comparison of the short-term forecasting accuracy on battery...

Research ArticleComparison of the Short-Term Forecasting Accuracyon Battery Electric Vehicle between Modified Bass andLotka-Volterra Model A Case Study of China

Shunxi Li Hang Chen and Guofang Zhang

School of Automotive Engineering Hubei Key Laboratory of Advanced Technology for Automotive Components and HubeiCollaborative Innovation Center for Automotive Components Technology Wuhan University of Technology Hubei 430070 China

Correspondence should be addressed to Shunxi Li lsxwhuteducn

Received 7 April 2017 Accepted 4 July 2017 Published 7 August 2017

Academic Editor Xing Wu

Copyright copy 2017 Shunxi Li et alThis is an open access article distributed under theCreative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The potential demand of battery electric vehicle (BEV) is the base of the decision-making to the government policy formulationenterprise manufacture capacity expansion and charging infrastructure construction How to predict the future amount of BEVaccurately is very important to the development of BEV both in practice and in theory The present paper tries to compare theshort-term accuracy of a proposed modified Bass model and Lotka-Volterra (LV) model by taking Chinarsquos BEV development asthe case study Using the statistics data of Chinarsquos BEV amount of 21 months from Jan 2015 to Sep 2016 we compare the simulationaccuracy based on the value of mean absolute percentage error (MAPE) and discuss the forecasting capacity of the two modelsaccording to Chinarsquos government expectation According to the MAPE value the two models have good prediction accuracy butthe Bass model is more accurate than LV model Bass model has only one dimension and focuses on the diffusion trend while LVmodel has two dimensions and mainly describes the relationship and competing process between the two populations In futureresearch the forecasting advantages of Bass model and LV model should be combined to get more accurate predicting effect

1 Introduction

To resolve the problem of environmental pollution andenergy shortage the development of new energy vehicleshas been paid much attention China has become one of thefastest growing markets in the world How to predict thefuture amount of BEV accurately is very important to thedevelopment of BEV both in practice and in theory

The time series model and the causal prediction methodhave been done on the forecasting of car ownership in thefollowing research Based on the GDP growth rate Yini(2005) used the Gompertz model to analysis the futurevehicle ownership in China [1] Gu et al (2010) made aforecast on the vehicle ownership based on the provincial dataof China [2] Ma et al (2009) used the AHPmethod and logitregression model to forecast the market share of new energyvehicles in China [3] Yue et al (2016) forecasted the newenergy vehicle ownership by the multiple linear regressionmethod [4] Apart from using mathematical methods to

calculate the ownership scholars are trying to figure outwhat makes vehicles attract customers Barth et al (2016)explored the current perspective of potential EV users fromGermany on electric mobility and to identify predictorsof a general goal intention to use EVs [5] Prateek andKara (2017) proposed a new simulation-based fleet evolutionframework to forecast Americansrsquo long-term adoption levelsof connected and autonomous vehicle technologies undereight different scenarios [6] Bass diffusion model has beenwidely used in new product promotion including the EVMing et al (2013) used the Bass model to predict the numberof EV and analyzed the amount of EV in China [7] Bin et al(2013) proposed an innovation diffusion model for Chineseelectric vehicles (EVs) based on the extension of generalizedBass model considering infrastructure and price reductioneffects [8] Yingqi et al (2016) tookToyota Priusrsquo internationaldata for reference and combined it with the characteristicsof the Chinese market to build the Bass prediction model ofChinarsquos new energy vehicles market sales and then used the

HindawiJournal of Advanced TransportationVolume 2017 Article ID 7801837 6 pageshttpsdoiorg10115520177801837

2 Journal of Advanced Transportation

model to predict the trend of the whole new energy vehiclesindustry pure electric vehicles and plug-in hybrid vehiclesindustry [9] In view of the limited historical data in theestimation of the parameters of the Bass model of the electricvehicle in China the parameters of BEV in China weredetermined by comparing the parameters of other consumerproducts In summary some achievements have been madein the application of Bass model in the prediction of newenergy automotive industry

Compared with Bass model LV model has been used forpredicting market share transition of silicon wafers technol-ogy substitution and market competition which seems tobe a natural way of portraying the competitive struggle ina market [10ndash15] H-T Wang and T-C Wang (2016) usedLV model to study on the diffusion and competition of TVand smart-phone industries [16]Haijun et al (2011) proposeda method for estimation the parameters of Lotka-Volterramodel based on the grey directmodeling [17]Wu et al (2012)analyzed the long-term relationship between the two vari-ables to predict the values of two variables in the social systemor economic system [18] In the present paper Lotka-Volterramodel has been used to predict the ownership of CVs andBEVs Lotka-Volterra model is a classical method to simulatenatural ecosystems especially when it is used for populationecosystem This model and its mathematical expressions arewidely applied for describing different populations compet-ing for environment resources and the relations among themThere are three classical relations of Lotka-Volterra modelThey are competitive relation predator-prey relation andsymbiotic relation The model can be used for predictingcertain systemrsquos change in the future and speculate certainpopulationsrsquo growth or extinction What is more this modelcan explain how the system changes The relations amongthese three type vehicles are unknown The real relationsneed to be simulated and then verified Lotka-Volterra modelfocuses on the relation between homogeneous species LVmodel has been used to forecast the development of otherindustry such as TV and mobile phone We try to explorethe forecasting accuracy between LV models initially basedon the benchmark of Bass model

2 Methodology

21 Bass Model Bass model is a model for the predictionof the market share of the innovation products technologyadoption and diffusion The core assumption of Bass modelis that the adoption of innovator is independent of othermembers of the social system However the time for theadoption of the new product is influenced by the pressure ofthe social system and the pressure increases with the increaseof the number of people who use it earlierThe potential usersare called imitator For example Massiania and Gohsb (2015)investigated the potential for the use of the Bass diffusionmodel to promote the market diffusion of electric vehicles inGermany [19]

The expression of Bass diffusion model is

119899 (119905) = 119889119873 (119905)119889119905 = 119901 [119898 minus 119873 (119905)] + 119902119898119873 (119905) [119898 minus 119873 (119905)] (1)

The meaning of the mathematical expression and parameterof (1) is explained as follows

(1) 119889119873(119905)119889119905 is the number of noncumulative adopters at119905

(2) 119873(119905) is the number of cumulative adopters at 119905(3) 119898 is the biggest marker potential

(4) 119901 is the external influence coefficient (also calledinnovation coefficient)

(5) 119902 is the internal influence coefficient (also calledimitation coefficient)

(6) 119901[119898minus119873(119905)] represents the number of adopters whosepurchase is influenced by external factors whichare called innovation adopters because they are notinfluenced by people who have already used thisproduct

(7) 119902119898 lowast 119873(119905) lowast [119898 minus 119873(119905)] represents the number ofadopters whose purchase is influenced by internalfactors which are called imitators because they areinfluenced by people who have already used thisproduct

The Bass model expresses the essence of the diffusion processwith mathematical equations which greatly simplifies theunderstanding of the diffusion of innovation The basicBass model is based on a series of important assumptionsNonetheless the basic Bass model does not consider theimpact of marketing strategy on the diffusion of innovationproducts In view of these defects Bass added decisionvariables into the Bassmodel and proposed a generalizedBassmodel

119899 (119905) = 119889119873 (119905)119889119905= 119901 [119898 minus 119873 (119905)] + 119902119898119873 (119905) [119898 minus 119873 (119905)] lowast 119909 (119905)

(2)

In (2) 119909(119905) is a modified variable which depends on decisionvariables

119909 (119905) = 1 + [ Δ119875119903 (119905)Pr (119905 minus 1)] 1205731 + [

ΔADV (119905)ADV (119905 minus 1)] 1205732 (3)

In (3) Pr(119905) represents the innovation product price on 119905ADV(119905) represents the advertisement cost for this product1205731and 1205732 are two coefficients which represent the price impactand advertisement cost impact respectively When 119909(119905) isa constant the generalized Bass model is equivalent to theoriginal Bass model

22 Lotka-Volterra Model Lotka-Volterra model is a classicalmethod to simulate natural ecosystems especially whenit is used for population ecosystem The model and itsmathematical expressions are widely applied for describingdifferent populations competing for environment resourcesand the relations among them The model can be used for

Journal of Advanced Transportation 3

predicting certain systemrsquos change in the future and speculatecertain populationsrsquo growth or extinction

119889119883 (119905)119889119905 = 1199031 lowast 119883 (119905) (1 minus 119886111198831198961 minus

119886211198841198962 )

119889119884 (119905)119889119905 = 1199032 lowast 119884 (119905) (1 minus

119886121198831198961 minus

119886221198841198962 )

(4)

In (4) 119883(119905) represents the amount of population 1 at 119905 time119884(119905) represents the amount of population 2 at 119905 time 119903119894represents the growth ratio of 119894 population 119886119894119895 representsthe competition between populations 119894 and 119895 119896119894 representsthe maximum number of species that can be carried by theenvironment

3 Data and Result

31 Simulation of BEV Based on Bass Model Accordingto the analysis of the current situation of BEV in Chinait is necessary to modify the original market efficiencyfunction 119909(119905) of basic Bass model First of all automotiveconsumerrsquos purchase decision is affected by the price whichwill be affected by the cost of the future operation so thefluctuation of fuel prices should also be taken into accountSecondly due to the fact that the BEV is still in the marketintroduction stage low battery capacity results in shortermileage Meanwhile the construction of infrastructure suchas charging station and charging pile is more important thanthe promotion of advertising Therefore the present paperwill use the number of charging facilities to replace the impactof advertising on the spread of BEV

119909 (119905) = 1 + [ ΔPv (119905)Pv (119905 minus 1) minus

ΔPg (119905)Pg (119905 minus 1)] 1205731

+max0 [ ΔCs (119905)Cs (119905 minus 1)]1205732

(5)

where Pv(119905) is the ratio of electric vehicle price to traditionalvehicle price Pg(119905) is the gas price on 119905 Cs(119905) is the amount ofnew charging stations1205731 is the price impact coefficient while1205732 is the infrastructure impact coefficient

As a new innovative product BEV its market potentialdepends on thematurity of the technology of the product thecoverage of public facilities and the amount of governmentsubsidies The amount of BEV ownership from Jan 2015to Sep 2016 in China is shown in Table 1 The statisticsdata of BEV is from National Bureau of Statistics of China(httpwwwstatsgovcn)

Despite the fact that currently national and local gov-ernments are promoting the development of BEV in Chinabut the effectiveness of BEV is still not as expected bymost consumers In 2012 the State Council of China passedthe ldquoenergy saving and new energy automotive industrydevelopment plan (2012ndash2020)rdquo which mentioned that in2015 the battery EV and plug-in hybrid EV production andsales volume would reach 500 thousand units and in 2020the cumulative production and sales would reach more than5 million vehicles Based on the plan the maximum market

Table 1 The amount of BEV ownership from Jan 2015 to Sep 2016in China

BEV Month273927 Jan 2015279972 Feb 2015294094 Mar 2015302414 Apr 2015313270 May 2015340224 Jun 2015357062 Jul 2015375962 Aug 2015404054 Sep 2015438370 Oct 2015463034 Nov 2015583200 Dec 2015604926 Jan 2016618926 Feb 2016641862 Mar 2016673634 Apr 2016708634 May 2016752634 Jun 2016788634 Jul 2016826634 Aug 2016870634 Sep 2016

potential is assumed to be 5 million units Through iterativecalculation 119901 and 119902 in (2) are fitted

119899 (119905) = 119889119873 (119905)119889119905= minus00013 lowast [5000000 minus 119873 (119905)]+ 008395000000119873 (119905) [5000000 minus 119873 (119905)]

(6)

After the model is confirmed Matlab is used for simulatingthe fitting model to get the forecast result of BEV which isshown in Table 2

32 Simulation of BEV Based on LV Model BEV and con-ventional car (CV) are the two most popular products in thecurrent automotive market Therefore only these two kindsare discussed for forecast the future vehicle ownership inChina The LV model can be modified similar to the Bassdiffusion model the parameter 119870 represents the maximumnumber of species that can be carried by the environmentFor CV the number of Chinese civil car ownerships hasexceeded 200million According to the average per capita carownership the largest market capacity can be 400 millionThe unknown parameters involved in (4) are more than 10and two119870 values are calibratedwith the following 8 unknownparameters 119903119894 can be estimated by the average growth ratemethod Based on the observed data of BEV and CV 1199031 is


Table 2 Simulated result of BEV based on Bass model

BEV (simulated data) BEV (observed data) Month266568 273927 Jan 2015282173 279972 Feb 2015299006 294094 Mar 2015317153 302414 Apr 2015336704 313270 May 2015357755 340224 Jun 2015380396 357062 Jul 2015404730 375962 Aug 2015430875 404054 Sep 2015458946 438370 Oct 2015489056 463034 Nov 2015521320 583200 Dec 2015555849 604926 Jan 2016592753 618926 Feb 2016632143 641862 Mar 2016674127 673634 Apr 2016718812 708634 May 2016766304 752634 Jun 2016816705 788634 Jul 2016870060 826634 Aug 2016926463 870634 Sep 2016

calculated as 00108 and 1199032 is calculated as 006054 Then theequation set can be fitted as shown in

119889119883 (119905)119889119905 = 001087 lowast 119883 (119905) (1 minus 072881198834 lowast 108 +

31561198845 lowast 106 )

119889119884 (119905)119889119905 = 006054 lowast 119884 (119905) (1 +

11201198834 lowast 108 minus

24451198845 lowast 106 )

(7)

Matlab is used for simulating the fitting model and two datagroups are listed The observed data and simulated of BEVand CV are shown in Table 3

33 Simulation Accuracy Comparison of the TwoModels Themean absolute percentage error (MAPE) as shown in (8) isdesigned for evaluating the forecast accuracy The higher theMAPE is the less accurate the model is

MAPE = 1119899119899

sum119894=1

100381610038161003816100381610038161003816100381610038161003816119886119894 minus 119886lowast119894119886119894100381610038161003816100381610038161003816100381610038161003816 lowast 100 (8)

In (8) 119886119894 is the actual observed value 119886lowast119894 is the simulatedvalue Prediction accuracy level divided by MAPE value isshown in Table 4

As a kind of new technology products electric vehicle hasentered into the mature automobile market Bass model iswidely used in the market diffusion of a single new productwhile LV model takes no less than two species into accountand it is used for forecasting less frequently In order tocompare the accuracy of these two models MAPE is used forcalculating forecasting errors

As Table 5 shows the two models have good predictionaccuracy but the Bass model is more accurate Part of the

Jan

2015

Jan

2016

Jan

2017

Jan

2018

Jan

2019

Jan

2020

Dec

202

0

Bass modelLV model

0500000

100000015000002000000250000030000003500000400000045000005000000

Figure 1 Forecasting of BEV ownership from 2017 to 2020 based onthe two models

reason is that the LV model is more complex than the Bassmodel so the variance is greater with the iterative fitting ofthe unknown parameters resulting in higher MAPE valueIn addition Bass model has only one dimension and focuseson the diffusion trend while LV model has two dimensionsandmainly describes the relationship and competing processbetween the two populations According to the MAPE valueBass model is proved to have better simulation capacitybecause of the modelrsquos precise expression

34 Forecasting of BEV Ownership from 2017 to 2020 Aftercomparison of simulation accuracy comparison the presentpaper gives the forecast of BEV ownership from 2017 to 2020as shown in Table 6 and Figure 1 From Jan 2015 to Sept 2016the simulation results are close between the twomodels whilethe forecasting results are greatly different The forecastingvalue of Bass model keeps growing rapidly while that of LVmodel increases slowly

The Bass model only considers the time series and doesnot take into account the factors that affect the developmentof new energy vehiclesMoreover the forecasting result needsthe sustainable development of the policy and the stabilityof the market environment as the guarantee condition Ifthe industrial policy and the market environment fluctuategreatly the forecasting result is no longer applicable Themaximummarket volume is assumed to be 5 million For theBass model it will be reached in 2022 while it will only reach158 million for LV model in 2022

4 Conclusion

To compare the prediction accuracy the present paper fittedthe parameters of modified Bass and the LV model The twomodels have good prediction accuracy but the Bass modelis more accurate Part of the reason is that the LV modelis more complex than the Bass model so the variance isgreater when the iterative fitting of the unknown parametersresulting in higher MAPE value In addition Bass modelhas only one dimension and focuses on the diffusion trendwhile LV model has two dimensions and mainly describes


Table 3 Simulated result of BEV and CV based on LV model

BEV(simulated data)

BEV(observed data)

CV(simulated data)

CV(observed data) Month

266567 273927 155969992 156244073 Jan 2015282173 279972 157493647 157634728 Feb 2015299006 294094 159052768 159491006 Mar 2015317153 302414 160649120 161151486 Apr 2015336704 313270 162284410 162749930 May 2015357755 340224 163960281 164234376 Jun 2015380396 357062 165678480 165486138 Jul 2015404730 375962 167440505 166885738 Aug 2015430875 404054 169247482 168608846 Sep 2015458946 438370 171100413 170511430 Oct 2015489056 463034 173000174 172683566 Nov 2015521320 583200 174947514 175005500 Dec 2015555849 604926 176943055 177373774 Jan 2016592753 618926 178987296 179056774 Feb 2016632143 641862 181080607 181473838 Mar 2016674127 673634 183223234 183564066 Apr 2016718812 708634 185415293 185621066 May 2016766304 752634 187656780 187648066 Jun 2016816705 788634 189947559 189464066 Jul 2016870060 826634 192287371 191497066 Aug 2016926463 870634 194675689 194017066 Sep 2016

Table 4 Prediction accuracy level divided by MAPE value

MAPE Prediction capabilitylt10 Highly accurate10ndash20 Good20ndash50 Reasonablegt50 Inaccurate

Table 5 MAPE Comparison between LV and Bass model

MAPEBass 46LV 91

Table 6 Forecasting of BEV ownership from 2017 to 2020 based onthe two models

2017 2018 2019 2020Bass model 2138387 3325383 4209993 4674325LV model 1008591 1134000 1263081 1410821

the relationship and competing process between the twopopulations According to the MAPE value Bass model isproved to have better simulation capacity because of themodelrsquos precise expression

There are still some differences between the results ofthe prediction and the observed formulation On the onehand the new energy vehicles in the Chinese market are

still in the policy support phase The growth of new energyvehicles depends largely on the amount of subsidies andthe corresponding tax benefits policy The correspondentfacilities cannot dispel consumer concerns Therefore theexisting data based on time series has strong policy relevanceOn the other hand to some extent the new energy vehicleshave technical defects Therefore the forecasting methodscannot adapt to the new energy vehicles after the technicalimprovement After a comparative study it is found thatalthough the Bass model is not able to consider the externalfactors but its prediction accuracy is better than the LVmodel

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This study is supported by theNationalNatural Science Foun-dation of China (51508432) the Natural Science Foundationof Hubei (2014CFB850) and the Fundamental ResearchFunds for the Central Universities of China (2014-IV-034)

References

[1] W Yini ldquoCar ownership forecast in Chinamdashan analysis basedon Gompertz equationrdquo Research on Financial and EconomicIssues vol 11 pp 44ndash50 2005


[2] J Gu F Qi and JWu ldquoForecasting on Chinarsquos civil automobile-owned based on Gompertz modelrdquo Technology Economics vol29 no 1 pp 57ndash62 2010

[3] J Ma N Wang and D Kong ldquoMarket forecasting modelingstudy for new energy vehicle based on AHP and logit regres-sionrdquo Journal of Tongji University vol 37 no 8 pp 1079ndash10842009

[4] Z Yue D Zhang K Cai et al ldquoResearch on the developmenttrend of new energy vehicle marketrdquo Science and TechnologyEconomic Guide vol 33 pp 47ndash49 2016

[5] M Barth P Jugert and I Fritsche ldquoStill underdetected ndash socialnorms and collective efficacy predict the acceptance of electricvehicles in Germanyrdquo Transportation Research Part F TrafficPsychology and Behaviour vol 37 pp 64ndash77 2016

[6] B Prateek and M K Kara ldquoForecasting Americans long-termadoption of connected and autonomous vehicle technologiesrdquoTransportation Research Part A vol 95 pp 49ndash63 2017

[7] ZMing Z Fanxiao Z Xiaoli and X Song ldquoForecast of electricvehicles in China based on bass modelrdquo Electric Power vol 46no 1 pp 37ndash39 2013

[8] R Bin S Luning and Y Jianxin ldquoDevelopment of a generalizedbass model for Chinese electric vehicles based on innovationdiffusion theoryrdquo Ruankexue vol 27 no 4 pp 17ndash22 2013

[9] L Yingqi W Meng andW Jingyu ldquoThe predictive research onChinarsquos new energy vehicles marketrdquo CNKI Journal vol 37 no4 pp 87ndash91 2016

[10] A Marasco A Picucci and A Romano ldquoMarket share dynam-ics using Lotka-Volterra modelsrdquo Technological Forecasting andSocial Change vol 105 pp 49ndash62 2016

[11] T Modis ldquoInsights on competition from a science-based anal-ysisrdquo Advances in Psychology Research vol 88 pp 1ndash25 2011

[12] S-Y Chiang ldquoAn application of Lotka-Volterra model to Tai-wanrsquos transition from 200 mm to 300 mm silicon wafersrdquoTechnological Forecasting and Social Change vol 79 no 2 pp383ndash392 2012

[13] S A Morris and D Pratt ldquoAnalysis of the Lotka-Volterracompetition equations as a technological substitution modelrdquoTechnological Forecasting and Social Change vol 70 no 2 pp103ndash133 2003

[14] V B Kreng and H T Wang ldquoThe interaction of the marketcompetition between LCD TV and PDP TVrdquo Computers andIndustrial Engineering vol 57 no 4 pp 1210ndash1217 2009

[15] H-C Hung Y-S Tsai and M-C Wu ldquoA modified Lotka-Volterra model for competition forecasting in Taiwanrsquos retailindustryrdquoComputers and Industrial Engineering vol 77 pp 70ndash79 2014

[16] H-T Wang and T-C Wang ldquoApplication of the grey Lotka-Volterra model to forecast the diffusion and competitionanalysis of the TV and smartphone industriesrdquo TechnologicalForecasting and Social Change vol 106 no 5 pp 37ndash44 2016

[17] C Haijun L Xijuan L Jie et al ldquoEstimation the parameters ofLotka-Volterra model based on the grey direct modeling and itsapplicationrdquo Mathematics in Practices and Theory vol 41 no23 pp 108ndash113 2011

[18] L Wu S Liu and Y Wang ldquoGrey Lotka-Volterra model and itsapplicationrdquo Technological Forecasting and Social Change vol79 no 9 pp 1720ndash1730 2012

[19] J Massiania and A Gohsb ldquoThe choice of Bass model coeffi-cients to forecast diffusion for innovative products an empiricalinvestigation for new automotive technologiesrdquo Research inTransportation Economics vol 50 pp 17ndash28 2015

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



model to predict the trend of the whole new energy vehiclesindustry pure electric vehicles and plug-in hybrid vehiclesindustry [9] In view of the limited historical data in theestimation of the parameters of the Bass model of the electricvehicle in China the parameters of BEV in China weredetermined by comparing the parameters of other consumerproducts In summary some achievements have been madein the application of Bass model in the prediction of newenergy automotive industry

Compared with Bass model LV model has been used forpredicting market share transition of silicon wafers technol-ogy substitution and market competition which seems tobe a natural way of portraying the competitive struggle ina market [10ndash15] H-T Wang and T-C Wang (2016) usedLV model to study on the diffusion and competition of TVand smart-phone industries [16]Haijun et al (2011) proposeda method for estimation the parameters of Lotka-Volterramodel based on the grey directmodeling [17]Wu et al (2012)analyzed the long-term relationship between the two vari-ables to predict the values of two variables in the social systemor economic system [18] In the present paper Lotka-Volterramodel has been used to predict the ownership of CVs andBEVs Lotka-Volterra model is a classical method to simulatenatural ecosystems especially when it is used for populationecosystem This model and its mathematical expressions arewidely applied for describing different populations compet-ing for environment resources and the relations among themThere are three classical relations of Lotka-Volterra modelThey are competitive relation predator-prey relation andsymbiotic relation The model can be used for predictingcertain systemrsquos change in the future and speculate certainpopulationsrsquo growth or extinction What is more this modelcan explain how the system changes The relations amongthese three type vehicles are unknown The real relationsneed to be simulated and then verified Lotka-Volterra modelfocuses on the relation between homogeneous species LVmodel has been used to forecast the development of otherindustry such as TV and mobile phone We try to explorethe forecasting accuracy between LV models initially basedon the benchmark of Bass model

2 Methodology

21 Bass Model Bass model is a model for the predictionof the market share of the innovation products technologyadoption and diffusion The core assumption of Bass modelis that the adoption of innovator is independent of othermembers of the social system However the time for theadoption of the new product is influenced by the pressure ofthe social system and the pressure increases with the increaseof the number of people who use it earlierThe potential usersare called imitator For example Massiania and Gohsb (2015)investigated the potential for the use of the Bass diffusionmodel to promote the market diffusion of electric vehicles inGermany [19]

The expression of Bass diffusion model is

119899 (119905) = 119889119873 (119905)119889119905 = 119901 [119898 minus 119873 (119905)] + 119902119898119873 (119905) [119898 minus 119873 (119905)] (1)

The meaning of the mathematical expression and parameterof (1) is explained as follows

(1) 119889119873(119905)119889119905 is the number of noncumulative adopters at119905

(2) 119873(119905) is the number of cumulative adopters at 119905(3) 119898 is the biggest marker potential

(4) 119901 is the external influence coefficient (also calledinnovation coefficient)

(5) 119902 is the internal influence coefficient (also calledimitation coefficient)

(6) 119901[119898minus119873(119905)] represents the number of adopters whosepurchase is influenced by external factors whichare called innovation adopters because they are notinfluenced by people who have already used thisproduct

(7) 119902119898 lowast 119873(119905) lowast [119898 minus 119873(119905)] represents the number ofadopters whose purchase is influenced by internalfactors which are called imitators because they areinfluenced by people who have already used thisproduct

The Bass model expresses the essence of the diffusion processwith mathematical equations which greatly simplifies theunderstanding of the diffusion of innovation The basicBass model is based on a series of important assumptionsNonetheless the basic Bass model does not consider theimpact of marketing strategy on the diffusion of innovationproducts In view of these defects Bass added decisionvariables into the Bassmodel and proposed a generalizedBassmodel

119899 (119905) = 119889119873 (119905)119889119905= 119901 [119898 minus 119873 (119905)] + 119902119898119873 (119905) [119898 minus 119873 (119905)] lowast 119909 (119905)

(2)

In (2) 119909(119905) is a modified variable which depends on decisionvariables

119909 (119905) = 1 + [ Δ119875119903 (119905)Pr (119905 minus 1)] 1205731 + [

ΔADV (119905)ADV (119905 minus 1)] 1205732 (3)

In (3) Pr(119905) represents the innovation product price on 119905ADV(119905) represents the advertisement cost for this product1205731and 1205732 are two coefficients which represent the price impactand advertisement cost impact respectively When 119909(119905) isa constant the generalized Bass model is equivalent to theoriginal Bass model

22 Lotka-Volterra Model Lotka-Volterra model is a classicalmethod to simulate natural ecosystems especially whenit is used for population ecosystem The model and itsmathematical expressions are widely applied for describingdifferent populations competing for environment resourcesand the relations among them The model can be used for




119886211198841198962 )

119889119884 (119905)119889119905 = 1199032 lowast 119884 (119905) (1 minus

119886121198831198961 minus

119886221198841198962 )

(4)


3 Data and Result



ΔPg (119905)Pg (119905 minus 1)] 1205731

+max0 [ ΔCs (119905)Cs (119905 minus 1)]1205732

(5)








(6)








31561198845 lowast 106 )

119889119884 (119905)119889119905 = 006054 lowast 119884 (119905) (1 +

11201198834 lowast 108 minus

24451198845 lowast 106 )

(7)



MAPE = 1119899119899

sum119894=1





Jan

2015

Jan

2016

Jan

2017

Jan

2018

Jan

2019

Jan

2020

Dec

202

0

Bass modelLV model

0500000

100000015000002000000250000030000003500000400000045000005000000





4 Conclusion




BEV(simulated data)

BEV(observed data)

CV(simulated data)






MAPEBass 46LV 91








Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119886211198841198962 )

119889119884 (119905)119889119905 = 1199032 lowast 119884 (119905) (1 minus

119886121198831198961 minus

119886221198841198962 )

(4)


3 Data and Result



ΔPg (119905)Pg (119905 minus 1)] 1205731

+max0 [ ΔCs (119905)Cs (119905 minus 1)]1205732

(5)








(6)








31561198845 lowast 106 )

119889119884 (119905)119889119905 = 006054 lowast 119884 (119905) (1 +

11201198834 lowast 108 minus

24451198845 lowast 106 )

(7)



MAPE = 1119899119899

sum119894=1





Jan

2015

Jan

2016

Jan

2017

Jan

2018

Jan

2019

Jan

2020

Dec

202

0

Bass modelLV model

0500000

100000015000002000000250000030000003500000400000045000005000000





4 Conclusion




BEV(simulated data)

BEV(observed data)

CV(simulated data)






MAPEBass 46LV 91








Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














31561198845 lowast 106 )

119889119884 (119905)119889119905 = 006054 lowast 119884 (119905) (1 +

11201198834 lowast 108 minus

24451198845 lowast 106 )

(7)



MAPE = 1119899119899

sum119894=1





Jan

2015

Jan

2016

Jan

2017

Jan

2018

Jan

2019

Jan

2020

Dec

202

0

Bass modelLV model

0500000

100000015000002000000250000030000003500000400000045000005000000





4 Conclusion




BEV(simulated data)

BEV(observed data)

CV(simulated data)






MAPEBass 46LV 91








Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











BEV(simulated data)

BEV(observed data)

CV(simulated data)






MAPEBass 46LV 91








Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









comparison of the short-term forecasting accuracy on battery...

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