population iterations less, obtain more preferable fitness
Value.
For checking PSO-GPR model prediction performances, BP neural network, SVM (SupportVector is respectively adopted
Machines), CG-GPR sets up Short-term Load Forecasting Model.Fig. 4 is that four kinds of forecast models predict the outcome and realized load curve.
It can be seen that four kinds of models can be provided and more accurately predicted the outcome, SVM and GPR model performances are better than neutral net
Model.The Gaussian process regression model of improved particle cluster algorithm optimization meets certain engineering precision need closer to actual value
Ask.Forecast model quantitative assessing index result as shown in table 2, never on the same day predict the outcome as can be seen that PSO-GPR it is relative
CG-GPR model prediction accuracies have different degrees of raising, demonstrate the validity for improving particle cluster algorithm.
The load prediction results of table 2 compare
In summary, the present invention is had following excellent based on the short-term load forecasting method that variables choice and Gaussian process are returned
Gesture:Optimal variables collection is chosen using random forests algorithm and based on sequence sweep forward strategy, it is to avoid artificial selection input becomes
The deficiency of amount, improves model prediction accuracy;Meanwhile, using improvement particle cluster algorithm optimization gauss process Parameters in Regression Model,
Traditional conjugate gradient method is avoided easily to be absorbed in locally optimal solution shortcoming, the Gaussian process regression model after optimization enhances predictability
Can, improve load prediction precision.Operation plan and ensure that power network safety operation has a few days ago for power system arrangement
Certain reference value.
Claims (7)
1. a kind of short-term load forecasting method returned based on variables choice and Gaussian process, it is characterised in that:Including following step
Suddenly:
(1) master data needed for Load Prediction In Power Systems is obtained:It is historical load data, temperature and humidity meteorological data, pre-
Survey date day categorical data;
(2) carry out bad data rejecting, supplement and normalization to sample data to pre-process, by sample data change of scale to interval
[0,1] in;
(3) candidate's input variable is angularly chosen from historical load, temperature and humidity, prediction day date type, by random gloomy
Woods algorithm calculates each variable importance and scores and sort;
(4) it is empty set to set initial optimal variables collection, by adding prominence score highest input variable one by one and utilizing
Gaussian process regression model calculates its predictablity rate, and optimal variables collection is can determine that by predicated error minimum;
(5) the optimal variables collection training Gaussian process regression model based on determination, and optimize mould using particle cluster algorithm is improved
Shape parameter;
(6) estimated performance of model is verified in test set.
2. the short-term load forecasting method as claimed in claim 1 returned based on variables choice and Gaussian process, its feature is existed
In:Candidate's input variable includes historical load data such as in step (3):Predict day previous daily load, preceding two daily load, first three day
Load, the first seven daily load, the first eight daily load, preceding 14 daily load, the same period last year load in the same time;Temperature data includes:Prediction
Degree/day, previous degree/day, preceding two degree/day, first three degree/day, the first seven degree/day, the first eight degree/day, preceding 14 degree/day, go
Year same period temperature in the same time;Humidity data includes:Predict day humidity, it is proxima luce (prox. luc) humidity, preceding humidity on the two, first three day humidity, preceding
The humidity in the same time of humidity, the first eight day humidity, preceding humidity, the same period last year on the 14th on the seven;Candidate's input variable is simultaneously including prediction
Day date type.
3. the short-term load forecasting method as claimed in claim 1 returned based on variables choice and Gaussian process, its feature is existed
In:Each input variable prominence score is provided using random forests algorithm in step (3), methods described detailed process is:
3.1 assume that (X, y) containing n observation, input variable dimension is M to Power system load data training set, utilizes bootstrap side
Method has that puts back to repeat b sub- sample sets of extraction from original training data set, and each subset sample number is n, thus can structure
Build b regression tree;Non-selected observation constitutes the outer data of bag;
3.2 construction biDuring regression tree, fixed qty is randomly selected for m from M dimension input variablestry(desirable mtry=M/3)
Input variable collection as this regression tree feature space, fission process using variance minimum chosen as branch's Criterion of goodness
Divide variable, i.e.,
In formula, n is number of training, XkFor variable k sample value,For variable k sample average, I is the division of this suboptimum
Variable;
3.3 by the estimated performance of data prediction accuracy estimating model outside bag, i.e.,
In formula, nOOBFor data sample quantity, y outside bagiFor true load value,Predicted the outcome for Random Forest model;
3.4 are tested b regression tree using data outside bag, are obtained mean square sesidual and are respectively:MSE1,MSE2,L,MSEb;Become
Measure XkData are concentrated use in randomized method displacement outside b bag, form the outer test set of new bag;Utilize data pair outside new bag
B regression tree re-starts test, constitutes the Square Error matrix after random permutation and is
3.5 k-th of input variable prominence score are:By MSE1,MSE2,L,MSEbPhase corresponding with Square Error matrix row k
Subtract and take b regression tree average value, last divided by b regression tree standard error SE, obtain variable XkMean square sesidual averagely reduce
Amount.Thus obtaining each input variable prominence score formula is
4. the short-term load forecasting method as claimed in claim 1 returned based on variables choice and Gaussian process, its feature is existed
In:Gaussian process forecast of regression model result is in step (4):
Wherein, n represents training sample point quantity, and X is training set input vector, and y ∈ R are the output scalar that training set corresponds to X;
X*Inputted for test set,Correspond to X for test set*Output scalar;For Gaussian Profile variance;InTo tie up unit matrix,
K (X, X)=KnRepresent n × n nuclear matrix, its element Kij=k (xi,xj);K(X,X*)=K (X*,X)TFor test data X*With instruction
Practice the covariance matrix between the input X of collection;
Choose square index covariance function and calculate nuclear matrix element, its formula is
Wherein, M=diag (l-2), l is variance measure;For kernel function signal variance,For noise variance, orderθ is the vector for including all hyper parameters, δijFor Kronecker delta functions, as i=j, function δij
=1.
5. the short-term load forecasting method as claimed in claim 1 returned based on variables choice and Gaussian process, its feature is existed
In:Using sequence sweep forward strategy and by the optimal variables collection of predicated error minimum determination in step (4), its predicated error is commented
Valency index is:
In formula:N is future position number, yiPoint load actual value is predicted for i-th,For i-th of future position model predication value.
6. the short-term load forecasting method as claimed in claim 1 returned based on variables choice and Gaussian process, its feature is existed
In:The improvement particle cluster algorithm optimization gauss process for adjusting inertia weight and accelerated factor using dynamic linear in step (5) is returned
Return model parameter, inertia weight is with accelerated factor adjustment formula:
W=wmax-(wmax-wmin)k/T
C1=Cmax-(Cmax-Cmin)k/T
C2=Cmin+(Cmax-Cmin)k/T
In formula:wmax、wminRespectively initial inertia weight maximum and minimum value;Cmax、CminRespectively the initial acceleration factor is most
Big value, minimum value, w, C1、C2The respectively inertia weight of kth time iteration, accelerated factor value;T is iterations.
7. the short-term load forecasting method as claimed in claim 1 returned based on variables choice and Gaussian process, its feature is existed
In:When step (5) is using PSO Algorithm parameter is improved, its fitness value is training sample log-likelihood function
Wherein,
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