Semi-empirical modeling of volumetric efficiency in engines equipped with variable valve timing system

Abstract

Volumetric efficiency and air charge estimation is one of the most demanding tasks in control of today’s internal combustion engines. Specifically, using three-way catalytic converter involves strict control of the air/fuel ratio around the stoichiometric point and hence requires an accurate model for air charge estimation. However, high degrees of complexity and nonlinearity of the gas flow in the internal combustion engine make air charge estimation a challenging task. This is more obvious in engines with variable valve timing systems in which gas flow is more complex and depends on more functional variables. This results in models that are either quite empirical (such as look-up tables), not having interpretability and extrapolation capability, or physically based models which are not appropriate for onboard applications. Solving these problems, a novel semi-empirical model was proposed in this work which only needed engine speed, load, and valves timings for volumetric efficiency prediction. The accuracy and generalizability of the model is shown by its test on numerical and experimental data from three distinct engines. Normalized test errors are 0.0316, 0.0152 and 0.24 for the three engines, respectively. Also the performance and complexity of the model were compared with neural networks as typical black box models. While the complexity of the model is less than half of the complexity of neural networks, and its computational cost is approximately 0.12 of that of neural networks and its prediction capability in the considered case studies is usually more. These results show the superiority of the proposed model over conventional black box models such as neural networks in terms of accuracy, generalizability and computational cost.