Application of stochastic design optimization to a passenger car diesel engine to reduce emission spread in a vehicle fleet

This paper demonstrates the advantages of stochastic design optimization on a passenger car diesel engine: the emission distribution in the vehicle fleet can be significantly reduced by optimizing the base engine calibration taking into account component tolerances. This paper is an extension to the work presented in [25]. The conventional calibration approach of using empirical safety coefficients is replaced by explicitly taking into account the uncertainty stemming from manufacturing tolerances. The method enables us to treat low-emission spread in a fleet as an optimization target. This process enables a more robust design and helps to avoid recalibration steps that potentially generate high costs. The method consists of four steps: an initial uncertainty analysis, which accounts for engine component tolerances and determines the underlying parameter uncertainty of the engine model—with parameter uncertainty being deviations in the model parameters resulting from component tolerances. Followed by a measurement campaign according to the design of experiments principles, the training of a stochastic engine model and the solving a stochastic optimization problem. The latter two are discussed in more detail. First, the stochastic models are validated on transient testbed measurements with different setups, which are subject to uncertainty. The model error for both engine-out particulate matter and nitrogen oxides (\({\text{NO}}_{{ x}}\)) is extremely low. Then, stochastic optimization is performed on a calibration task aiming to minimize engine-out PM for the entire fleet while ensuring that the \({\text{NO}}_{{ x}}\) emission remains below a given upper threshold, again for the entire fleet. Boundary constraints and smoothness constraints are employed to ensure feasibility and smooth engine maps. The optimization results are compared to the original calibration of the test engine—both for a representative nominal engine and the expected fleet behavior. The results show a significant improvement in engine-out PM while complying with the imposed constraints, including the \({\text{NO}}_{{ x}}\) emission limit for the entire fleet.