Chance-constrained robust co-design optimization for fuel cell hybrid electric trucks

The co-design optimization that simultaneously couples embodiment design and control design is widely applied in fuel cell hybrid electric vehicles. However, due to imperfect manufacture process, modeling simplification and uncertain parameters during vehicle operation, the optimal results obtained from a deterministic co-design optimization might not be robust to variations of parameters and optimization variables. This paper introduces a chance-constrained robust co-design optimization framework, where the chance constraint firstly translates into a deterministic constraint. The robust objective is computed as a function of the second-order approximated mean and inequality constraints are computed by shifting 3 times of their standard deviations inside of deterministic bounds. The vehicle movement in long-haul trucking application is considered as an uncertain parameter and the propagation of uncertainties to state variables are also illustrated with considerations of uncertainties in design decision variables. A deterministic and stochastic co-design problem are formulated and decomposed into two steps, i.e. electric machine sizing and sizing of fuel cell and battery as well as the energy management. A case study of a fuel cell hybrid electric long-haul truck indicates the importance of the robust approach in the joint component sizing and energy management. The uncertainties of the truck movement results in uncertainties of the battery energy and power, leading to a bigger battery capacity. The energy capacity is around 2.34 times higher than that without considering uncertainties.