Abstract

Many simulation models representing the longitudinal dynamics of a train are based on a single point-mass description. This leads to a second-order nonlinear ordinary differential equation, together with algebraic relationships. More complex multi-mass models may be used for models representing long trains involving many separate vehicles. However, in both cases, accuracy is limited by important underlying assumptions, approximations and parametric uncertainties. Another important aspect of train models concerns the direction of information flow. Input variables within conventional train models may represent power or tractive force, with acceleration, speed and distance travelled as output variables. However, inverse simulation methods can also be used, with the required speed or distance as inputs and tractive force, power, or energy as outputs. This allows energy requirements to be established for a given schedule and is useful when investigating fuel or energy economy. Inverse methods can also be used in powertrain design, such as for hybrid hydrogen fuel-cell/battery-electric trains. Issues of fitness for purpose are important in all such applications, both in terms of model uncertainties and in the additional insight offered by inverse simulation methods.