Intrinsic differences between backward and forward vehicle simulation models
Paul Pettersson, Bengt Jacobson, Fredrik Bruzelius, Pär Johannesson, Lars Fast
Abstract
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 the 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.