Predicting Short-Term Electricity Demand by Combining the Advantages of ARMA and XGBoost in ...

19 Pages·2017·2.41 MB·English

Hindawi
Wireless Communications and Mobile Computing
Volume 2018, Article ID 5018053, 18 pages
https://doi.org/10.1155/2018/5018053
Research Article
Predicting Short-Term Electricity Demand by
Combining the Advantages of ARMA and XGBoost in
Fog Computing Environment
ChuanbinLi ,XiaosenZheng ,ZikunYang ,andLiKuang
SchoolofSoftware,CentralSouthUniversity,Changsha410075,China
CorrespondenceshouldbeaddressedtoLiKuang;[email protected]
Received 26 January 2018; Accepted 25 March 2018; Published 6 May 2018
AcademicEditor:XuyunZhang
Copyright©2018ChuanbinLietal.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
With the rapid development of IoT, the disadvantages of Cloud framework have been exposed, such as high latency, network
congestion,andlowreliability.Therefore,theFogComputingframeworkhasemerged,withanextendedFogLayerbetweenthe
Cloudandterminals.Inordertoaddressthereal-timepredictiononelectricitydemand,weproposeanapproachbasedonXGBoost
andARMAinFogComputingenvironment.BytakingtheadvantagesofFogComputingframework,wefirstproposeaprototype-
basedclusteringalgorithmtodivideenterpriseusersintoseveralcategoriesbasedontheirtotalelectricityconsumption;wethen
proposeamodelselectionapproachbyanalyzingusers’historicalrecordsofelectricityconsumptionandidentifyingthemost
importantfeatures.Generallyspeaking,ifthehistoricalrecordspassthetestofstationarityandwhitenoise,ARMAisusedto
modeltheuser’selectricityconsumptionintimesequence;otherwise,ifthehistoricalrecordsdonotpassthetest,andsomediscrete
featuresarethemostimportant,suchasweatherandwhetheritisweekend,XGBoostwillbeused.Theexperimentresultsshow
thatourproposedapproachbycombiningtheadvantageofARMAandXGBoostismoreaccuratethantheclassicalmodels.
1.Introduction aims at providing enterprises with safe, reliable, and high-
quality electric power, has become an indispensable part in
Inrecentyears,withtheriseofCloudComputing[1,2],more theconstructionofnationaleconomyandpeople’slife,soit
andmorecomputingandstorageprocessingaretakingplace is affected at first. Under the current technical conditions,
inCloud,andthevastemploymentofCloudinevitablyleads it is still not possible to achieve large-scale storage of elec-
tohighlatency,networkcongestion,andlowreliability.Atthe tric energy; therefore, it is required to generate electricity
sametime,withthewideadoptionofIoTservices,avariety accordingtothesystemloadatanytime,orelsethequality
ofhouseholdappliancesandsensorswillbeconnectedtothe ofelectricitysupplyandusagemaybeaffected,andeventhe
Internetandproducealargeamountofdata[3–5].Ithasbeen safetyandstabilityofthesystemmaybeendangered.Ithas
estimatedthatthenumberofdevicesconnectedbyIoTwill become an urgent and important research issue to improve
reach 50 billion to 100 billion by 2020, which means there the accuracy of electricity demand prediction in Fog Com-
will be more and more data without the control of existing putingframework.
techniquesondataprocessingandanalysis,privacyleaksmay Inthefieldofelectricitydemandprediction,scholarshave
becaused,andthequalityofservicewillbedecreased[6,7]. carried out extensive research. In the early stage, scholars
In this regard, the rapid development of IoT has deepened basically followed the technology in the field of economic
the dilemma of Cloud Computing. The emergence of Fog prediction,focusingontheruleoftheloadsequenceinthe
Computingmakesupfortheseshortcomingsbutalsobrings formoftimeseriesitself.Thepredictionmodelisestablished
newopportunitiesandchallengestothetransformationand byanalyzingthequalitativerelationshipbetweenthehistori-
upgradingoftraditionalindustries.Electricitysystem,which calloadandrelatedfactors,andtheparametersareestimated
2 WirelessCommunicationsandMobileComputing
accordingtohistoricaldata.However,timeseriesbasedap- [14–16], Neural Network [17–20], Bayes [21], Fuzzy Theory
proachrequireshistoricaldatawithhighaccuracy,insensitive [20,22],andWaveletEchoStateNetwork[23].Eachkindof
tothefactorssuchasweatherandholidays.Actually,itisvery method has its own applicable scenario, and no model can
difficulttoexpressthenonlinearrelationbetweentheinput achievedesiredsatisfyingresultalone.
andoutputbyusingaclearmathematicalequationsincethe Inordertoimprovetheaccuracyofprediction,thecur-
electricitydataarenonlinear,time-varying,anduncertain.In rent research works mainly focus on three directions. The
ordertofurtherimprovetheaccuracyofelectricitydemand firstoneistoexploretheoptimizationofsinglemodel.Zhu
prediction,artificialintelligencemethodshavebeenapplied et al. [24] propose to predict daily load roughly by ARMA
sincethe1990s,suchasneuralnetwork,expertsystem,and first,thenobtainthedifferencesequencesthatarenoncyclical
waveletanalysis.However,theexistingmethodsusuallycan andstronglyinfluencedbytheweather,andfinallyproposean
just be applied to a limited scenario and only effective for improvedARIMApredictionmodelwithstrongadaptability
simpleelectricitysystemswithasmallquantityoffactors. toweather.Factorswhichinfluencetheelectricityconsump-
The main deficiencies of existing work include the fol- tion are recognized and the mapping relation between key
lowing:(1)electricitydatasampleshavebeenproventohave factors and electricity consumption are mined [25, 26].
anomalies but few of the existing solutions detect and deal Ghelardonietal.[27]usetheempiricalmodedecomposition
withtheabnormaldata.(2)Whenclassifyingusersandtheir methodtodividethetimeseriesintotwoparts,describingthe
data,thenumberofclustersneedstobespecifiedinadvance, trendandthelocaloscillationofenergyconsumptionvalues,
and the density distribution on electricity consumption is respectively, and then use them to train the support vector
usuallyignoredinclusteringusers.(3)Intheprocessofmod- regressionmodel.Cheetal.[28]usethehumanknowledge
eling, the temporal features of data are not fully excavated, to construct fuzzy membership functions for each similar
andtheinteractionamongthefeaturesisnotfullyconsidered. subgroup and then build an adaptive fuzzy comprehensive
(4) Most of the solutions just adopt a sole model, which model based on self-organizing mapping, support vector
cannotgivefullplaytotheadvantageofeachmodel. machine, and fuzzy reasoning for prediction. An electricity
Inordertoovercometheshortcomingsofexistingsolu- loadmodelisestablishedbasedonimprovedparticleswarm
tions, in this paper, we propose a short-term electrical- optimizationalgorithmandgeneticalgorithm[29,30].
demandpredictionapproachbycombiningtheadvantagesof Theseconddirectionistoimprovetheaccuracyofpre-
XGBoostandARMAinFogComputingframework.Firstly, dictionbyintegratingdifferentmodels.Haqueetal.propose
sensorscollectthereal-timedataofelectricityconsumption, a hybrid intelligent algorithm based on wavelet transform
andthentheFogNodeswouldclassifyenterpriseusersinto and fuzzy adaptive resonance theory [31]. In [32–34], the
differentgroupsaccordingtotheamountofelectricitycon- wavelet decompositionis used to project theload sequence
sumption and perform anomaly and outlier data detection decomposition onto different scales, different models are
and procession for each group. Secondly, a model selection usedtopredictthedifferentcomponents,andfinallythefinal
process would be performed, that is, based on a series of result is obtained by reconstructing the components. Pin-
tests including stationarity, white noise and Pearson corre- doriyaetal.[35]proposeanadaptivewaveletneuralnetwork
lation coefficient of data, as well as the observed electricity (AWNN) for short-term price prediction in the electricity
consumptionrule;wewilldecidewhethertousetimeseries market.PanyandGhoshal[36]proposealocallinearwavelet
model or decision tree based model for the modeling of neural network (LLWNN) model instead of wavelet neural
eachenterprisegroup.Finally,thepredictionvaluesofeach network for the electricity price prediction. Che and Wang
enterprise user are combined to obtain the final result. The [37] propose a hybrid model that combines the unique
accuracy of the proposed approach is verified to be 20% advantagesofSVRandARIMAmodelsinbothnonlinearand
higherthanclassicalmodelsbyexperiments. linearmodeling.
The rest of the paper is organized as follows: Section2 The third direction is to explore composite models for
reviewstherelatedworkonpredictingshort-termelectricity prediction.Theweightedaverageofalltheresultsbyvarious
demand.Section3describestheframeworkoftheproposed algorithmisusuallyused,andtherearetwokindsofwaysto
solution,aswellasthedetailsoftheinvolvedkeytechniques. determinetheweights.Thefirstkindistoimprovethefitting
Section4introducestheexperimentandanalyzestheresults. accuracy of historical electricity consumption by minimiz-
Section5 summarizes our work and provides the future ing the fitting error. The main methods include monotone
researchplan. iterativealgorithm[38],evolutionaryprogramming[39],and
quadraticprogramming[40].Wangetal.[41]proposeusing
2.RelatedWork adaptivepracticalswarmoptimizationalgorithmtooptimize
the weight of the integrated model. The second kind is to
Becauseofthenonlinear,time-varying,anduncertaintychar- determine the weights by evaluating the algorithm’s score.
acteristicsofelectricitydata,itisdifficulttoaccuratelygrasp Elliott and Timmermann [42] introduce the concept of the
the related factors and the rules of electricity consumption lossfunction,quantifythenegativeimpactcausedbydifferent
change. How to effectively improve the accuracy of elec- prediction errors, then take the minimum loss expectation
tricity demand prediction has become a major challenge to as the goal, and perform optimization to get the weights.
researchers[8].Atpresent,themethodsusedforshort-term Yaoetal.[43,44]employanalytichierarchyprocess(AHP)
electricitydemandpredictionmainlyincludetimeseries[9– inmultiobjectivedecisionanalysistogettherelativemerits
11], Regression Analysis [12, 13], Support Vector Regression of each algorithm in fitting accuracy, model adaptability,
WirelessCommunicationsandMobileComputing 3
Table1:Examplesoftheenterpriseelectricityconsumptiondataset. AsanextensionofCloudComputing,theframeworkpre-
processesenterprisedataandmakesreal-timedecisionand
record date user id power consumption
providestemporarystoragetoenhancetheusers’experience.
2015/1/1 1 1135 Inthecurrentelectricitysystems,thenumberofhopsfrom
2015/1/2 1 570 enterpriseterminaltoCloudisgenerally3to4orevenmore,
2015/1/3 1 3418 sothesystemwillhavetofacethenetworkdelaywhenmak-
2015/1/4 1 3968 ing real-time decisions. Figure1 shows the framework of a
smartelectricitysysteminFogComputing.Electricitymeters
collectdataassensors,and,forsomeenterpriseswithmajor
and result reliability, the judgment matrices are obtained, changesofdataandhighreal-timerequirement,wecanmake
andthentheweightsarecombinedbycalculatingthemain real-time decisions in Fog Nodes to meet the need of real-
eigenvectors of each matrix. Petridis et al. study the use of time electrical-demand prediction; otherwise, the data can
probability models to determine the weight of each model bebufferedatFogNodes,compressedtosavenetworkband-
andcombinethevaluesofeachalgorithmtoobtainthefinal width,andthentransmittedtotheCloud.
result [45]. Without enough quantitative theoretical basis,
the weights of such models only reflect the advantages and
3.2.2. Process of Electricity Demand Prediction Approach.
disadvantagesofthealgorithms.
Figure2showstheprocessofelectricitydemandprediction
Insummary,therehavebeenmanyresearchworksonthe
approach based on multimodel fusion algorithm, which
prediction of short-term electricity demand, and exploring
includesfivemainsteps.
compositemodelsforpredictionisthemaintrend.However,
existingmethodsstillhavelimitations.Inthecontextofthe
(1) Data Preprocessing. After data are collected, the missing
rapiddevelopmentofsmartelectricitygrid,inthispaper,we
valueswillbefilledandtheirformwillbeunified.
proposeashort-termelectricitydemandpredictionmethod
basedonXGBoostandARMA.
(2)EnterpriseUsersClustering.Thesizeofelectricitydemand
for each enterprise user is measured by counting the total
3.PredictingShort-TermElectricityDemand
amountofitshistoricalelectricityconsumption.Thenenter-
prisesuserswillbedividedintodifferentgroupsbyclustering
3.1.ProblemDefinition. Givenadataset𝑅 = {𝑟1,𝑟2,𝑟3⋅⋅⋅𝑟𝑛}, themaccordingtotheirsizesofelectricitydemand.
𝑟𝑖 is the 𝑖th electricity consumption record for a certain
enterprise user, and 𝑟𝑖 can expressed as a 3-tuple, that is, (3)ModelSelection.Wethenaimtodetermineanappropriate
𝑟𝑖 = ⟨record date, user id, power consumption⟩, where trainingmodelforeachgroupofenterpriseusers.First,the
record date represents the date time, user id is the ID of
rulesofelectricityconsumptionfordifferentgroupsofenter-
the enterprise user, and power consumption represents the
priseusersareanalyzedforprejudgementofmodelselection.
electricityconsumptionamountoftheenterpriseuseronthat
If the electricity consumption changes with time, showing
day.
a periodical change or an obvious rising/falling trend, we
We use the dataset from Tianchi, which contains the
consider to model the users’ data by XGBoost. If the elec-
historical records of 1454 enterprises in Yangzhong High-
tricityconsumptionshowsanirregularchangeovertimeor
TechIndustrialDevelopmentZoneofJiangshuProvincefrom
fluctuatesaroundacertainconstantandthefluctuationrange
2015-01-01 to 2016-11-30, for the following illustration and
islimited,weconsidertomodeltheusers’databytimeseries
experiments.ExamplesofthedatasetareshowninTable1.
model.
Giventhedataset𝑅andamonthtimeinfuture,weaim
Second,aseriesoftestswouldbeperformedtoverifythe
topredictthetotalamountoftheelectricitydemandonthe
prejudgement and finally determine the selected model for
desiredmonthinthisregiononthebasisofhistoricalrecords.
eachgroupofusers.Featurecorrelationanalysisandfeature
importance scores would be performed before selecting
3.2.FrameworkoftheProposedApproach XGBoost modeling. Stationary and white noise test would
be performed before selecting ARMA modeling. If neither
3.2.1.SmartElectricitySysteminFogComputing. FogCom- XGBoostnorARMAisappropriate,meanmodelwillbeused.
putingframeworkhastheadvantagesoflowlatency,saving
corebandwidth,andhighreliability[46,47].FogNodesare (4) Model Building. After model is selected for a given
located lower in the network topology and thus they have group of users, data cleaning is performed first, including
lessnetworklatencyandmorereactivity.Asanintermediate thedetectionandprocessingofanomaliesandoutliers.For
between Cloud and terminals, Fog Layer can filter and XGBoost modeling, anomalies and outliers will be deleted
aggregate enterprise messages and only send the necessary first, the influence of time factor and temperature on the
messages to Cloud, thus reducing the pressure on the core predictionwillbeconsideredemphatically,Pearsoncorrela-
network. In order to serve enterprises in different regions, tion coefficient will be used to identify redundant features,
thesameserviceswillbedeployedontheFogNodesineach andappropriatefeatureswillbeselectedtobuildthemodel
region.Oncetheservicesinacertainareaareabnormal,the bycombiningthefeatureimportanceoutputtedbypretrain-
requests can be quickly forwarded to other same services ing. For AMRA modeling, anomalies and outliers will be
nearby,whichmakestheframeworkhighlyreliable. modified by average value, and parameters 𝑝 and 𝑞 will be
4 WirelessCommunicationsandMobileComputing
Cloud layer
Core network
Fog layer
User terminal
Figure1:SmartelectricitysysteminFogComputing.
Data
Collecting Processing Unifying Data
Preprocessing
Data Missing values Form
Enterprise Users Counting Size of Clustering Users based on
Clustering Electricity Demand Prototype-based K-means
Model Model Pre-judgement Model Determination based
Selection based on Observation on a Series of Tests
Model
Building XGBoost ARMA Mean
Predicting
Predicting Values for Summing up to Get Total
Electricity
Different User Groups Electricity Demand
Demand
Figure2:Processofelectricitydemandpredictionapproach.
optimized based on the minimum amount of information collect external weather data from http://lishi.tianqi.com.
principleofBIC. SamplesareshowninTable2.
(5)PredictingElectricityDemand.Aftermodelingfordifferent (2) Processing Missing Value. We find that there are some
enterprisegroups,thepredictionvaluesofeachgroupwillbe missingvaluesinTianchidataset,sowethenfillthemissing
summed up to get the final daily electricity demand in the valueswiththemeanvalueofthethreedaysbeforeandafter
desiredmonthofthisregion. thedatewithmissingvalue.Thedetailedcalculationisshown
asfollows:
3.3.KeyTechniques. Inthissection,wewillelaborateonthe
(𝑐 +𝑐 +𝑐 +𝑐 +1,𝑐 ,𝑐 )
detailed key techniques in the five steps of the electricity 𝑐 = 𝑖,𝑗−3 𝑖,𝑗−2 𝑖,𝑗−1 𝑖,𝑗 𝑖,𝑗+2 𝑖,𝑗+3 , (1)
demandpredictionapproach. 𝑖𝑗 6
inwhich𝑐𝑖𝑗 representsuser𝑖’smissingrecordonthe𝑗thday
3.3.1.DataPreprocessing oftheyear.
(1)CollectingExternalWeatherData.Takingintoaccountthe (3)UnifyingDataForm.Theelectricityconsumptionrecords
impact of temperature on electricity consumption, we first are reorganized to facilitate the follow processing. Each
WirelessCommunicationsandMobileComputing 5
Table2:Samplesofweatherinformation.
Record date Highesttemperature Lowesttemperature Conditions Winddirection Windforce
2016/10/12 21 16 Overcast West breezy
2016/10/13 20 16 PartlyCloudy Calm lightbreeze
2016/10/14 19 17 MostlyCloudy West lightbreeze
2016/10/15 20 16 Showers East breezy
2016/10/16 23 17 Overcast NorthWest lightbreeze
column represents records of an enterprise user, and there classifiedtothesecondcategory.TheuserswithID90,129,
are totally 1454 users. Each row represents the records on 1262,1307,and1310,whoserelativedistancesarebetween100
a certain day, and the dates are sorted in ascending order. to20,shouldbethethirdcategory.Andtheremaining1447
Eachgridrepresentstheelectricityconsumptionofaspecific enterpriseusers,whoserelativedistancesarebelow20,should
user on a certain day, which can be expressed as 𝑟𝑖𝑗 = bethefourthcategory.Sowesetk=4whenusingK-means
{Record date𝑗,Power𝑖,𝑐𝑖𝑗}.Theunifieddatasheetisshownas algorithm.Andthefinalresultofusersclusteringisshownas
Table3. Table4.
3.3.2. Clustering Users by Prototype-Based K-Means Algo-
3.3.3. Model Selection. Model selection is the basis of next
rithm. Clustering analysis can find locally strongly related
stepanditisespeciallyimportant.Figure4showstheprocess
object groups. Outlier detection can detect objects that are
and rules of model selection, which mainly includes four
significantly different from most objects by detecting the
parts.
discreteness of the data. Based on the characteristics of the
two techniques, in this paper, we use a prototype-based
(1) Data Preparing. The data now mainly include the enter-
clusteringmethodtodetectthedegreeofdatadiscreteness,
priseuserID,itsgroupID,thehistoryelectricityconsump-
soastolearnthedistributionofthedataandthendetermine
tion,andtheweatherdatafrom2015/1/1to2016/11/30.
the range of 𝑘 first, and next use K-means algorithm to
clusterenterpriseusersinordertoachieveenterprisegroups (2)ModelPrejudgementBasedon
division. Periodicity/TrendandNonlinear/WeakStationaryAnalyzing
Theprincipleoftheprototype-basedclusteringmethodis
toclusteralltheobjectsfirstandthenevaluatethedegreethat (2a) Periodicity/Trend Analyzing. Periodicity analyzing is to
theobjectsbelongtotheclustersaccordingtothedistance.In findoutwhetherelectricityconsumptionofauserwillchange
traditionalmethod,thedistancebetweentheobjectandthe periodically with time. If a user’s electricity consumption
cluster center is used to measure the degree that the object showsregularfluctuations,theincreasingspeedisthesimilar
belongstothecluster.Inthispaper,weconsiderthedensity at both sides of the wave peak, and the appearance of peak
of data distribution and adopts the relative distance. Based isstronglyrelatedtotimeperiod,thatis,Power(𝑛)=Power
onthisidea,wedesigntheclusteringalgorithmforenterprise (𝑛 + 𝑇), where 𝑇 is the time span; then we can make a
groupsdivisionasshowninAlgorithm1. prejudgement that XGBoost model would be appropriate
WewilltaketheTianchidatasetasanexampletoillustrate withthischaracter.
the process of prototype-based K-means clustering algo- Trend analyzing is to find out whether change pattern
rithm: of electricity consumption will show some trend. If a user’s
First,wecalculatethehistoricalelectricityconsumption electricityconsumptionshowsatendencytoriseorfall,orthe
ofeachenterprisefrom01/01/2015to10/31/2016,andcluster appearanceofpeakchangeswithtimeandshowsarelationof
allthesamplesbyusingprototype-basedalgorithm.Wetake positiveandnegativecorrelation,thenwecanalsoconsider
therelativedistancetomeasurethediscretedegreeofsamples usingXGBoostmodelforthischaracter.
andchoosethethreshold𝜆as20,sothesamplewithrelative
distance greater than 20 is deemed as an outlier. Figure3 (2b)Nonlinear/WeakStationaryAnalyzing.Iftheuser’selec-
showsthediscretepointswithrelativedistances. tricityconsumptionpresentsirregularchangeormutationor
EachofthepointsinFigure3ismarkedwithapair,which noobviouschange,itshowsthatthesequenceofelectricity
indicates the enterprise ID and its relative distance to the consumptionisnonlinear.Iftheuser’selectricityconsump-
clustercenter.Thereare7pointswithhigherdispersionthat tion shows a fluctuation around a certain constant and the
are 1416, 175, 174, 90, 129, 1262, 1307, and 1310 from high to fluctuationisapproximatelyinthesamerange,itcanbeseen
low.AccordingtoFigure3,thedataaregenerallydistributing thatthemeanandvarianceofthedataareallconstant,which
infourdistancesegments.User1416islocatedatthetopof indicates that the data has no obvious trend. If the mean
thefigure,whoserelativedistanceisgreaterthan400,much value has nothing to do with the change of time, and the
higherthantheotherpoints,anditshouldbeclassifiedtothe influence among the sequence variables is almost the same
firstcategory.Atthemiddleofthefigure,175and174,whose afterdelaying𝑘periods,itreflectstheweakstationaryofdata.
relativedistancesarebetweenabout150and200,shouldbe Sowecanmakeaprejudgementthattimeseriesmodelinglike
6 WirelessCommunicationsandMobileComputing
Table3:Unifieddatasheet.
Record date Power1 Power2 Power3 Power4 Power5 Poweri Power1454
2015/1/1 1135 24 385 206 156 ⋅⋅⋅ 976
2015/1/2 570 22 475 5134 368 ⋅⋅⋅ 520
2015/1/3 3418 18 526 6784 359 ⋅⋅⋅ 536
2015/1/4 3968 119 1 6475 467 ⋅⋅⋅ 488
2015/1/5 3986 108 535 6592 433 ⋅⋅⋅ 406
2015/1/6 4082 109 663 6742 452 ⋅⋅⋅ 554
2015/1/7 4172 86 606 6963 467 ⋅⋅⋅ 803
2015/1/8 4022 106 735 6301 495 ⋅⋅⋅ 975
2015/1/9 4025 103 698 6693 542 ⋅⋅⋅ 796
Input:HistoricalelectricityconsumptionrecordsR
Output:thegroupdivisionofenterpriseusersClusterSet(Power)
∗ i ∗
(1)/ Calculatethehistoricaltotalelectricityconsumptionofeachenterprise /
INPUT:𝑅={Record date𝑗,user𝑖,𝑐𝑖𝑗}
FOR𝑖=1Tolength(user)
i
DO
SumPower𝑖=0
FOR𝑗=1Tolength(Record date)
j
DO
SumPoweri=SumPoweri+𝑐𝑖𝑗;
END
END
OUTPUT:{SumPower𝑖}
∗
(2)/ Selecttheclusteringalgorithm(K-means)toclusteralltheobjectsandthenchoosek=
∗
1toclusterallthesamplesintoaclusterandfindthecentroidofthecluster /
INPUT:{SumPower𝑖}
DO
Select𝐾=1
ClusterCenter=Kmeans(SumPower𝑖)
END
OUTPUT:ClusterCenter
∗ ∗
(3)/ Calculatetherelativedistance /
INPUT:ClusterCenter,{SumPower𝑖}
FOR𝑖=1Tolength(user𝑖)
DO
AbsoluteDistance𝑖=SumPower𝑖−ClusterCenter
MedianDistance𝑖=median(AbsoluteDistance𝑖)
RelativeDistance𝑖=AbsoluteDistance𝑖/MedianDistance𝑖
END
OUTPUT:{RelativeDistance𝑖}
(4)Makediscretepointrelativedistanceerrorfigureandroughlydeterminetherangeofk
accordtotherelativedistance
(5)/∗Use𝐾-meansalgorithmtodoclusteringforenterprises,andgetthegroupsofenterprises
∗
accordingtotheresultofclustering /
INPUT:{⟨user𝑖,SumPower𝑖⟩},k
DO
Select𝐾=𝑘
ClusterSet(user𝑖)=Kmeans(user𝑖)
END
OUTPUT:ClusterSet(user𝑖)
Algorithm1:Prototype-basedK-meansclusteringalgorithm
WirelessCommunicationsandMobileComputing 7
Table4:Clusteringresult.
ClusterID EnterpriseuserID Semanticmeaning
400<relativedistance,
1 1416
largeenterprise
150<relativedistance<200,
2 174,175
Secondlargeenterprise
20<relativedistance<100,
3 90,129,1262,1307,1310
mediumenterprise
0<relativedistance<20,
4 Otherenterprisesexcept1416,174,175,90,129,1262,1307,1310
smallenterprise
(1416, 424.86) eachfeatureandthetargetvalueandstudyingtheinfluence
400 of each feature on the change of the target. By outputting
the importance of all features through the pretraining of
XGBoost model, if the factors which cannot be character-
e 300 izedintimeseries,suchasweather,vacation,andworkday/
c
an nonworkday, have high scores, it can be determined to use
dist XGBoostmodel.
ve 200 (175, 194.30)
Relati (174, 157.40) dataIfabreotnhottessutsithabavleefloorwXsGcoBroeos,stitminoddiecla,teasndthwatetchaenutsuerrn’s
100 totestwhethertheyaresuitableforthetimeseries(ARMA)
model.
(90, 60.59) (1262, 35.77)
(129, 35.33) ((11331007,, 2244..5533))
0 (4)ModelVerificationforARMA.IfARMAisprejudgedasan
0 200 400 600 800 1000 1200 1400 appropriatechoiceforauser,orifXGBoostisnotsuitable,we
thenperformaseriesoftestsincludingPearsoncorrelation
ID
coefficient, stationarity testing, and white noise testing to
Figure3:Discretepointswithrelativedistances.
verifywhetherARMAissuitable.
(4a)CorrelationAnalyzing.Sameasin(3b),wetestthecorre-
lation between features and the target value by using Pear-
ARMAwouldbeappropriateforsuchkindofdatawithweak
son’s correlation coefficient. If the correlation between the
stationary.
targetanddiscretefeaturesislow,wecanconsidertousethe
timeseries(ARMA)modelpreliminarily.
(3)ModelVerificationforXGBoost.IfXGBoostisprejudged
as an appropriate choice for a user, a series of tests includ-
(4b) Stationarity Testing. Stationarity is the prerequisite for
ing Pearson correlation coefficient and feature importance
timeseriesmodeling.Ifthedataisstationary,thefittingcurve
analyzingwouldbeperformedbeforefinallydecidingtouse
obtained through the sample time series can still inertially
XGBoost.
continue for a period of time in the future. If the data
is not stationary, it indicates that the shape of the sample
(3a)FeatureGenerating.Featureistheinformationextracted
fittingcurvedoesnothavethecharacteristicof“inertia”con-
fromthedatathatisusefulinprediction.Featureextraction
tinuation;thatis,thecurvefittingbasedonthesampletime
is mainly based on the existing background knowledge, so
seriestobeobtainedinthefuturewillbedifferentfromthe
thatthefeaturecanplayabetterroleinthemachinelearning
currentsamplefittingcurve.Totestthestationarityofdata,
algorithm. Based on thorough analysis of the features, we
weusetheunitrootforinspection.Iftheelectricityconsump-
mainly extract the time and weather features as the input
tionsequencedatahasunitroot,thedataisstationary.
features.
(4c)WhiteNoiseTesting.Whitenoisesequenceisastationary
(3b)CorrelationAnalyzing.WethenusePearsoncorrelation
randomsequencewithoutanyinformation.Ifthesequenceis
coefficienttesttoanalyzethecorrelationbetweenthefeatures
whitenoise,itindicatesthatthereisnorelationshipbetween
and the prediction value. We use the results of feature
thevaluesofsequence,anditisapurelyrandomsequence.
generationandelectricityconsumptiondatafortesting.Ifthe Theautocorrelationcoefficientisequaltozero,thatis,𝜆(𝑘)=
correlationbetweenthepredictiontargetandsomediscrete 0, 𝑘 ≠ 0. If the white noise test is passed, it shows that the
features,suchasweather,holidays,workday/nonworkday,is
sequenceisanon-whitenoisesequence.
strong,itisbettertouseXGBoostformodeling.
Ifbothstationarityandwhitenoisetestingarepassed,we
(3c)FeatureImportanceAnalyzing.Featureimportanceanal- candeterminethatARMAmodelissuitableformodelingthe
ysisreferstoanalyzingtheimportancerelationshipbetween user’sdata.
8 WirelessCommunicationsandMobileComputing
(1) Data preparing
user (2a) Periodicity/Trend analyzing (2b) Nonlinear/Weak stationary
category analyzing
∘C wedaatthaer −−00000.....1100005005 20040060080010001200 876543210000000006008001000120014001600
Periodicity Tendency Weak stationary Nonlinear
electricity
demand
Periodicity/Tendency Nonlinear/weak stationary
(3a) Feature generating
Day Mon YearDoy
1 1 1 4
2 1 1 5
(4a) Correlation analyzing (4b) Stationary testing
(3b) Correlation analyzing (3c) Feaatnuarely izminpgortance Lowfe faetautruer ree ilmevpaonrctea nsccoer/elow SSS123SSS123 000３...１000３974...１26819742681／000／３...000787１３...582787１15821＃000＃３...000788１３...852788１18521 TTn1::{{！！＄＄·＆＆·,,·......,,００ＬＬＩＩ＜＜}}
SSS132SSS123 000３...１000３974...１26819742681／000／３...000787１３...582787１15821＃000＃３...000788１３...852788１18521 Feature importrance score111420864200000000 f2 f0 f7Featurfe9 Impof1r0tancesf1 f6 f3 Ffaaiilleedd wcohrirtee lnatoioisne tteesstt/ ARMA model (4c) White noise testing
110
110086 T1:{！＝＝ＩＬ,...,０ＬＩ＜}
XGBoost model (5) Mean value model 110042 ···
Tree 1 Tree 2 10908 Tn:{３２n1,...,０ＬＩ＜}
YIs mYale?AgNe < 15N YUse cdoamilyputerN 96969800020406081012
+2 +0.1 −1 +0.9 −0.9
f()=2+0.9=2.9f()=−1+0.9=−0.1
Mean value model
XGBoost model
ARMA model
Figure4:Frameworkofmodelselection.
(5) Mean Value Model. If neither XGBoost nor ARMA is andnonlinear.SoitcanbeprejudgedtoemployARMAfor
suitableformodeling,wethenusethemeanmodelasafinal modeling.
choice.Themeanmodeltakesthemeanofthehistoricalelec- Figure6showsthedataofasmallenterprise.
tricityconsumptiondataasthepredictionvalue. From Figure6, it can be seen that the curve presents a
We then show the process of model selection by two cyclicalfluctuationwiththechangeoftime.Throughanalysis,
examples: one is a small enterprise and another one is the wecanfindthatcurvepresentsa“W”shape,itissymmetric
enterprise with ID 1307. Figure5 shows the daily electricity on the 1/1/2016, and every small peak fluctuates in the unit
consumptionamountofthe1307thenterprisefrom1/1/2015 of week. The data wave within each week is like a convex
to10/31/2016,inwhichthe𝑥-axisisrepresentedasthe𝑥thday line,showingahighmiddleandlowsides.Itcanbejudged
intheperiod. thattheelectricityconsumptionofsmallenterprisesisgreatly
From Figure5, we can find that the curve of the 1307th influencedbytheyearandweek.Soitcanbeprejudgedtouse
enterprise fluctuates on the mean value line from 2015 to XGBoostformodeling.
2016 and the fluctuation amplitudes are almost the same, From the analysis above, we can find out that most
which is consistent with characteristics of weak stationarity enterprisesarehighlycorrelatedwithtimefeatures,sowecan
WirelessCommunicationsandMobileComputing 9
300000 Line charts of 1307th enterprise FromTable6,aftersmoothprocessing,wecanfindthat
the𝑝valueoftheunitrootteststatistic(0.0089)oftheseries
is significantly less than 0.01, so the original hypothesis is
250000
strictly rejected, which judges that the series is a stationary
sequence.The𝑝valueofwhitenoisetestissignificantlyless
200000
Mean value than0.01,sowestrictlyrejecttheoriginalhypothesis,which
wer 150000 judges that the logarithmic processed series is a stationary
o non-whitenoisesequence.Combinedwiththeprejudgement
P
andtheresultofthethreetests,wecandeterminetochoose
100000
ARMAformodelingthedataofthe1307thenterprise.
FromFigure8,wecanfindthatthescoresoftimefeatures
50000
for the small enterprise are relatively high, so it can be in-
ferredthattheelectricityconsumptioncharacteristicsofsmall
0
enterprises are highly correlated with the time features. In
0 100 200 300 400 500 600
particular,thefeature“holidays”hasthestrongestcorrelation,
Daydistance
whiletimeseriesmodelcannotmakefulluseoftemperature
Figure5:Dailyelectricityconsumptionamountofthe1307thenter- andholidayfeatures.Sotimeseriesmodelingisnotsuitable
prise. forsmallenterprises.
Wethencalculatefeatureimportancescoresforthesmall
enterprisebypretraininginXGBoost,andtheresultisshown
inFigure9.
2500000
Aftertraining,theXGBoostsortstheimportanceoffea-
turesfromhightolowandtheresultisdoy,daydis,dow,maxt,
2000000
mint,dom,holiday,andwoy(f2,f7,f0,f9,f10,f1,f6,andf3).
Wecanfindoutthatsmallenterprisesareinfluencedbydoy,
1500000 dow,daydis,maxt,andmintgreatly,whichisconsistentwith
wer previousanalysis.
o
P1000000 Combining the prejudgement with the test of Pearson
correlationcoefficientandfeatureimportancescores,wecan
500000 determinethatXGBoostmodelingismoresuitableforsmall
enterprises.
0
0 100 200 300 400 500 600 3.3.4. Abnormal Data Processing. Data quality is crucial for
theperformanceofmodels.Alargenumberofabnormaldata
Daydistance
intheoriginaldatamayleadtothedeviationoftheresult,so
Figure6:Dailyelectricityconsumptionamountofasmallenter- itisnecessarytocleanthedata.Missingvalueprocessinghas
prise. beendoneinthedatapreprocessing,andthen,inthispart,
wemainlyperformthedetectionandprocessingofabnormal
data.
extract temporal features [48] as attributes for feature con- Inordertodetectabnormaldata,outlierdetectionisusu-
struction.Sahayetal.[49]introducedtheinfluenceoftem- allyusedtofindoutthevalueswhichobviouslydeviatefrom
peraturetoelectricityconsumption,sowealsoconsiderthe mostofthesamples.Forsomeenterprises,weusepretraining
effectoftemperature.ThenweusePearsoncorrelationcoeffi- modelingtomarkthesuddenpointswhichdeviatetoomuch
cienttotestthecorrelationbetweenelectricityconsumption from the fitted curve as the outlier. Prototype-based clus-
andfeaturesforenterprisesfromeachgroup. tering outlier detection method is used to detect the out-
Themainfactorswhichmaycausechangesinelectricity liers which are deviating from the centroid obviously. This
consumptionarespecificallyshowninTable5. outlierdetectionalgorithmalsoadoptstherelativedistance
Figure7 is the Pearson correlation coefficient test result whichissimilartoAlgorithm1.Andthereisalittledifference;
of1307thenterprise. that is, the outlier detection algorithm based on prototype
Thecorrelationcoefficientmatrixisasymmetricmatrix. clusteringfilterstheoutliersbyusingtheappropriatethresh-
The correlation between the feature and the target can be oldvalue𝑎inthe4thstepandoutputsthedetectedoutliers.
regarded as the importance of the feature, which is more Figure10showstheoriginaldailyelectricityconsumption
important if it is closer to 1 or−1. From Figure7, we can amountofthe175thenterprise.
find that the scores of time features for the 1307th enter- ItcanbeseenfromFigure10thattheelectricityconsump-
prisearerelativelylow,soitcanbeinferredthatitselectricity tionofthe175thenterprisehasalargedifferencebetweenthe
consumption characteristics are irrelevant to the time fea- first year and the second year, so segment detection will be
tures.Nextweperformstationaritytestandwhitenoisetest used.Wetakeyearasaunittocarryoutsegmentdetection.
onthedataofthe1307thenterprise. Figure11 shows the results of outlier detection based on
Table6showsthetestresultsofthe1307thenterprise. prototype-basedclustering.
10 WirelessCommunicationsandMobileComputing
target 1 0.0096 0.12 0.017 0.012 0.0092 0.0093 −0.24 −0.045 −0.05 0.2 0.19 −0.0011
0.8
f0 0.0096 1 0.004 −0.007 −0.011 −0.0074 0.79 0.098 −0.0013−0.0015 0.0066 0.0031 0.0013
f1 0.12 0.004 1 0.099 0.072 0.01 0.0069 −0.24 0.052 0.0071 0.012 0.032 0.012
f2 0.017 −0.007 0.099 1 0.97 1 −0.0041 −0.07 0.37 0.37 0.39 0.46 0.96
0.4
f3 0.012 −0.011 0.072 0.97 1 0.97 −0.006 −0.019 0.34 0.34 0.37 0.44 0.94
f4 0.0092 −0.0074 0.01 1 0.97 1 −0.0047 −0.05 0.36 0.36 0.4 0.46 0.97
f5 0.0093 0.79 0.0069 −0.0041 −0.006 −0.0047 1 0.098 0.0016 0.0013 −0.0048−0.0024 0.002 0.0
f6 −0.24 0.098 −0.24 −0.07 −0.019 −0.05 0.098 1 −0.014 −0.0035 −0.03 −0.021 −0.032
f7 −0.045 −0.0013 0.052 0.37 0.34 0.36 0.0016 −0.014 1 1 0.29 0.33 0.36
−0.4
f8 −0.05 −0.0015 0.0071 0.37 0.34 0.36 0.0013 −0.0035 1 1 0.3 0.34 0.36
f9 0.2 0.0066 0.012 0.39 0.37 0.4 −0.0048 −0.03 0.29 0.3 1 0.95 0.39
f10 0.19 0.0031 0.032 0.46 0.44 0.46 −0.0024 −0.021 0.33 0.34 0.95 1 0.45 −0.8
f11 −0.0011 0.0013 0.012 0.96 0.94 0.97 0.002 −0.032 0.36 0.36 0.39 0.45 1
target f0 f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11
Figure7:Pearsoncorrelationcoefficienttestresultofthe1307thenterprise.
target 1 −0.26 0.13 0.2 0.18 0.19 −0.32 −0.56 0.22 0.22 0.17 0.18 0.18
0.8
f0 −0.26 1 0.004 −0.007 −0.011 −0.0074 0.79 0.098 −0.0013−0.0015 0.0066 0.0031 0.0013
f1 0.13 0.004 1 0.099 0.072 0.01 0.0069 −0.24 0.052 0.0071 0.012 0.032 0.012
f2 0.2 −0.007 0.099 1 0.97 1 −0.0041 −0.07 0.37 0.37 0.39 0.46 0.96
0.4
f3 0.18 −0.011 0.072 0.97 1 0.97 −0.006 −0.019 0.34 0.34 0.37 0.44 0.94
f4 0.19 −0.0074 0.01 1 0.97 1 −0.0047 −0.05 0.36 0.36 0.4 0.46 0.97
f5 −0.32 0.79 0.0069 −0.0041 −0.006 −0.0047 1 0.098 0.0016 0.0013 −0.0048−0.0024 0.002 0.0
f6 −0.56 0.098 −0.24 −0.07 −0.019 −0.05 0.098 1 −0.014 −0.0035 −0.03 −0.021 −0.032
f7 0.22 −0.0013 0.052 0.37 0.34 0.36 0.0016 −0.014 1 1 0.29 0.33 0.36
−0.4
f8 0.22 −0.0015 0.0071 0.37 0.34 0.36 0.0013 −0.0035 1 1 0.3 0.34 0.36
f9 0.17 0.0066 0.012 0.39 0.37 0.4 −0.0048 −0.03 0.29 0.3 1 0.95 0.39
f10 0.18 0.0031 0.032 0.46 0.44 0.46 −0.0024 −0.021 0.33 0.34 0.95 1 0.45 −0.8
f11 0.18 0.0013 0.012 0.96 0.94 0.97 0.002 −0.032 0.36 0.36 0.39 0.45 1
target f0 f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11
Figure8:Pearsoncorrelationcoefficienttestresultofasmallenterprise.