This article discusses highly flexible and accurate physics-based mean value modeling (MVM) for internal combustion engines and its wide applicability towards virtual vehicle calibration. The requirement to fulfill the challenging Real Driving Emissions (RDE) standards has significantly increased the demand for precise engine models, especially models regarding pollutant emissions and fuel economy. This has led to a large increase in effort required for precise engine modeling and robust model calibration. Two best-practice engine modeling approaches will be introduced here to satisfy these requirements. These are the exclusive MVM approach, and a combination of MVM and a Design of Experiments (DOE) model for heterogeneous multi-domain engine systems. Both are evaluated using multiple engine operating conditions, transient cycles and different engines in order to highlight the practicability of MVM for a Hardware-in-the-Loop (HiL) virtual calibration platform and the consistency of extrapolated simulation results in all conditions.
The study demonstrates the application of both methods to establish adequate modeling approaches. These approaches enable the optimal trade-off between real-time computation, model complexity and effort required for model training. The proper choice of a model often depends on various project boundaries, such as the accessibility of base engine measurements for the characterization of the thermodynamic and kinetic processes in the engine sub-models. Additionally, the coverage of required phenomena for virtual engines is strongly related to the type of calibration tasks to be conducted on a HiL setup. As an example, the full MVM and the adapted air path MVM, integrated with a Gaussian process DOE in-cylinder combustion model, are introduced to meet diverse requirements from the calibration field. The further focus of the paper considers the optimization of a base model and its calibration in order to produce consistent simulation results, when compared with various driving cycles under extended environmental and various transient conditions. Also, the performance of scalable MVM for other hardware will be validated in the paper using a different reference engine application.