Intrinsic differences between backward and forward vehicle simulation models
Paper in proceeding, 2020

Two common methods for predicting the energy usage in vehicles through mathematical simulation, the `backward' and the `forward' schemes, are discussed and compared in terms of what longitudinal vehicle behaviour they predict. In the backward scheme, the input driving cycle is initially assumed to be followed perfectly and therefore the vehicle speed is not a dynamic state. In the forward scheme, a driver model controls the vehicle in an attempt to follow the input driving cycle, and the vehicle speed is intrinsically a dynamic state. A theoretical study is made with a simple mathematical vehicle model, where it is shown that the two methods neither predict the same expected energy use nor energy variation. Next, the simulation model that is
used for the CO2 rating of heavy-duty trucks in Europe, VECTO, is used as an example of the backward method, and an equivalent implementation in a forward scheme is attempted. Two numerical experiments are made with these models: a detailed study of the longitudinal vehicle behaviour on a reference mission; and a study of the predicted CO2 emissions on a family of stochastically generated missions. The conclusion is that the backward method is easier to use but the forward method has a greater potential to predict realistic behaviour.

backward simulation

fuel consumption

CO2 emissions

operating cycle

forward simulation


Pär Pettersson

Chalmers, Mechanics and Maritime Sciences, Vehicle Engineering and Autonomous Systems

Bengt J H Jacobson

Chalmers, Mechanics and Maritime Sciences, Vehicle Engineering and Autonomous Systems

Fredrik Bruzelius

The Swedish National Road and Transport Research Institute (VTI)

Pär Johannesson

RISE Research Institutes of Sweden

Lars Fast

RISE Research Institutes of Sweden

IFAC Proceedings Volumes (IFAC-PapersOnline)

14746670 (ISSN)

21st IFAC World Congress
Berlin, Germany,

Operating cycle energy management (OCEAN)

Swedish Energy Agency (2013-006720), 2014-01-01 -- 2017-12-31.

COVER – Real world CO2 assessment and Vehicle enERgy efficiency

VINNOVA (2017-007895), 2018-01-01 -- 2021-12-31.

Swedish Energy Agency (2017-007895), 2018-01-01 -- 2021-12-31.


ReVeRe (Research Vehicle Resource)

Subject Categories

Vehicle Engineering



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