Discrete Train Speed Profile Optimization for Urban Rail

Research ArticleDiscrete Train Speed Profile Optimization for Urban RailTransit A Data-Driven Model and Integrated Algorithms Basedon Machine Learning

Kang Huang 123 Jianjun Wu 12 Xin Yang1 Ziyou Gao12 Feng Liu4 and Yuting Zhu35

1 State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University Beijing 100044 China2Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive TransportMinistry of Transport Beijing Jiaotong University Beijing 100044 China

3School of Traffic and Transportation Beijing Jiaotong University Beijing 100044 China4Transportation Research Institute (IMOB) Hasselt University Wetenschapspark 5 Bus 6 3590 Diepenbeek Belgium5Beijing Transport Institute Beijing 100073 China

Correspondence should be addressed to JianjunWu jjwu1bjtueducn

Received 19 October 2018 Accepted 26 March 2019 Published 2 May 2019

Academic Editor Hocine Imine

Copyright copy 2019 Kang Huang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Energy-efficient train speed profile optimization problem in urban rail transit systems has attractedmuch attention in recent yearsbecause of the requirement of reducing operation cost and protecting the environment Traditionalmethods on this problemmainlyfocused on formulating kinematical equations to derive the speed profile and calculate the energy consumption which causedthe possible errors due to some assumptions used in the empirical equations To fill this gap according to the actual speed andenergy data collected from the real-world urban rail system this paper proposes a data-driven model and integrated heuristicalgorithm based on machine learning to determine the optimal speed profile with minimum energy consumption Firstly a data-driven optimization model (DDOM) is proposed to describe the relationship between energy consumption and discrete speedprofile processed from actual data Then two typical machine learning algorithms random forest regression (RFR) algorithm andsupport vectormachine regression (SVR) algorithm are used to identify the importance degree of velocity in the different positionsof profile and calculate the traction energy consumption Results show that the calculation average error is less than 01 kwh andthe energy consumption can be reduced by about 284 in a case study of Beijing Changping Line

1 Introduction

In recent years urban rail transit has developed rapidlyaround the world due to its high capacity safety superiorenergy performance and reliable service with sufficientpunctuality [1] which is becoming increasingly important forlarge cities development [2] For example 35 cities in Chinahave urban rail transit with total length over 4750 km in 2017[3] According to the Web of China Rail Transit there will bemore than 50 cities operating urban rail transit in the next fewyears In 2020 the total mileage of urban rail transit in Chinawill be 6000 km making the rail systems an important com-ponent of urban public transportation Around the worldmore and more cities are traveling oriented to public trans-portation As shown in Figure 1 (which is from Global Cities

Public Transit Usage Report of moovit) urban rail transitsystem has attracted much attention in recent years especiallyin some large cities and accounts for a high proportion ofpublic transportationHowever the quick expansion of urbanrail transit networks led to the problem of larger energyconsumption Taking Beijing rail transit as an example in2011 the total electric consumption of Beijing urban railtransit was 750 million kwh and 470 million kwh was usedfor traction energy consumption with the proportion as highas 55 which has attracted tremendous attention in recentyears (Yin et al [4]) In 2015 it reached 14 billion kwhaccounting for 40of the total operating cost of themetro[5]which was equivalent to the annual electricity consumptionof 730000 households (annual electricity consumption ofone household is based on 2016 BEIJING STATISTICAL

HindawiJournal of Advanced TransportationVolume 2019 Article ID 7258986 17 pageshttpsdoiorg10115520197258986

2 Journal of Advanced Transportation

BeijingGuangzhou

New YorkSeoul

SingaporeParis

LondonHong Kong

Tokyo0 025 05 075 1

Percentage ()

Public transportation percentageUrban rail transit percentage in public transportation

4555

5150

71

40

38

76

65

44

92

56

61

63

64

72

85

86

Proportions of public transportation and urban rail transit

Figure 1 Proportions of public transportation and urban railtransit

YEARBOOK from Beijing statistical information website)In the European Union (EU) for instance transport causesapproximately 31 of total greenhouse gas (GHG) emissionsWithin this sector metropolitan transportation is responsiblefor about 25 of the total CO2 emissions (Gonzalez-Gil et al[6])Therefore energy saving has become an important issuein real train operating in order to reduce the operation costand satisfy the requirement of environment protection

To reduce the energy consumption in urban rail transita lot of models have been developed in recent years whichmainly considered the train controlling between two stationsbased on the kinematic equations There are three types ingeneral ie mathematical optimization models simulationmethods and multiple linear regression and neural networkmodel based on the data Although a lot of works had beendone in optimizing speed profiles existing methods havesome limitations (1)The mathematical optimization modelin theoretical aspects has been sounded However the actualsituation is often more complex and the theory of opti-mization may not get a good performance when the actualfacts are taken into consideration (2) The establishment ofthe simulation model (eg agent-based simulation [7]) iscomplicated and costly Further there is a certain deviationbetween the simulation results and the actual measurementdata (3)The traction energy consumption and its influencefactors are not linear and the precision of the multiple linearregression model is limited The neural network relies toomuch on the empirical information extracted from historicaldata The phenomenon of overfitting is prone to occur andthe generalization abilitymay be hard to guarantee Besides itis easy to fall into the local optimum In contrast from view ofthe data-driven optimization on the basis ofmachine learningtheories the limitations could be avoided Firstly real-worlddata that contains the influences from actual factors canbe utilized well Secondly machine learning has been wellapplied in many fields which provides a method to studythe existing information from data acquire new informationand improve performance of data setThe process that utilizesinput data (real-world profile) to obtain output data (energyconsumption) is easier to be realized Thirdly machinelearning is stable For instance the RFR and the SVR have

Section II

LiteratureReview

Section III

Data overview

Section IV

DDOM

Section VGreedily heuristic

algorithm

FRF module

SVR module

Optimizationflow

Data selection

Dimensionalityreduction

Assumptions

Constraints

Objectivefunction

Section VI

Case study

Section VII

Conclusion

Figure 2 Overall framework

stable performance in the data set and they have been widelyused in many fields such as biology medicine economymanagementm and so on [8] Therefore it becomes possibleto optimize the train speed profile in the urban rail transitsystem on the premise of verifying their effectiveness

Main contributions of this research can be summarizedas follows(1) A data-driven optimization model (DDOM) is pro-posed to optimize the speed profile in urban rail transitsystem The traditional speed profile optimization model iseasy to be analyzed in the theoretical aspects In this paper thetrain speed profile is optimized based on the view of discreteprofile which can be applied in the practice easily(2) Based on actual data obtained by experimental mea-surements a novel method of utilizing the machine learningalgorithm to calculate the energy consumption of speedprofile is proposed which can avoid considering longitudinaltrain dynamics Besides the calculation error of machinelearning algorithm (RFR and SVR) on speed profile energyis verified(3) To solve the proposed model an integrated heuristicoptimization algorithm based on RFR and SVR is developedIn addition comparison of real data results show average284 energy reduction

The framework of this paper is shown in Figure 2

2 Literature Review

During last years many studies have focused on the energy-efficiency analysis of train traction Scheepmaker et al [23]

Journal of Advanced Transportation 3

Table 1 Some typical publications about energy-efficient

View Publication Years Model type Objective Energy consumptioncalculational method Solution method

I Cheng andHowlett [9] 1993 Discrete control

modelEnergy consumption

of profileEmpirical-formulanumerical integration Optimize control

I Howlett et al [10] 1996 Continuous controlmodel

Energy consumptionof profile

Empirical-formulanumerical integration Optimize control

I Wong and Ho [11] 2004 Discrete controlmodel

Energy consumptionof profile Genetic method Genetic search

I Albrecht et al [12] 2013 Continuous controlmodel



I Albrecht Howlettet al [13 14] 2016 aampb Continuous control



I Yin et al [15] 2014 Reinforcementlearning


Empirical-formulanumerical integrationSimulation platform

Dynamicprogramming

Iamp II Nasri et al [16] 2010 Simulation model Energy consumptionof timetable


Simulation

II Sun et al [17] 2013 MILP Energy consumptionof timetable

Empirical-formulanumerical integration Genetic search

II Yang et al [18] 2015a MILP Energy consumptionof whole line

Taking intoconsideration recovery

energyGenetic search

II Li and Lo [19 20] 2014 aampb Integrated-operationmodel

Energy consumptionof network


II Canca and Zarzo[21] 2017 MILP Energy consumption

of whole lineEmpirical-formulanumerical integration

Iterative algorithmand

Python+Gurobi

II Yin et al [22] 2017 MILPEnergy consumptionand the passenger

waiting time

Empirical-formulanumerical integration

Lagrangianrelaxation(LR)-based

heuristic algorithmI speed profilesdriving strategy II energy-efficient timetable

summarized and gave a review from two aspects (1) opti-mizing the speed profiles and driving strategies to reduce theenergy consumption (eg Howlett [24 25] Albrecht et al[12] Scheepmaker and Goverde[26] Yang et al [18 27] Tianet al [28] Sun et al [17] Yang et al [29]) and (2) optimizingthe timetable by means of utilization of regenerative energywith minimum energy consumption (eg Chevrier et al[30] Li and Lo [19 20] Wang and Goverde [31] Wang etal [32] Zhao et al [33]) Some typical publications aboutenergy-efficient research are listed in Table 1 In essenceenergy consumption is related to the train traction processIt is a fundamental work to improve the speed profilesOver the past 25 years the challenges in the train speedprofile optimization have resulted in a variety of analysisframeworks (1) Mathematical optimization models Themodern theory of optimal train control was developed duringthe years 1992-2014 by the Scheduling and Control Group(SCG) at the University of South Australia in a collection ofpapers For example Howlett and Cheng [9] built a discretecontrol model and confirmed the fundamental optimalityof the accelerate-coast-brake strategy for energy-efficienttrain operation On the basis of the Pontryagin maximum

principle if no energy is recovered during braking thenit becomes an optimal switching strategy Wong and Ho[11] showed that a genetic algorithm was more robust incalculational processes After reformulating the necessaryconditions for optimal switchingHowlett et al [34] proposeda less general model that the optimal switching points foreach steep section can be found by minimizing an intrinsiclocal energy function Albrecht et al [13] used the Pontryaginprinciple to find necessary conditions on an optimal strategyand showed that a strategy of optimal type uses only a limit-ed set of optimal control modes Maximum Power HoldP(Hold using Power) Coast HoldR (Hold using Regenerativebraking) andMaximum Brake Albrecht et al [14] developedgeneral bounds on the position of optimal switching pointsand proved that an optimal strategy always exists And anintrinsic local energy minimization principle for determina-tion of optimal switching pointswas established which showsthat the optimal strategy is unique Huang et al [35] pro-posed an integrated approach for the energy-efficient drivingstrategy and timetable which was solved by a particle swarmoptimization (PSO) algorithm Yang et al [36] employedan energy-efficient through the Taylor approximation They


CHANFPINGLine

CHANGPINGXISHANKOU

Ming Tombs

CHANG PING

CHANGPING DONGGUANBEISHAO WA

NANSHAO

SHAHE UniversityParkSHAHE

GONGHUA CHENG Line 8

ZHUXINZHUANG

Line 13

Life Science Park

XIrsquo ERQI

Figure 3 Illustration of the Changping Line

Table 2 Overview of measurement characteristics

Parameter Unit ResolutionSpeed kmh 0001Position m 0001Time s 02Train weight ton 1Current slope 1permil 1EBI speed kmh 0001Station spacing m 0001Expected acceleration of PID (kmh)s 1Electric energy consumption Kwh 1

transformed the train scheduling problem using a nonconvexformation into a quadratic formation and search the solutionby a PSO method (2) Simulation method Yin et al [15]built an ITO (intelligent train operation) simulation platformon the basis of the multiple-point-mass train model thatthe platform consists of four parts ie the Input Modulethe Algorithm Module the Train Module and the OutputModule (3) Multiple linear regression model and neuralnetwork model based on the data Fernandeza et al [37]modeled electric trains energy consumption using neuralnetworks providing a reliable estimation of the consumptionalong a specific route when being fed with input data such astrain speed acceleration or track longitudinal slope

Big data analytics (BDA) has increasingly attracted astrong attention of analysts researchers and practitioners inrailway transportation and engineering filed [38] From adata-driven view this paper mainly focuses on how to obtainthe optimal speed profile based on well-developed machinelearning algorithms There are still seldom researches aimingat optimal speed profile by this proposed method

3 Data Analysis and Preprocessing

31 Data Overview During the operation of the subwaythe most widely used power is electricity Some are usedfor the consumption of facilities in the train such as air

conditioning lighting etc The rest is for traction of metrotrains Our data resources are formed by urban rail transittrain running state and corresponding energy consumptionwhich are derived from Changping Line of Beijing urbanrail transit The operation section of Changping Line isfrom the Xirsquoerqi station to the Changpingxishankou stationwith operating mileage of 319 kilometers and total of 12stations opened (as illustrated in Figure 3) In order toaccurately capture the actual traction power consumptionduring the operation of the subway we installed sensors andcomputers on the train The total energy consumption andthe energy consumptions of various electrical appliances inthe train are both recorded Then the total consumptionis subtracted from the electrical energy consumed by theelectrical appliances and the rest is the energy consumed bythe traction of the subway train The provided data coversrunning stage of 4 months There are two circle runningtests every night in the up and down direction The types ofrecorded data are showed in Table 2

32 Data Preprocessing

Symbols

119899 number of section is discretized toV0119895 119895th speed point of original profile 119862119894


Table 3 Part types of the original data

Time Velocity(kmh) Distance(m)11990501 V01 1199040111990502 V02 11990402 1199050119894 V0119894 1199040119894 1199050119898 V0119898 1199040119898

80

70

60

50

40

30

20

10

0

minus10

velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)

MingTombs-CHANGPINGXISHANKOU

ＦＣＧ2

ＦＣＧ1 ＦＣＧ3

Starting

Accelerating

Accelerating

Accelerating

Coasting

Coasting

Light Decelerating

Limiting speed

Deep Decelerating

StopsＦＣＧ2sＦＣＧ1

Figure 4 MingTombs-Changpingxishankou

1199040119895 119895th position point of original profile 1198621198941199050119895 119895th time point of original profile 119862119894119904119894 it is the 119894th displacement from the beginning ofthe urban rail transit sectionV119894 the speed at 119904119894119905119894 the time at 119904119894nabla119905 the time interval used to record the speed anddisplacement data during train traction1198780119894 distance set at a time interval nabla119905 1198780119894 =1199040119895 | 119895 =1 2 119899

Using these recorded data we can draw out the runningprocess of the urban rail transit train Taking MingTombs-Changpingxishankou of the down direction for instance(showed in Figure 4) the train operation process is dividedinto three stagesThefirst stage is accelerating until approach-ing the maximum speed limit the second stage is fluctuatingin the high-speed zone the third stage is the decelerationbraking until the train stops Normally differences in trackconditions are caused by construction and geological reasonsThere will be limited speed at different locations in eachsection of the urban rail transit In this section there arethree speed limiting sections 0 997888rarr 1198781198971198941198981 1198781198971198941198981 997888rarr1198781198971198941198982 1198781198971198941198982 997888rarr 119864119899119889 Each part has its maximum speedlimit

Train running state form is shown in Table 3 (m thenumber of data recorded on an original speed profile) A

speed profile has three elements speed time and distanceThe time interval between records in the table is 02 secondsHowever the running time between two stations varies fromalmost one to several hundred seconds This means thata speed profile may be made up of thousands of recordsWe need to calculate the energy consumption from theprofile that is to say to find the relationship between energyconsumption and the thousands of data records which is theso-called ldquohigh-dimensionalrdquo data in statistics

Although machine learning algorithms under the back ofbig data are suitable for dealing with high-dimensional datafor extremely high-dimensional situations large amounts ofdata are needed as training sets and calculation precision ishard to be gained [39] Therefore we choose dimensionalityreduction for the limitation of data quantity Not only can thealgorithm achieve good training effect but also the accuracyof the original high-dimensional data can be reserved

Process of reducing the dimension is as follows (1)Thesection length 1198780 can be obtained from records then 1198780is divided into 119899 small sections (the uniform segmentationmethod is chosen in this paper) Thus the (n+1) points arerepresented by 1199040 119904119894 119904119899 | 119894 = 0 1 119899 Clearly1199040 = 0 119904119899 = 1198780 (section total length) Taking MingTombs-Changpingxishankou of the down direction for instance asshown in Figure 5 a uniform interval of 50m and 5m isselected for discrete process In Figure 5(a) the speed profilerecord number drops to 26 getting 26 control points duringthe train traction respectively in Figure 5(b) speed profilerecord number is 247 and the density of control points ishigher(2) Find the latter and previous positions of 119904119894 in originalprofile within nabla119905 interval recorded as 119904minus119894 and 119904+119894 Sequence119904minus0 119904minus119894 119904minus119899 119904+0 119904+119894 119904+119899 is obtained(3) In the original velocity profile we can get the velocityand time corresponding to the 119904minus119894 and 119904+119894 recorded as Vminus119894 V

+119894 119905minus119894 and 119905+119894 In the small section from 119904minus119894 to 119904+119894 the train is

assumed to be in a uniformly accelerated state As shown inFigure 6 by using Vminus119894 V

+119894 119904minus119894 and 119904+119894 the V119894 can be obtained

Therefore we can get the V0 V119894 V119899 where V0 = V119899 =0 Figure 6(a) indicates speed profile can be represented byfewer points Figure 6(b) shows error between the simplifiedprofile and original one could be ignored when compared thewhole length of section

33 Extraction of Training Data Set and Testing Data SetAfter processing above V119894 minus 119904119894 V+119894 minus 119904+119894 minus 119905+119894 Vminus119894 minus 119904minus119894 minus 119905minus119894 can be obtained For example let 119904119894(119894 = 0 1 119899) be with


80

70

60

50

40

30

20

10

0

minus10

Velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)

ＦＣＧ2

ＦＣＧ1

ＦＣＧ3

Starting

Accelerating

Accelerating

AcceleratingCoasting

Light Decelerating

Limiting speed

Deep Decelerating


After Processing MingTombs-CHANGPINGXISHANKOU

(a)

ＦＣＧ2


Starting

Accelerating

Accelerating

Accelerating

Coasting

Coasting

Light Decelerating

Limiting speed

Deep Decelerating


80

70

60

50

40

30

20

10

0

minus10

Velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)


(b)

Figure 5 Profiles description at different distance intervals (a) 50m interval (b) 5m interval

Complete CurveSimplified Curve

25

20

15

10

5

0

Velo

city

-A (k

mh

)

0

Error rarr 0

1

2

i

i+1

s1 s2 si si+1

Distance (m)

(a)

Orginal Velocity Curve

20

10

0

Velo

city

(km

h)

0 5 10 15 20sminusi s+i

nablatnablatnablatnablat

siminus1 si si+1

i

minusi = 0jminus1

+i = 0j

Distance (m)

(b)

Figure 6 Dimension reduction process of velocity profile (a) Get the V0 V119894 V119899 (b) Error in simplified profile

a uniform interval of 5m and part of results are shown inTable 4

The speed profile sequence V119894 minus 119904119894 119894 = 1 2 119899 andthe traction energy consumptions of each sequence 119864 areextracted And the data is shown in Table 5 (q number ofprocessed data records) Then to eliminate dimension thedata is normalized The extracted data is divided into twoparts 80 is as the training set and 20 is as the test set

4 Formulation

In this section a data-driven optimization model (DDOM)is proposed to optimize the urban rail transit traction energyconsumption which discretizes velocity profile and describesthe relation between velocity profile and energy consumptionas a complex mapping-relation

41 Symbols and Assumptions

Parameters

1198810119894 velocity set at a time interval nabla119905 1198810119894 =V0119895 | 119895 =1 2 1198991198780119894 distance set at a time interval nabla119905 1198780119894 =1199040119895 | 119895 =1 2 1198991198790119894 time set with a time interval of nabla119905 1198790119894 =1199050119895 | 119895 =1 2 119899119862lowast set of processed speed profiles and V119894 minus 119904119894 |119894 = 0 1 119899 isin 119862lowast119886119894 the acceleration at 119904119894119864119905 energy consumption of urban rail transit trac-tion under running time of 119905


Table 4 Part of the velocity series after being processed

119894 Vminus119894 (119896119898ℎ) 119904minus119894 (m) 119905minus119894 (nabla119905) V119894(119896119898ℎ) 119904119894(119898) V+119894 (119896119898ℎ) 119904+119894 (119898)1 0 0 0 0 0 0 02 918 464 21 9657 5 99 5193 14256 933 28 14811 10 1494 10164 18612 14928 34 18659 15 19296 165 21492 19462 38 21824 20 22248 206986 24408 24646 42 24593 25 25128 260427 26568 28954 45 27042 30 27252 304688 28764 33622 48 29371 35 29484 35269 30888 38652 51 31442 40 31608 4040810 33012 4404 54 33419 45 33804 4591811 35172 49786 57 3525 50 35892 517812 36576 53812 59 36991 55 37296 5588413 37944 57992 61 38617 60 38664 601414 40068 64554 64 40197 65 40716 6681615 41436 69118 66 41709 70 42156 714616 42804 73838 68 43134 75 43488 7625417 44172 78708 70 44528 80 44856 81218 45576 83732 72 45897 85 46224 86319 46944 88908 74 47213 90 47592 9155220 48204 9423 76 48368 95 4878 9694

Table 5 Data format of training and testing set

Serial number 1199040 1199041 119904119899minus1 119904119899 Time Energy consumption1 V10 V11 V1119899minus1 V1119899 1199051 11986412 V20 1199052 1198642 q-1 V119902minus10 119864119902minus1q V1199020 V1199021 V119902119899minus1 V119902119899 119905119899 119864119902

V119898119894119899119878119894 minimum speed limit corresponding to 119904119894V119898119886119909119878119894 maximum speed limit corresponding to 119904119894119886119898119894119899 minimum acceleration limit in operationalsection

119886119898119886119909 maximum acceleration limit in operationalsection

119879119898119894119899 minimum time limit in operational section

119879119898119886119909 maximum time limit in operational section

Assumption During the process of 119904minus119894 997888rarr 119904119894 997888rarr 119904+119894 because the interval is small enough it is assumed that thetrain is in uniform acceleration According to the theorem ofV119890119897119900119888119894119905119910minus119889119894119904119901119897119886119888119890119898119890119899119905 relationship in physics the quadraticfunction can be given

((V+119894 )2 minus V1198942)(119904+119894 minus 119904119894) = 2119886119894 119894 = 1 119899 (1)

(V1198942 minus (Vminus119894 )2)(119904119894 minus 119904minus119894 ) = 2119886119894 119894 = 1 119899 (2)

119886119894 = (V+119894 minus Vminus119894 )nabla119905 119894 = 1 119899 (3)

Derived by formulas (1)-(3) we get the velocity sequenceV0 V119894 V119899 as followsV119894 = radic2119886119894 (119904119894 minus 119904minus119894 ) + (Vminus119894 )2

= radic 2 (V+119894 minus Vminus119894 ) (119904119894 minus 119904minus119894 )nabla119905 + (Vminus119894 )2 119894 = 1 119899(4)

or

V119894 = radic(V+119894 )2 minus 2119886119894 (119904+119894 minus 119904119894)= radic(V+119894 )2 minus 2 (V

+119894 minus Vminus119894 ) (119904+119894 minus 119904119894)nabla119905 119894 = 1 119899

(5)


42 Train Operation Constraints During the running statefrom one station to a neighboring station some constraintsshould be satisfied

Speed limit (SL) constraints the speed limit of the sectionat 119904119894 should be satisfied

V119898119894119899119904119894 lt V119904119894 lt V119898119886119909119904119894 119894 = 1 119899 (6)

V119898119886119909119904119894 and V119898119894119899119904119894 are determined by the actual speed limit of thesection

Acceleration constraints in order to satisfy the comfort ofpassengers on the train the acceleration needs to be kept ina suitable range As shown in formula (7)-(8) 119886119898119894119899 and 119886119898119886119909are determined by actual empirical parameters and 119886119898119886119909 gt0 119886119898119894119899 lt 0((V119894+1)2 minus V1198942)(2 (119904119894+1 minus 119904119894)) = 119886119894 isin [119886119898119894119899 119886119898119886119909] 119894 = 1 (119899 minus 1) (7)

(V1198942 minus (V119894minus1)2)(2 (119904119894 minus 119904119894minus1)) = 119886119894 isin [119886119898119894119899 119886119898119886119909] 119894 = 1 119899 (8)

Train operation time constraints transportation effi-ciency also should be taken into account Therefore the trainrunning time 119905 also needs to be within a certain range asshown in formula (9)

119905 isin [119879119898119894119899 119879119898119886119909] (9)

where 119879119898119894119899 and 119879119898119886119909 are determined by the service leveland operational condition

Train operation distance constraints to ensure that thetrain can reach the station accurately the total displacementof the train in the section must be equal to the length of thesection

119904119899 = 1198780 (10)

43 Objective Function When the section running time oftrain is 119905 the corresponding energy consumption is 119864119905 whichhas a complicated relationship with the sequence of velocitypointsThat is119864119905(1199040minusV0 119904119894minusV119894 119904119899minusV119899) i=01 nTheoptimization of urban rail transit speed profile is to minimizethe energy consumption under the condition of satisfyingtransportation task and the objective function of data-drivenoptimization model (DDOM) is showed in (11)

min119864 = min119905119864119905 (V119894 minus 119904119894 | 119894 = 0 1 119899)

119905 isin [119879119898119894119899 119879119898119886119909] (V119894 minus 119904119894 | 119894 = 0 1 119899) isin 119862lowast (11)

5 A Greedily Heuristic Algorithm for Model

In this section firstly two energy consumption calculationmethods based on machine learning algorithm are intro-ducedThen by analysis the characters of them an integratedoptimization flow is developed with a combination of theirmerits

51 Energy Consumption Calculation Based on MachineLearning Algorithm From the view of data-driven methodurban rail transit train runs within each section and pro-duces a traction speed profile that corresponds to an energyconsumption value Although the factors affecting the energyconsumption of each train are not only related to thespeed profile the external factors are determined once theoperational section is fixed Moreover the transmissioncharacteristic of the train is determinedwhen the type of trainis selected then the energy consumption is only related to thespeed profile during the traction processTherefore the speedprofile becomes the key to the energy consumption of traintraction

In this paper two typical machine learning algorithms(RFR and SVR) are introduced where RFR is utilized toget velocity pointsrsquo importance degrees in different positionswhich can be responsible for obtaining these pairs space-speed with a major contribution to the energy consumptionAnd SVR is employed to calculate the energy consumptionof the profileTheprogramming environment is Python 3 andits machine learning module is scikit-learn

511 Random Forest Regression (RFR) Algorithm ModuleRandom forest is a kind of ensemble learning algorithmwhich uses multiple trees to train and predict a classifier andalso can be used for regression [40] Based on decision treescombined with aggregation and bootstrap ideas randomforests were introduced by Breiman in 2001 which addedan additional layer of randomness to bagging In additionto constructing each tree using a different bootstrap sampleof the data random forests change how the classificationor regression trees are constructed They are a powerfulnonparametric statistical method allowing consideration in asingle and versatile framework regression problem [41] Therandom forest optionally produces two additional pieces ofinformation a measure of the importance of the predictorvariables and a measure of the internal structure of the data(the proximity of different data points between one andanother) In this paper we can take advantages of this moduleto get velocity pointsrsquo importance degree in different positionswhich can be used in heuristic solution process for model

Evaluation and Analysis of RFR In the utilization of RFRalgorithm two important parameters should be calibratedthe number of split attributes (Mtry) and number of decisiontrees (Ntree) For simplicity the enumeration method is usedto traverse the two parameters The convergence process isshown in Figure 7 over ten experiments We can see thatwhen Ntreege50 the average error is close to 01kwh Fordifferent Mtrys errors are shown in Figure 8(a) and thereis an acceptable convergence range in Figure 8(b) When the


RFR-Average Error Value (kwh)02402202

01801601401201

008006

Aver

age E

rror

Val

ue (k

wh)

10 20 30 40 50 60 70 80 90 100

Ntree

DataViolationCenterLCLUCL

Figure 7The error values at different Ntrees

Mtry=2 or 3 the error is minimal Therefore the optimalparameter combination used in this paper is Mtry=2 or 3andNtreege50 By using the FR algorithm the traction energyconsumption evaluation average error is less than 01kwh andwithin range of 1

In addition to the high precision evaluation ability wealso get importance degrees of the velocity in differentdisplacements during the traction energy consumption of theurban rail transitWe canfind that the speed at which positionis more significant to the energy consumption in a sectionwhich indicates contributions to energy consumption of pairsspace-speed For instance in the section of MingTombs-Changpingxishankou section length is 1230m the impor-tance degrees at different positions are shown in Figure 9

512 Support Vector Machine Regression (SVR) AlgorithmModule Support vector machine (SVM) algorithm is fromstatistical learning theory (SLT) which is based on the struc-tural risk minimization principle that can avoid excessivelearning problems and ensure the generalization ability ofthe model In essence it can solve the convex quadraticprogramming problem and avoid falling into the local min-imum It can be applied not only to classification problemsbut also to the case of regression [42] Therefore it can bedivided into support vector classification (SVC) and supportvector regression (SVR) Because of its solid theoreticalfoundation and its complete theoretical derivation supportvector machine is an effective tool in dealing with smallsamples nonlinear local issues In this paper it is applied tocalculate the energy consumption based on real data

Before using the SVR the first step requires the determi-nation of the kernel functions The second step is to optimizeparameters corresponding to different kernel functions Inthis paper three typical kernel functions are verified radialbasis kernel function (RBF) linear kernel function (LIN-EAR) and polynomial kernel function (POLY)(1) For RBF calibration parameters include119862 penalty fac-tor and119866119886119898119898119886 value As shown in Figure 10(a) convergencerate of RBF is very fast When 119862 ge 20 the error will drop toa lower level As 119862 ge 100 the average error of traction energy

consumption can reach about 01kwh The best combinationof parameters is 119862 ge 30 and 119866119886119898119898119886 = 3(2) For LINEAR calibration parameter is 119862 penalty fac-tor As shown in Figure 10(b) the convergence is slow When119862 ge 900 the average error of traction energy consumptionalso can reach about 01kwh which means that it will take alittle longer time to reach minimum errors(3) For POLY calibration parameter is 119862 penalty factorAs shown in Figure 10(c) average error is fluctuating up-down at 01Kwh and not stable which fails to achieve betterconvergence results

Comparing the performance of the three kernel func-tions average error of the RBF kernel function is the bestwhich means that the traction energy consumption can becalculated under the optimal parameter conditions

513 Analysis of the Two Machine Learning Algorithms ForRFR algorithm stable performance is in the data set andthe evaluation results are satisfactory At the same time themore momentous point is that the importance degrees of thevelocity points in different positions can be sorted whichwill be a valid guiding to the optimization control of thespeed profile For example we can adjust the speed withhigh importance degree in the speed profile optimizationprocess As for the SVR algorithm although the performanceis not good in some kernel conditions the ability to calculatein the RBF kernel function is also serviceable enough Foroptimizing the speed profile of an urban rail transit train weshould find a speed profile that is not less than the existingenergy consumption or is even lower than the existing energyconsumption However the RFR algorithm has a fatal flawrandom forest cannot make the output beyond the rangeof data set which may lead to overfitting in modelingof some specific data with noise Therefore the design ofurban rail transit speed profile optimization algorithms couldbe beneficial to the combination virtues of the SVR andRFR

52 Optimization Process Form the view of discrete trainspeed profile optimization the key problem is how to designa method to get a more energy-efficient profile thus a groupof combinations V119894 minus 119904119894(119894 = 0 1 119899) should be foundVelocity V119894 in every position can be in a range and thenumber of V119894minus119904119894(119894 = 0 1 119899) combinations will be beyondimagination It is necessary to discretize the speed changingvalue Thus there should be a step size used for the speedadjustment A simple and effective step size is the unit fromrecording instrument (in our experiment it is 0001kmh)Further a heuristic process can be proposed to reduce thecombinations we can utilize important degree from RFRto adjust the velocity with fixed order Then energy-savingprofile will be easier to get by the heuristic process As shownin Figure 11 in one operation section of the real-world datathere are many profiles under the same running time butwith different energy consumptions Under every runningtime condition we can try to find a satisfactory profile atthis fixed running time Then the best of them with differentfixed running time is taken as the optimal solution Based


RFR-Mtry-Average Error Value (kwh)09

08

07

06

05

04

03

02

01

0

Aver

age E

rror

Val

ue (k

wh)

Mtry=1Mtry=2Mtry=3Mtry=4Mtry=5


100 20 30 40 50 60 70 80 90 100

Ntree

(a)

0908070605040302010Av

erag

e Err

or V

alue

(kw

h)

RFR-Average Error Value (kwh) Range

1 2 3 4 5 6 7 8 9 10Mtry

(b)

Figure 8 Convergence process and errors in RFR (a) Errors in different Mtrys (b) Convergence range

Importance-Distance02

018

016

014

012

01

008

006

004

002

0

Impo

rtan

ce d

egre

e val

ue

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

9501000

1050

1100

1150

1200 12

30

Distance (m)

Figure 9 Importance of velocity at different locations in the section

SVR-RBF-Gamma5

45

4

35

3

25

2

15

1

05

0

Aver

age E

rror

Val

ue (k

wh)

0 10 20 30 40 50 60 70 80 90 100

C Value

(a) (b) (c)

01kwh

Gamma=1Gamma=2Gamma=3Gamma=4Gamma=5


C Value

SVR-Linear1

09

08

07

06

05

04

03

02

01

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

X 9472Y 01099

SVR-POlY-Average Error Value (kwh)018

016

014

012

01

008

006

004

002

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

C Value

Figure 10 Convergence process in different kernel functions (a) SVR-RBF-Gamma (b) SVR-LINEAR (c) SVR-POLY

on this we develop an integrated greedily heuristic algorithmcombined with RFR and SVR

Parameters

119868+ set of index values corresponding to the speed atwhich the importance degree is arranged in descend-ing order

119868minus set of index values corresponding to the speed atwhich the importance degree is arranged in ascendingorder119868(119896)+ in descending order the speed index valuecorresponding to the 119896119905ℎ importance degree119868(119896)minus in ascending order the speed index valuecorresponding to the 119896119905ℎ importance degree


Collection ofall solutions

Feasible solutions atdifferent times

Local optimal solutionsat different time

Global optimalsolutions

Et0

Et1

Et

Et

ETmax

ETminE

Figure 11 Distribution of solutions

Step 1 In the case of optimal parameters random forestregression (RFR) Algorithm Module (Section 511)) is usedto obtain the importance degree of speed series V119894minus119904119894Thensort them (because the importance degrees of V0 minus 1199040 V119899 minus119904119899 are zero they are excluded) in descending order Andthe 119870 speed sequences V119896+ minus 119904119896+ of the previous m(119870 =119899 lowast 119898100) are selected For the corresponding importancedegree 119890+119896 (1 le 119896 le 119870) we can get 119890+1 ge 119890+2 ge 119890+119896 ge 119890+119870Then in ascending order similarly the 119870 speed sequencesV119896minus minus 119904119896minus of the previous m are selected and get 119890minus1 le119890minus2 le 119890minus119896 le 119890minus119870Step 2 Initialize the operation time 119905 of the urban rail transittrain and set 1199050 = 119879119898119894119899 According to the minimum andmaximum time in the data 119879119898119894119899 119879119898119886119909 are determined anddiscretized unit of time is nabla119905 Then let 119896 = 1 119903 = 0Step 3 In the case of 119905 = 1199050 + 119903 lowast nabla119905(119903 = 0 1 2 119903119898119886119909) isin[119879119898119894119899 119879119898119886119909] we choose the minimum energy speed profile119862119898119894119899119905 from the data set and begin to adjust the velocitysequence The adjustment process is as follows assume thatthe 119890+119896 119896 = 1 2 119870 importance degree corresponds toV119894 minus 119904119894 then adjusted speed V119894 is V

and119894 = V119894 + 119892 lowast 120590(119892 =119892119898119894119899 0 1 2 119892119898119886119909) (119892119898119894119899 119892119898119886119909 Vlowast119894119898119894119899 and Vlowast119894119898119886119909 should

meet acceleration constraints and speed constraints) Toensure the train can reach the station displacement changecaused by adjusting V119894 isnabla119904and119894 (in formula (12)) whichmust beoffset by another displacement change nabla119904minus119895 (in formula (13))in different positions As shown in Figure 12 we choose thespeed V119895 at (119890minus119896 119896 = 1 2 119870 corresponds to V119895) to offset thedisplacement change

Step 4 Then we can get a new profile after adjustment ofV119894 and V119895 Support vector machines regression algorithm(SVR) module (Section 512) is used to calculate the energyconsumption We adjust the velocity until 119892 = 119892119898119886119909 andget the minimum energy consumption 119864119898119894119899119905119896 during theadjustment process and the corresponding speed Vand119894 Thenlet V119894 = Vand119894 and V119895 = Vand119895

Formulas (12) and (13) show the calculation of nabla119904and119894 andnabla119904minus119895 where velocity changes are nablaVand119894 and nablaVminus119894 To ensure the

Original profileImproved profile

35

30

25

20

15

10

5

0

Velo

city

(km

h)

0 5 10 15 20 25 30 35 40 45 50

Distance (m)

nablasandi = (andi minus i) (tminusi+1 minus tminusiminus1) 2 gt 0

1

j

0

2

i+1 minus ti+1 andj

nablasandj = (andj minus j) (tminusj+1 minus tminusjminus1) 2 lt 0

iminus1 minus timinus1 iminus ti

middot middot middot middot middot middot

andi minus timiddot middot middot middot middot middot


Figure 12 Explanation of changes of velocity and displacement

balance of displacement let nabla119904and119894 = nabla119904minus119895 nabla119904and119894 = nablaVand119894 lowast (119905

minus119894 minus 119905minus119894minus1)2 + nablaVand119894 lowast (119905

minus119894+1 minus 119905minus119894 )2

= nablaVand119894 lowast (119905minus119894+1 minus 119905minus119894minus1)2 = (Vand119894 minus V119894) (119905minus119894+1 minus 119905minus119894minus1)2

(12)

nabla119904minus119895 = nablaVminus119895 lowast (119905minus119895 minus 119905minus119895minus1)2 + nablaVminus119895 lowast (119905


= nablaVminus119895 lowast (119905minus119895+1 minus 119905minus119895minus1)2 = (Vminus119895 minus V119895) (119905minus119895+1 minus 119905minus119895minus1)2

(13)

Step 5 If 119896 = 119870 then go to Step 6 if 119896 = 119896 + 1 repeat Step 3

Step 6 If 119905 = 119879119898119886119909 then go to Step 7 if 119903 = 119903+1 repeat Step 3Step 7 Get all the energy consumption 119864119898119894119899119905119870 119905 isin [119879119898119894119899 119879119898119886119909]Then119872119894119899119864 = 119898119894119899119905 119864119898119894119899119905119870 119870 = 119898 lowast 119899100 119905 isin [119879119898119894119899 119879119898119886119909]


Start

End

MIN

RFR algorithm module

Training RFR algorithmGet importance degree i of is i minus si

Prepare for adjusting velocity

Sorting importance degree ei in descendingorder get e+i sequences andCorresponding velocity series i minus si | i isin I+

Sorting importance degree ei in ascendingorder get eminusi sequences andCorresponding velocity series i minus si | i isin Iminus

velocity series i minus si i isin I+K i minus si || i isin IminusK

Begin to adjustvelocity

k = 1 r = 0

t = TＧＣＨ u = 0

t = TＧＣＨ + Ｌ lowast nablaＮ

g = gＧＣＨ EＧＣＨtk = E0

tk

r = r + 1

SVR algorithm module

YES

YES

YES

YES

YES NONO

NO

NO

NO

calculating get

consumption Egtk after adjusting the vi and v minusj

of the previous m (K=nlowastm100) And correspondingselect the K Importance degree sequencee+i

eminusi

and calculatinggetg = g + 1 Ｐand

and

i = i + g

g

lowast (Ｃ = ）+K(Ｅ))Ｐminusj (Ｄ = ）minusK(Ｅ)) calculate the energy

EＧＣＨtk gt E

tk

EＧＣＨtk = E

Ａ

tk u = g

k = K + 1

EＧＣＨK gt EＧＣＨ

tK

E=EＧＣＨtK

EＧＣＨK = EＧＣＨ

tK

R = rr = r + 1

r = rＧＲ + 1

Ｐi = Ｐi + Ｏ lowast (Ｃ = ）+K(Ｅ))

Ｐj (Ｄ = ）minusK(Ｅ))

g=g_max

k = k + 1

Figure 13 Algorithm flow

Finally algorithm flow is shown in Figure 13

6 Numerical Experiment

61 Section Parameters

Section Parameters

Sectional length(119904119899) 1230m

Speed limits(SL) (1)0 minus 200119898 119878119871 = 60119896119898ℎ (2) 200119898 minus 1100119898 119878119871 = 80119896119898ℎ (3)1100119898 minus1230119898 119878119871 = 50119896119898ℎ

Acceleration 119886119898119886119909 = minus119886119898119894119899 = 151198981199042Operation time 119879119898119894119899 = 954(119904) 119879119898119886119909 = 1034(119904)

We take Changping Line MingTombs-Changpingxishankousection of down direction as a numerical experiment toexplain the optimization process and the section parametersare listed as above And there are two cases in differentintervals A complete operation state is showed in Figure 14

62 Optimization Result

Case 1 119904119894(119894 = 0 1 119899) is set as an uniform interval of5m and let V0 = V246 = 0 1199040 = 0 119904246 = 1230 The


MingTombs--gtChangpingxishankou90

80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092

Distance (m)Target velocity (kmh)Actual velocity (kmh)

Figure 14 Train operation state

Comparison of velocity before and after optimization100

80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

Distance (m)Before optimizationAfter optimization

Figure 15 Optimization result with small intervals

Distance (m)

Before optimizationAfter optimization

Comparison of velocity before and after optimization

Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)

Distance (m)Before optimizationAfter optimization1


0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)

Figure 16 Optimization results with big intervals (a) m=50 (b) m=100

operation time is 1034s The results after optimization areshown in Figure 15 We can see that the optimal profile is notsmooth It suddenly increases or decreases in some placesApparently the availability of the optimized profile is notenough

Case 2 119904119894(119894 = 0 1 119899) is set as an uniform interval of 50mand let V0 = V26 = 0 1199040 = 0 11990426 = 1230 Figure 16shows the optimal results when 119898 = 50 (showed in

Figure 16(a)) and119898 = 100 (showed in Figure 16(b)) In thiscase the operation time is also 1034s The optimized energyconsumption can be reduced by 065 kwh We can see thatthe speed profile is much smoother than Case 1 with rate ofenergy reduction is 31(06521lowast100) In Figure 16(a) form=50 after optimization the acceleration stage is slightlyflat However in Figure 16(b) when m=100 whole speedprofile is flatter compared to the original profile and it ismorevaluable in practice


Xierqi --gtLife Science Park 908070605040302010

0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)

Life Science Park --gtZhu Xinzhuang

0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)

Zhuxinzhaung--gtGonghuacheng

020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)

Gonghuacheng--gtShahe

010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)

Shahe--gtShahe University Park

010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)

Shahe University Park --gtNanshao

040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)

Nanshao --gt Beishaowa

010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)

Beishaowa--gtChangping dongguan

010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)

Changping dongguan--gtChangping

020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)

Changping--gtMingTombs

020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)

Figure 17 The obtained profiles in different sections Section (a)ndash(j) are listed in Table 6

Operation sections with different distances should nothave the same discrete interval For longer section theinterval could be bigger For example distance of Xirsquoerqi-Life Science Park is 5455m and interval could be 200m

In addition the comparison of profile before and afteroptimization is shown in Figures 17(a)ndash17(j) Optimizationresults of other operation sections are listed in Table 6 Wecan see that in some section the maximum energy saving


Table 6 Optimization results of other sections

Section nameMinimum energy

consumption of actualdata(KWh)

Afteroptimization

(KWh)

Net energysaving(KWh)

Energy saving()

Sectionlength(m) interval(m)

Xirsquoerqi-Life Science Park 28 2694 106 379 5455 200Life SciencePark-Zhuxinzhuang 19 1844 056 295 2405 100

Zhuxinzhaung-Gonghuacheng 19 1836 064 339 3810 200

Gonghuacheng-Shahe 20 1913 087 435 2037 100Shahe-Shahe UniversityPark 22 2088 112 508 1967 100

Shahe UniversityPark-Nanshao 30 2945 055 183 5364 200

Nanshao-Beishaowa 14 1355 045 321 2003 100Beishawa-Changpingdongguan 16 1566 034 213 1687 100

Changpingdongguan-Changping 22 2158 042 191 2439 100

Changping-MingTombs 39 3856 044 113 3522 200MingTombs-Changpingxishankou 21 2035 065 310 1230 50

Total 250 2429 71 284 31964 -Average value 2273 2208 065 - - -

is 508 (in the section Shahe to Shahe University Park)which is a good performance And for a 319km lengthwith 12stations train line energy saving is 284 The improvementmay look modest when compared with previous researches(most claim saving energy above 4) However our improve-ment is compared with a real-world result that had alreadybeen imposed with an optimal control (traditional trainoptimal control with on the basis of Pontryagin maximumprinciple) There is an ATO (automatic train system whichis equipped with optimal control) in Beijing Changping Lineand Yizhuang Line Yizhuang Line and Changping Linehave some similar features train type number of organizedgroup passenger intensity power supply mode and so onA well-designed method in real world that is applied intoYizhuang Line can achieve average saving energy blow 3from the operatorrsquos statement Therefore the improvementbased on an ATO profile which makes it look modest isreasonable Besides for different section there are differentimprovements The results may be triggered by many factorslike different section external environments (radius of curveslope air humidity and so on) The optimized control effectsin different sections are key to the room for improvement Ifthe room for improvement is limited the real improvementmay be also limited Therefore there is no quantitative resultto illustrate the different improvements in each section

7 Conclusion

Reducing train traction energy consumption is one of theefficient ways to cut energy cost in urban rail transit systemsAnd to protect the environment the optimization of urban

rail transit traction energy conservation has been a significanttask in urban rail transit operation and management Thetraction energy consumption of a single train is related to thespeed profile between stationsWhen energy-efficient profilesare applied in every section there will be a positive effect onreducing energy consumption of the urban rail transit systemTherefore train speed profile optimization is a fundamentalwork

In this paper the speed profile optimization problem isdiscretized and the decision variables of the speed profilebecome a series of space-speed points From this viewpoint adata-driven urban rail transit train speed profile optimizationmodel (DDOM) is proposed to describe the relationshipbetween profiles and energy consumption Two machinelearning algorithms namely random forest regression (RFR)and support vector regression (SVR) are taken into accountRFR is applied to get the important degree of velocity inpositions and the degree is utilized as heuristic informationto decide the optimization order of velocity in differentpositions SVR is used to calculate energy consumption ofprofiles with a high accuracy (95) Combined with theadvantages of the two algorithms an integrated heuristicgreedy optimization algorithm is developed to solve themodel which can reduce energy consumption by 284In some theory research energy conservation percentage ishigher than our results However few are verified based onthe real-world data Furthermore our methods may be quitesimple and can be applied to practice easily

Nevertheless because the data samples are far fromenough when adjusting velocity in different positions to geta new profile in the optimization process range of velocity


change is limited There is still some room for an improve-ment on the basis of the optimization results Although thereare many different views the data-driven method is newto the problem and applying machine learning algorithmsto the field of energy saving in urban rail transit is theinnovation Future research can be focused on the followingareas Firstly a further improved algorithm for a differentheuristic strategy could be studied For instance based on thedata machine learning method the regenerative electricityconsumption in the braking process may be reused in thetrains from neighboring sections Thus instead of optimizingone single train speed profile in each section separately trainspeed profiles fromneighboring sections should be taken intoaccount Secondly in the urban rail transit networks if powersupply in the network nodes (transfer stations) is transmittedfrom the same transformer substation the energy-savingoptimization of trains can be extended to the urban rail transitnetwork

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work is supported by the China National Funds forDistinguished Young Scientists (71525002) National NatureScience Foundation of China (7189097271890970 71771018and 71621001) and Beijing Municipal Natural Science Foun-dation (L181008)

References

[1] X Guo J Wu J Zhou X Yang D Wu and Z Gao ldquoFirst-traintiming synchronization using multi-objective optimization inurban transit networksrdquo International Journal of ProductionResearch 2018

[2] L Kang X Zhu H Sun J Wu Z Gao and B Hu ldquoLast traintimetabling optimization and bus bridging servicemanagementin urban railway transit networksrdquo OMEGA -e InternationalJournal of Management Science vol 74 no 1 pp 31ndash44 2018

[3] X Yang H Yin JWu Y Qu Z Gao and T Tang ldquoRecognizingthe critical stations in urban rail networks an analysis methodbased on the smart-card datardquo IEEE Intelligent TransportationSystems Magazine vol 11 no 1 pp 29ndash35 2019

[4] J Yin Y Wang T Tang J Xun and S Su ldquoMetro trainrescheduling by adding backup trains under disrupted scenar-iosrdquo Frontiers of Engineering Management vol 4 no 4 pp 418ndash427 2017

[5] T Tang and J Xun ldquoResearch on energy-efficient drivingstrategy in Beijing Yizhuang linerdquo Journal of BeijingJiaoTongUniversity vol 40 no 4 pp 20ndash24 2016

[6] A Gonzalez-Gil R Palacin P Batty and J P Powell ldquoA systemsapproach to reduce urban rail energy consumptionrdquo EnergyConversion and Management vol 80 pp 509ndash524 2014

[7] H Yin J Wu Z Liu H Yin Y Qu and H Sun ldquoOptimizingthe release of passenger flow guidance information in urban railtransit network via agent-based simulationrdquoAppliedMathemat-ical Modelling vol 72 no 8 pp 337ndash355 2019

[8] R Genuer J-M Poggi C Tuleau-Malot andNVilla-VialaneixldquoRandom forests for big datardquo Big Data Research vol 9 no 3pp 28ndash46 2017

[9] J X Cheng and PHowlett ldquoA note on the calculation of optimalstrategies for the minimization of fuel consumption in thecontrol of trainsrdquo IEEE Transactions on Automatic Control vol38 no 11 pp 1730ndash1734 1993

[10] P Howlett ldquoOptimal strategies for the control of a trainrdquoAutomatica vol 32 no 4 pp 519ndash532 1996

[11] K Wong and T Ho ldquoCoast control for mass rapid transitrailways with searching methodsrdquo IEE Proceedings - ElectricPower Applications vol 151 no 5 pp 365ndash376 2004

[12] A R Albrecht P G Howlett P J Pudney and X VuldquoEnergy-efficient train control from local convexity to globaloptimization and uniquenessrdquo Automatica vol 49 no 10 pp3072ndash3078 2013

[13] A Albrecht P Howlett P Pudney X Vu and P Zhou ldquoThe keyprinciples of optimal train controlmdashPart 1 Formulation of themodel strategies of optimal type evolutionary lines locationof optimal switching pointsrdquo Transportation Research Part BMethodological vol 94 pp 482ndash508 2016

[14] A Albrecht P Howlett P Pudney X Vu and P Zhou ldquoThekey principles of optimal train controlmdashPart 2 Existenceof an optimal strategy the local energy minimization prin-ciple uniqueness computational techniquesrdquo TransportationResearch Part B Methodological vol 94 pp 509ndash538 2016

[15] J YinD Chen andL Li ldquoIntelligent train operation algorithmsfor urban rail transit by expert system and reinforcement learn-ingrdquo IEEE Transactions on Intelligent Transportation Systemsvol 15 no 6 pp 2561ndash2571 2014

[16] A Nasri M Fekri Moghadam and H Mokhtari ldquoTimetableoptimization for maximum usage of regenerative energy ofbraking in electrical railway systemsrdquo in International Sympo-sium on Power Electronics Electrical Drives Automation andMotion pp 1218ndash1221 Pisa Italy 2010

[17] H Sun J Wu H Ma X Yang and Z Gao ldquoA bi-objectivetimetable optimization model for urban rail transit based onthe time-dependent passenger volumerdquo IEEE Transactions onIntelligent Transportation Systems vol 20 no 2 pp 604ndash6152019

[18] X Yang A Chen J Wu Z Gao and T Tang ldquoAn energy-efficient rescheduling approach under delay perturbations formetro systemsrdquo Transportmetrica B Transport Dynamics vol 7no 1 pp 386ndash400 2019

[19] X Li and K Lo Hong ldquoAn energy-efficient scheduling andspeed control approach for metro rail operationsrdquo Transporta-tion Research Part B Methodological vol 64 pp 73ndash89 2014

[20] X Li and H K Lo ldquoEnergy minimization in dynamic trainscheduling and control for urban rail transit rail operationsrdquoTransportation Research Part B Methodological vol 70 no 1pp 269ndash284 2014

[21] D Canca and A Zarzo ldquoDesign of energy-Efficient timetablesin two-way railway rapid transit linesrdquo Transportation ResearchPart B Methodological vol 102 pp 142ndash161 2017


[22] J Yin L Yang T Tang Z Gao and B Ran ldquoDynamic pas-senger demand oriented metro train scheduling with energy-efficiency and waiting time minimization Mixed-integer linearprogramming approachesrdquo Transportation Research Part BMethodological vol 97 pp 182ndash213 2017

[23] G M Scheepmaker R M Goverde and L Kroon ldquoReviewof energy-efficient train control and timetablingrdquo EuropeanJournal ofOperational Research vol 257 no 2 pp 355ndash376 2017

[24] P G Howlett I P Milroy and P J Pudney ldquoEnergy-efficienttrain controlrdquo in Advances in Industrial Control SpringerLondon UK 1995

[25] P Howlett ldquoA new look at the rate of change of energyconsumption with respect to journey time on an optimal trainjourneyrdquo Transportation Research Part B Methodological vol94 pp 387ndash408 2016

[26] G M Scheepmaker and R M P Goverde ldquoThe interplaybetween energy-efficient train control and scheduled runningtime supplementsrdquo Journal of Rail Transport Planning andManagement vol 5 no 4 pp 225ndash239 2015

[27] X Yang X Li B Ning and T Tang ldquoA survey on energy-efficient train operation for urban rail transitrdquo IEEE Transac-tions on Intelligent Transportation Systems vol 17 no 1 pp 2ndash132016

[28] Z Tian P Weston N Zhao S Hillmansen C Roberts andL Chen ldquoSystem energy optimisation strategies for metroswith regenerationrdquo Transportation Research Part C EmergingTechnologies vol 75 pp 120ndash135 2017

[29] S Yang J Wu X Yang F Liao D Li and Y Wei ldquoAnalysis ofenergy consumption reduction in metro system using rollingstop-skipping patternsrdquo Computers amp Industrial Engineeringvol 127 no 1 pp 129ndash142 2019

[30] R Chevrier P Pellegrini and J Rodriguez ldquoEnergy saving inrailway timetabling a bi-objective evolutionary approach forcomputing alternative running timesrdquo Transportation ResearchPart C Emerging Technologies vol 37 pp 20ndash41 2013

[31] PWang andR M P Goverde ldquoMulti-train trajectory optimiza-tion for energy efficiency and delay recovery on single-trackrailway linesrdquo Transportation Research Part B Methodologicalvol 105 pp 340ndash361 2017

[32] L Wang L Yang Z Gao and Y Huang ldquoEnergy-savingoperation approaches for urban rail transit systemsrdquo Frontiersof Engineering Management vol 4 no 4 pp 408ndash417 2017

[33] N Zhao C Roberts S Hillmansen Z Tian P Westonand L Chen ldquoAn integrated metro operation optimization tominimize energy consumptionrdquo Transportation Research PartC Emerging Technologies vol 75 pp 168ndash182 2017

[34] P G Howlett P J Pudney and X Vu ldquoLocal energy minimiza-tion in optimal train controlrdquo Automatica vol 45 no 11 pp2692ndash2698 2009

[35] Y Huang H Yu J Yin et al ldquoAn integrated approach for theenergy-efficient driving strategy optimization of multiple trainsby considering regenerative brakingrdquo Computers amp IndustrialEngineering vol 126 pp 399-400 2018

[36] S Yang J Wu X Yang H Sun and Z Gao ldquoEnergy-efficient timetable and speed profile optimization with multi-phase speed limits theoretical analysis and applicationrdquoAppliedMathematical Modelling vol 56 no 4 pp 32ndash50 2018

[37] P M Fernandez C G Roman and R I Franco ldquoModellingelectric trains energy consumption using neural networksrdquoTransportation Research Procedia vol 18 pp 59ndash65 2016

[38] F Ghofrani Q He R M P Goverde and X Liu ldquoRecentapplications of big data analytics in railway transportationsystems A surveyrdquo Transportation Research Part C EmergingTechnologies vol 90 pp 226ndash246 2018

[39] R S Michalski I Bratko and M Kubat ldquoMachine learningand data mining methods and applicationrdquo ACM SIGKDDExplorations Newsletter vol 2 no 2 pp 110ndash114 2004

[40] L Breiman ldquoRandom forestsrdquoMachine Learning vol 45 no 1pp 5ndash32 2001

[41] A Liaw and M Wiener ldquoClassification and regression byrandom forestrdquo R News vol 23 no 23 pp 18ndash22 2002

[42] D Basak and S Pal ldquoSupport vector regressionrdquo Statistics andComputing vol 11 no 10 pp 203ndash224 2007

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom


BeijingGuangzhou

New YorkSeoul

SingaporeParis

LondonHong Kong

Tokyo0 025 05 075 1

Percentage ()

Public transportation percentageUrban rail transit percentage in public transportation

4555

5150

71

40

38

76

65

44

92

56

61

63

64

72

85

86

Proportions of public transportation and urban rail transit

Figure 1 Proportions of public transportation and urban railtransit

YEARBOOK from Beijing statistical information website)In the European Union (EU) for instance transport causesapproximately 31 of total greenhouse gas (GHG) emissionsWithin this sector metropolitan transportation is responsiblefor about 25 of the total CO2 emissions (Gonzalez-Gil et al[6])Therefore energy saving has become an important issuein real train operating in order to reduce the operation costand satisfy the requirement of environment protection

To reduce the energy consumption in urban rail transita lot of models have been developed in recent years whichmainly considered the train controlling between two stationsbased on the kinematic equations There are three types ingeneral ie mathematical optimization models simulationmethods and multiple linear regression and neural networkmodel based on the data Although a lot of works had beendone in optimizing speed profiles existing methods havesome limitations (1)The mathematical optimization modelin theoretical aspects has been sounded However the actualsituation is often more complex and the theory of opti-mization may not get a good performance when the actualfacts are taken into consideration (2) The establishment ofthe simulation model (eg agent-based simulation [7]) iscomplicated and costly Further there is a certain deviationbetween the simulation results and the actual measurementdata (3)The traction energy consumption and its influencefactors are not linear and the precision of the multiple linearregression model is limited The neural network relies toomuch on the empirical information extracted from historicaldata The phenomenon of overfitting is prone to occur andthe generalization abilitymay be hard to guarantee Besides itis easy to fall into the local optimum In contrast from view ofthe data-driven optimization on the basis ofmachine learningtheories the limitations could be avoided Firstly real-worlddata that contains the influences from actual factors canbe utilized well Secondly machine learning has been wellapplied in many fields which provides a method to studythe existing information from data acquire new informationand improve performance of data setThe process that utilizesinput data (real-world profile) to obtain output data (energyconsumption) is easier to be realized Thirdly machinelearning is stable For instance the RFR and the SVR have

Section II

LiteratureReview

Section III

Data overview

Section IV

DDOM

Section VGreedily heuristic

algorithm

FRF module

SVR module

Optimizationflow

Data selection

Dimensionalityreduction

Assumptions

Constraints

Objectivefunction

Section VI

Case study

Section VII

Conclusion

Figure 2 Overall framework

stable performance in the data set and they have been widelyused in many fields such as biology medicine economymanagementm and so on [8] Therefore it becomes possibleto optimize the train speed profile in the urban rail transitsystem on the premise of verifying their effectiveness

Main contributions of this research can be summarizedas follows(1) A data-driven optimization model (DDOM) is pro-posed to optimize the speed profile in urban rail transitsystem The traditional speed profile optimization model iseasy to be analyzed in the theoretical aspects In this paper thetrain speed profile is optimized based on the view of discreteprofile which can be applied in the practice easily(2) Based on actual data obtained by experimental mea-surements a novel method of utilizing the machine learningalgorithm to calculate the energy consumption of speedprofile is proposed which can avoid considering longitudinaltrain dynamics Besides the calculation error of machinelearning algorithm (RFR and SVR) on speed profile energyis verified(3) To solve the proposed model an integrated heuristicoptimization algorithm based on RFR and SVR is developedIn addition comparison of real data results show average284 energy reduction

The framework of this paper is shown in Figure 2

2 Literature Review

During last years many studies have focused on the energy-efficiency analysis of train traction Scheepmaker et al [23]





















Dynamicprogramming



Simulation












Python+Gurobi


waiting time







CHANFPINGLine

CHANGPINGXISHANKOU

Ming Tombs

CHANG PING


NANSHAO



ZHUXINZHUANG

Line 13

Life Science Park

XIrsquo ERQI










Symbols





80

70

60

50

40

30

20

10

0

minus10

velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)


ＦＣＧ2


Starting

Accelerating

Accelerating

Accelerating

Coasting

Coasting

Light Decelerating

Limiting speed

Deep Decelerating















80

70

60

50

40

30

20

10

0

minus10

Velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)

ＦＣＧ2

ＦＣＧ1

ＦＣＧ3

Starting

Accelerating

Accelerating


Light Decelerating

Limiting speed

Deep Decelerating



(a)

ＦＣＧ2


Starting

Accelerating

Accelerating

Accelerating

Coasting

Coasting

Light Decelerating

Limiting speed

Deep Decelerating


80

70

60

50

40

30

20

10

0

minus10

Velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)


(b)



25

20

15

10

5

0

Velo

city

-A (k

mh

)

0

Error rarr 0

1

2

i

i+1

s1 s2 si si+1

Distance (m)

(a)


20

10

0

Velo

city

(km

h)

0 5 10 15 20sminusi s+i


siminus1 si si+1

i

minusi = 0jminus1

+i = 0j

Distance (m)

(b)




4 Formulation



Parameters












((V+119894 )2 minus V1198942)(119904+119894 minus 119904119894) = 2119886119894 119894 = 1 119899 (1)





or



(5)




V119898119894119899119904119894 lt V119904119894 lt V119898119886119909119904119894 119894 = 1 119899 (6)





119905 isin [119879119898119894119899 119879119898119886119909] (9)



119904119899 = 1198780 (10)


min119864 = min119905119864119905 (V119894 minus 119904119894 | 119894 = 0 1 119899)










01801601401201

008006

Aver

age E

rror

Val

ue (k

wh)

10 20 30 40 50 60 70 80 90 100

Ntree













08

07

06

05

04

03

02

01

0

Aver

age E

rror

Val

ue (k

wh)



100 20 30 40 50 60 70 80 90 100

Ntree

(a)

0908070605040302010Av

erag

e Err

or V

alue

(kw

h)


1 2 3 4 5 6 7 8 9 10Mtry

(b)



018

016

014

012

01

008

006

004

002

0

Impo

rtan

ce d

egre

e val

ue

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

9501000

1050

1100

1150

1200 12

30

Distance (m)


SVR-RBF-Gamma5

45

4

35

3

25

2

15

1

05

0

Aver

age E

rror

Val

ue (k

wh)

0 10 20 30 40 50 60 70 80 90 100

C Value

(a) (b) (c)

01kwh



C Value

SVR-Linear1

09

08

07

06

05

04

03

02

01

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

X 9472Y 01099


016

014

012

01

008

006

004

002

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

C Value



Parameters








Et0

Et1

Et

Et

ETmax

ETminE








35

30

25

20

15

10

5

0

Velo

city

(km

h)

0 5 10 15 20 25 30 35 40 45 50

Distance (m)


1

j

0

2

i+1 minus ti+1 andj











(12)




(13)




Start

End

MIN








k = 1 r = 0




tk

r = r + 1


YES

YES

YES

YES

YES NONO

NO

NO

NO

calculating get



eminusi


and

i = i + g

g


EＧＣＨtk gt E

tk

EＧＣＨtk = E

Ａ

tk u = g

k = K + 1


tK

E=EＧＣＨtK


tK

R = rr = r + 1

r = rＧＲ + 1



g=g_max

k = k + 1





Section Parameters









80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092




80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200



Distance (m)



Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)



0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)







0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






















Dynamicprogramming



Simulation












Python+Gurobi


waiting time







CHANFPINGLine

CHANGPINGXISHANKOU

Ming Tombs

CHANG PING


NANSHAO



ZHUXINZHUANG

Line 13

Life Science Park

XIrsquo ERQI










Symbols





80

70

60

50

40

30

20

10

0

minus10

velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)


ＦＣＧ2


Starting

Accelerating

Accelerating

Accelerating

Coasting

Coasting

Light Decelerating

Limiting speed

Deep Decelerating















80

70

60

50

40

30

20

10

0

minus10

Velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)

ＦＣＧ2

ＦＣＧ1

ＦＣＧ3

Starting

Accelerating

Accelerating


Light Decelerating

Limiting speed

Deep Decelerating



(a)

ＦＣＧ2


Starting

Accelerating

Accelerating

Accelerating

Coasting

Coasting

Light Decelerating

Limiting speed

Deep Decelerating


80

70

60

50

40

30

20

10

0

minus10

Velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)


(b)



25

20

15

10

5

0

Velo

city

-A (k

mh

)

0

Error rarr 0

1

2

i

i+1

s1 s2 si si+1

Distance (m)

(a)


20

10

0

Velo

city

(km

h)

0 5 10 15 20sminusi s+i


siminus1 si si+1

i

minusi = 0jminus1

+i = 0j

Distance (m)

(b)




4 Formulation



Parameters












((V+119894 )2 minus V1198942)(119904+119894 minus 119904119894) = 2119886119894 119894 = 1 119899 (1)





or



(5)




V119898119894119899119904119894 lt V119904119894 lt V119898119886119909119904119894 119894 = 1 119899 (6)





119905 isin [119879119898119894119899 119879119898119886119909] (9)



119904119899 = 1198780 (10)


min119864 = min119905119864119905 (V119894 minus 119904119894 | 119894 = 0 1 119899)










01801601401201

008006

Aver

age E

rror

Val

ue (k

wh)

10 20 30 40 50 60 70 80 90 100

Ntree













08

07

06

05

04

03

02

01

0

Aver

age E

rror

Val

ue (k

wh)



100 20 30 40 50 60 70 80 90 100

Ntree

(a)

0908070605040302010Av

erag

e Err

or V

alue

(kw

h)


1 2 3 4 5 6 7 8 9 10Mtry

(b)



018

016

014

012

01

008

006

004

002

0

Impo

rtan

ce d

egre

e val

ue

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

9501000

1050

1100

1150

1200 12

30

Distance (m)


SVR-RBF-Gamma5

45

4

35

3

25

2

15

1

05

0

Aver

age E

rror

Val

ue (k

wh)

0 10 20 30 40 50 60 70 80 90 100

C Value

(a) (b) (c)

01kwh



C Value

SVR-Linear1

09

08

07

06

05

04

03

02

01

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

X 9472Y 01099


016

014

012

01

008

006

004

002

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

C Value



Parameters








Et0

Et1

Et

Et

ETmax

ETminE








35

30

25

20

15

10

5

0

Velo

city

(km

h)

0 5 10 15 20 25 30 35 40 45 50

Distance (m)


1

j

0

2

i+1 minus ti+1 andj











(12)




(13)




Start

End

MIN








k = 1 r = 0




tk

r = r + 1


YES

YES

YES

YES

YES NONO

NO

NO

NO

calculating get



eminusi


and

i = i + g

g


EＧＣＨtk gt E

tk

EＧＣＨtk = E

Ａ

tk u = g

k = K + 1


tK

E=EＧＣＨtK


tK

R = rr = r + 1

r = rＧＲ + 1



g=g_max

k = k + 1





Section Parameters









80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092




80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200



Distance (m)



Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)



0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)







0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



CHANFPINGLine

CHANGPINGXISHANKOU

Ming Tombs

CHANG PING


NANSHAO



ZHUXINZHUANG

Line 13

Life Science Park

XIrsquo ERQI










Symbols





80

70

60

50

40

30

20

10

0

minus10

velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)


ＦＣＧ2


Starting

Accelerating

Accelerating

Accelerating

Coasting

Coasting

Light Decelerating

Limiting speed

Deep Decelerating















80

70

60

50

40

30

20

10

0

minus10

Velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)

ＦＣＧ2

ＦＣＧ1

ＦＣＧ3

Starting

Accelerating

Accelerating


Light Decelerating

Limiting speed

Deep Decelerating



(a)

ＦＣＧ2


Starting

Accelerating

Accelerating

Accelerating

Coasting

Coasting

Light Decelerating

Limiting speed

Deep Decelerating


80

70

60

50

40

30

20

10

0

minus10

Velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)


(b)



25

20

15

10

5

0

Velo

city

-A (k

mh

)

0

Error rarr 0

1

2

i

i+1

s1 s2 si si+1

Distance (m)

(a)


20

10

0

Velo

city

(km

h)

0 5 10 15 20sminusi s+i


siminus1 si si+1

i

minusi = 0jminus1

+i = 0j

Distance (m)

(b)




4 Formulation



Parameters












((V+119894 )2 minus V1198942)(119904+119894 minus 119904119894) = 2119886119894 119894 = 1 119899 (1)





or



(5)




V119898119894119899119904119894 lt V119904119894 lt V119898119886119909119904119894 119894 = 1 119899 (6)





119905 isin [119879119898119894119899 119879119898119886119909] (9)



119904119899 = 1198780 (10)


min119864 = min119905119864119905 (V119894 minus 119904119894 | 119894 = 0 1 119899)










01801601401201

008006

Aver

age E

rror

Val

ue (k

wh)

10 20 30 40 50 60 70 80 90 100

Ntree













08

07

06

05

04

03

02

01

0

Aver

age E

rror

Val

ue (k

wh)



100 20 30 40 50 60 70 80 90 100

Ntree

(a)

0908070605040302010Av

erag

e Err

or V

alue

(kw

h)


1 2 3 4 5 6 7 8 9 10Mtry

(b)



018

016

014

012

01

008

006

004

002

0

Impo

rtan

ce d

egre

e val

ue

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

9501000

1050

1100

1150

1200 12

30

Distance (m)


SVR-RBF-Gamma5

45

4

35

3

25

2

15

1

05

0

Aver

age E

rror

Val

ue (k

wh)

0 10 20 30 40 50 60 70 80 90 100

C Value

(a) (b) (c)

01kwh



C Value

SVR-Linear1

09

08

07

06

05

04

03

02

01

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

X 9472Y 01099


016

014

012

01

008

006

004

002

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

C Value



Parameters








Et0

Et1

Et

Et

ETmax

ETminE








35

30

25

20

15

10

5

0

Velo

city

(km

h)

0 5 10 15 20 25 30 35 40 45 50

Distance (m)


1

j

0

2

i+1 minus ti+1 andj











(12)




(13)




Start

End

MIN








k = 1 r = 0




tk

r = r + 1


YES

YES

YES

YES

YES NONO

NO

NO

NO

calculating get



eminusi


and

i = i + g

g


EＧＣＨtk gt E

tk

EＧＣＨtk = E

Ａ

tk u = g

k = K + 1


tK

E=EＧＣＨtK


tK

R = rr = r + 1

r = rＧＲ + 1



g=g_max

k = k + 1





Section Parameters









80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092




80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200



Distance (m)



Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)



0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)







0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





80

70

60

50

40

30

20

10

0

minus10

velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)


ＦＣＧ2


Starting

Accelerating

Accelerating

Accelerating

Coasting

Coasting

Light Decelerating

Limiting speed

Deep Decelerating















80

70

60

50

40

30

20

10

0

minus10

Velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)

ＦＣＧ2

ＦＣＧ1

ＦＣＧ3

Starting

Accelerating

Accelerating


Light Decelerating

Limiting speed

Deep Decelerating



(a)

ＦＣＧ2


Starting

Accelerating

Accelerating

Accelerating

Coasting

Coasting

Light Decelerating

Limiting speed

Deep Decelerating


80

70

60

50

40

30

20

10

0

minus10

Velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)


(b)



25

20

15

10

5

0

Velo

city

-A (k

mh

)

0

Error rarr 0

1

2

i

i+1

s1 s2 si si+1

Distance (m)

(a)


20

10

0

Velo

city

(km

h)

0 5 10 15 20sminusi s+i


siminus1 si si+1

i

minusi = 0jminus1

+i = 0j

Distance (m)

(b)




4 Formulation



Parameters












((V+119894 )2 minus V1198942)(119904+119894 minus 119904119894) = 2119886119894 119894 = 1 119899 (1)





or



(5)




V119898119894119899119904119894 lt V119904119894 lt V119898119886119909119904119894 119894 = 1 119899 (6)





119905 isin [119879119898119894119899 119879119898119886119909] (9)



119904119899 = 1198780 (10)


min119864 = min119905119864119905 (V119894 minus 119904119894 | 119894 = 0 1 119899)










01801601401201

008006

Aver

age E

rror

Val

ue (k

wh)

10 20 30 40 50 60 70 80 90 100

Ntree













08

07

06

05

04

03

02

01

0

Aver

age E

rror

Val

ue (k

wh)



100 20 30 40 50 60 70 80 90 100

Ntree

(a)

0908070605040302010Av

erag

e Err

or V

alue

(kw

h)


1 2 3 4 5 6 7 8 9 10Mtry

(b)



018

016

014

012

01

008

006

004

002

0

Impo

rtan

ce d

egre

e val

ue

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

9501000

1050

1100

1150

1200 12

30

Distance (m)


SVR-RBF-Gamma5

45

4

35

3

25

2

15

1

05

0

Aver

age E

rror

Val

ue (k

wh)

0 10 20 30 40 50 60 70 80 90 100

C Value

(a) (b) (c)

01kwh



C Value

SVR-Linear1

09

08

07

06

05

04

03

02

01

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

X 9472Y 01099


016

014

012

01

008

006

004

002

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

C Value



Parameters








Et0

Et1

Et

Et

ETmax

ETminE








35

30

25

20

15

10

5

0

Velo

city

(km

h)

0 5 10 15 20 25 30 35 40 45 50

Distance (m)


1

j

0

2

i+1 minus ti+1 andj











(12)




(13)




Start

End

MIN








k = 1 r = 0




tk

r = r + 1


YES

YES

YES

YES

YES NONO

NO

NO

NO

calculating get



eminusi


and

i = i + g

g


EＧＣＨtk gt E

tk

EＧＣＨtk = E

Ａ

tk u = g

k = K + 1


tK

E=EＧＣＨtK


tK

R = rr = r + 1

r = rＧＲ + 1



g=g_max

k = k + 1





Section Parameters









80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092




80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200



Distance (m)



Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)



0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)







0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



80

70

60

50

40

30

20

10

0

minus10

Velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)

ＦＣＧ2

ＦＣＧ1

ＦＣＧ3

Starting

Accelerating

Accelerating


Light Decelerating

Limiting speed

Deep Decelerating



(a)

ＦＣＧ2


Starting

Accelerating

Accelerating

Accelerating

Coasting

Coasting

Light Decelerating

Limiting speed

Deep Decelerating


80

70

60

50

40

30

20

10

0

minus10

Velo

city

(km

h)

0 200 400 600 800 1000 1200 1400Distance (m)


(b)



25

20

15

10

5

0

Velo

city

-A (k

mh

)

0

Error rarr 0

1

2

i

i+1

s1 s2 si si+1

Distance (m)

(a)


20

10

0

Velo

city

(km

h)

0 5 10 15 20sminusi s+i


siminus1 si si+1

i

minusi = 0jminus1

+i = 0j

Distance (m)

(b)




4 Formulation



Parameters












((V+119894 )2 minus V1198942)(119904+119894 minus 119904119894) = 2119886119894 119894 = 1 119899 (1)





or



(5)




V119898119894119899119904119894 lt V119904119894 lt V119898119886119909119904119894 119894 = 1 119899 (6)





119905 isin [119879119898119894119899 119879119898119886119909] (9)



119904119899 = 1198780 (10)


min119864 = min119905119864119905 (V119894 minus 119904119894 | 119894 = 0 1 119899)










01801601401201

008006

Aver

age E

rror

Val

ue (k

wh)

10 20 30 40 50 60 70 80 90 100

Ntree













08

07

06

05

04

03

02

01

0

Aver

age E

rror

Val

ue (k

wh)



100 20 30 40 50 60 70 80 90 100

Ntree

(a)

0908070605040302010Av

erag

e Err

or V

alue

(kw

h)


1 2 3 4 5 6 7 8 9 10Mtry

(b)



018

016

014

012

01

008

006

004

002

0

Impo

rtan

ce d

egre

e val

ue

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

9501000

1050

1100

1150

1200 12

30

Distance (m)


SVR-RBF-Gamma5

45

4

35

3

25

2

15

1

05

0

Aver

age E

rror

Val

ue (k

wh)

0 10 20 30 40 50 60 70 80 90 100

C Value

(a) (b) (c)

01kwh



C Value

SVR-Linear1

09

08

07

06

05

04

03

02

01

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

X 9472Y 01099


016

014

012

01

008

006

004

002

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

C Value



Parameters








Et0

Et1

Et

Et

ETmax

ETminE








35

30

25

20

15

10

5

0

Velo

city

(km

h)

0 5 10 15 20 25 30 35 40 45 50

Distance (m)


1

j

0

2

i+1 minus ti+1 andj











(12)




(13)




Start

End

MIN








k = 1 r = 0




tk

r = r + 1


YES

YES

YES

YES

YES NONO

NO

NO

NO

calculating get



eminusi


and

i = i + g

g


EＧＣＨtk gt E

tk

EＧＣＨtk = E

Ａ

tk u = g

k = K + 1


tK

E=EＧＣＨtK


tK

R = rr = r + 1

r = rＧＲ + 1



g=g_max

k = k + 1





Section Parameters









80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092




80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200



Distance (m)



Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)



0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)







0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












((V+119894 )2 minus V1198942)(119904+119894 minus 119904119894) = 2119886119894 119894 = 1 119899 (1)





or



(5)




V119898119894119899119904119894 lt V119904119894 lt V119898119886119909119904119894 119894 = 1 119899 (6)





119905 isin [119879119898119894119899 119879119898119886119909] (9)



119904119899 = 1198780 (10)


min119864 = min119905119864119905 (V119894 minus 119904119894 | 119894 = 0 1 119899)










01801601401201

008006

Aver

age E

rror

Val

ue (k

wh)

10 20 30 40 50 60 70 80 90 100

Ntree













08

07

06

05

04

03

02

01

0

Aver

age E

rror

Val

ue (k

wh)



100 20 30 40 50 60 70 80 90 100

Ntree

(a)

0908070605040302010Av

erag

e Err

or V

alue

(kw

h)


1 2 3 4 5 6 7 8 9 10Mtry

(b)



018

016

014

012

01

008

006

004

002

0

Impo

rtan

ce d

egre

e val

ue

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

9501000

1050

1100

1150

1200 12

30

Distance (m)


SVR-RBF-Gamma5

45

4

35

3

25

2

15

1

05

0

Aver

age E

rror

Val

ue (k

wh)

0 10 20 30 40 50 60 70 80 90 100

C Value

(a) (b) (c)

01kwh



C Value

SVR-Linear1

09

08

07

06

05

04

03

02

01

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

X 9472Y 01099


016

014

012

01

008

006

004

002

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

C Value



Parameters








Et0

Et1

Et

Et

ETmax

ETminE








35

30

25

20

15

10

5

0

Velo

city

(km

h)

0 5 10 15 20 25 30 35 40 45 50

Distance (m)


1

j

0

2

i+1 minus ti+1 andj











(12)




(13)




Start

End

MIN








k = 1 r = 0




tk

r = r + 1


YES

YES

YES

YES

YES NONO

NO

NO

NO

calculating get



eminusi


and

i = i + g

g


EＧＣＨtk gt E

tk

EＧＣＨtk = E

Ａ

tk u = g

k = K + 1


tK

E=EＧＣＨtK


tK

R = rr = r + 1

r = rＧＲ + 1



g=g_max

k = k + 1





Section Parameters









80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092




80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200



Distance (m)



Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)



0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)







0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





V119898119894119899119904119894 lt V119904119894 lt V119898119886119909119904119894 119894 = 1 119899 (6)





119905 isin [119879119898119894119899 119879119898119886119909] (9)



119904119899 = 1198780 (10)


min119864 = min119905119864119905 (V119894 minus 119904119894 | 119894 = 0 1 119899)










01801601401201

008006

Aver

age E

rror

Val

ue (k

wh)

10 20 30 40 50 60 70 80 90 100

Ntree













08

07

06

05

04

03

02

01

0

Aver

age E

rror

Val

ue (k

wh)



100 20 30 40 50 60 70 80 90 100

Ntree

(a)

0908070605040302010Av

erag

e Err

or V

alue

(kw

h)


1 2 3 4 5 6 7 8 9 10Mtry

(b)



018

016

014

012

01

008

006

004

002

0

Impo

rtan

ce d

egre

e val

ue

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

9501000

1050

1100

1150

1200 12

30

Distance (m)


SVR-RBF-Gamma5

45

4

35

3

25

2

15

1

05

0

Aver

age E

rror

Val

ue (k

wh)

0 10 20 30 40 50 60 70 80 90 100

C Value

(a) (b) (c)

01kwh



C Value

SVR-Linear1

09

08

07

06

05

04

03

02

01

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

X 9472Y 01099


016

014

012

01

008

006

004

002

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

C Value



Parameters








Et0

Et1

Et

Et

ETmax

ETminE








35

30

25

20

15

10

5

0

Velo

city

(km

h)

0 5 10 15 20 25 30 35 40 45 50

Distance (m)


1

j

0

2

i+1 minus ti+1 andj











(12)




(13)




Start

End

MIN








k = 1 r = 0




tk

r = r + 1


YES

YES

YES

YES

YES NONO

NO

NO

NO

calculating get



eminusi


and

i = i + g

g


EＧＣＨtk gt E

tk

EＧＣＨtk = E

Ａ

tk u = g

k = K + 1


tK

E=EＧＣＨtK


tK

R = rr = r + 1

r = rＧＲ + 1



g=g_max

k = k + 1





Section Parameters









80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092




80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200



Distance (m)



Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)



0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)







0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




01801601401201

008006

Aver

age E

rror

Val

ue (k

wh)

10 20 30 40 50 60 70 80 90 100

Ntree













08

07

06

05

04

03

02

01

0

Aver

age E

rror

Val

ue (k

wh)



100 20 30 40 50 60 70 80 90 100

Ntree

(a)

0908070605040302010Av

erag

e Err

or V

alue

(kw

h)


1 2 3 4 5 6 7 8 9 10Mtry

(b)



018

016

014

012

01

008

006

004

002

0

Impo

rtan

ce d

egre

e val

ue

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

9501000

1050

1100

1150

1200 12

30

Distance (m)


SVR-RBF-Gamma5

45

4

35

3

25

2

15

1

05

0

Aver

age E

rror

Val

ue (k

wh)

0 10 20 30 40 50 60 70 80 90 100

C Value

(a) (b) (c)

01kwh



C Value

SVR-Linear1

09

08

07

06

05

04

03

02

01

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

X 9472Y 01099


016

014

012

01

008

006

004

002

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

C Value



Parameters








Et0

Et1

Et

Et

ETmax

ETminE








35

30

25

20

15

10

5

0

Velo

city

(km

h)

0 5 10 15 20 25 30 35 40 45 50

Distance (m)


1

j

0

2

i+1 minus ti+1 andj











(12)




(13)




Start

End

MIN








k = 1 r = 0




tk

r = r + 1


YES

YES

YES

YES

YES NONO

NO

NO

NO

calculating get



eminusi


and

i = i + g

g


EＧＣＨtk gt E

tk

EＧＣＨtk = E

Ａ

tk u = g

k = K + 1


tK

E=EＧＣＨtK


tK

R = rr = r + 1

r = rＧＲ + 1



g=g_max

k = k + 1





Section Parameters









80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092




80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200



Distance (m)



Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)



0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)







0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




08

07

06

05

04

03

02

01

0

Aver

age E

rror

Val

ue (k

wh)



100 20 30 40 50 60 70 80 90 100

Ntree

(a)

0908070605040302010Av

erag

e Err

or V

alue

(kw

h)


1 2 3 4 5 6 7 8 9 10Mtry

(b)



018

016

014

012

01

008

006

004

002

0

Impo

rtan

ce d

egre

e val

ue

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

9501000

1050

1100

1150

1200 12

30

Distance (m)


SVR-RBF-Gamma5

45

4

35

3

25

2

15

1

05

0

Aver

age E

rror

Val

ue (k

wh)

0 10 20 30 40 50 60 70 80 90 100

C Value

(a) (b) (c)

01kwh



C Value

SVR-Linear1

09

08

07

06

05

04

03

02

01

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

X 9472Y 01099


016

014

012

01

008

006

004

002

Aver

age E

rror

Val

ue (k

wh)

0 100 200 300 400 500 600 700 800 900 1000

C Value



Parameters








Et0

Et1

Et

Et

ETmax

ETminE








35

30

25

20

15

10

5

0

Velo

city

(km

h)

0 5 10 15 20 25 30 35 40 45 50

Distance (m)


1

j

0

2

i+1 minus ti+1 andj











(12)




(13)




Start

End

MIN








k = 1 r = 0




tk

r = r + 1


YES

YES

YES

YES

YES NONO

NO

NO

NO

calculating get



eminusi


and

i = i + g

g


EＧＣＨtk gt E

tk

EＧＣＨtk = E

Ａ

tk u = g

k = K + 1


tK

E=EＧＣＨtK


tK

R = rr = r + 1

r = rＧＲ + 1



g=g_max

k = k + 1





Section Parameters









80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092




80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200



Distance (m)



Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)



0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)







0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Et0

Et1

Et

Et

ETmax

ETminE








35

30

25

20

15

10

5

0

Velo

city

(km

h)

0 5 10 15 20 25 30 35 40 45 50

Distance (m)


1

j

0

2

i+1 minus ti+1 andj











(12)




(13)




Start

End

MIN








k = 1 r = 0




tk

r = r + 1


YES

YES

YES

YES

YES NONO

NO

NO

NO

calculating get



eminusi


and

i = i + g

g


EＧＣＨtk gt E

tk

EＧＣＨtk = E

Ａ

tk u = g

k = K + 1


tK

E=EＧＣＨtK


tK

R = rr = r + 1

r = rＧＲ + 1



g=g_max

k = k + 1





Section Parameters









80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092




80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200



Distance (m)



Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)



0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)







0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Start

End

MIN








k = 1 r = 0




tk

r = r + 1


YES

YES

YES

YES

YES NONO

NO

NO

NO

calculating get



eminusi


and

i = i + g

g


EＧＣＨtk gt E

tk

EＧＣＨtk = E

Ａ

tk u = g

k = K + 1


tK

E=EＧＣＨtK


tK

R = rr = r + 1

r = rＧＲ + 1



g=g_max

k = k + 1





Section Parameters









80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092




80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200



Distance (m)



Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)



0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)







0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




80

70

60

50

40

30

20

10

0

Velo

city

(km

h)

0

0662

7078

2329

49786

863

13019

17401

22113

6

27654

34016

4

406

18

47033

532604

596308

66314

727

982

79076

855172

917

132

97299

1023

902

1068306

1109

394

1144314

1173054

1195754

1212

548

1223

286

1228

092




80

60

40

20

0

Velo

city

(km

h)

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200



Distance (m)



Velo

city

(km

h)

8070605040302010

00 50

100150

200250

300350

400450

500550

600650

700750

800850

900950

10001050

11001150

120012

30

(a)

Velo

city

(km

h)



0

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1230

(b)







0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0

Vel

ocity

(km

h)


0400

8001200

160020

002400

28003200

36004000

44004800

52005455

Distance (m)

(a)


0 200

400 600

800 1000

12001400

16001800

20002200

2400

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(b)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0036

0038

0038

10


Distance (m)

908070605040302010

0

Vel

ocity

(km

h)

(c)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

37100

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(d)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0019

67

100908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(e)


040

080

012

0016

0020

0024

0028

0032

0036

0040

0044

0048

0052

00

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(f)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0017

0018

0019

0020

0020

03

8070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(g)


010

020

030

040

050

060

070

080

090

010

0011

0012

0013

0014

0015

0016

0016

87

100

80

60

40

20

0

Vel

ocity

(km

h)


Distance (m)

(h)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

00

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(i)


020

040

060

080

010

0012

0014

0016

0018

0020

0022

0024

0026

0028

0030

0032

0034

0035

22

908070605040302010

0

Vel

ocity

(km

h)


Distance (m)

(j)








Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Afteroptimization

(KWh)


Energy saving()











7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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