Fuzzy-tree-constructed data-efficient modelling methodology for volumetric efficiency of dedicated hybrid engines

The accurate characterization of volumetric efficiency is essential for modern combustion engines to achieve better performance, lower emissions, and reduced fuel consumption. To minimize experimental effort on sample collection and maintain high-precision volumetric efficiency characterization, this paper proposes a new methodology of fuzzy-tree-constructed data-efficient modelling to precisely quantify the air mass flow through the engine. Differing from conventional data-driven modelling, this methodology introduces a hierarchical fuzzy inference tree (HFIT) with three original topologies that accommodates simplicity by combining several low-dimensional fuzzy inference systems. Driven by two derivative-free optimization algorithms, a two-step tuning process is introduced to speed up the convergence process when traversing HFIT parameters. A Gaussian distributed resampling technique is developed to screen a small number of samples with diverse engine operations to maintain sample diversity. The experimental dataset is obtained from steady-state tests carried out in a BYD 1.5L gasoline engine specially made for a hybrid powertrain. The results demonstrate that the proposed fuzzy-tree-constructed data-efficient modelling methodology performs with superior learning efficiency on volumetric efficiency characterization than those of a fuzzy inference system, a neural network, or an adaptive neuro-fuzzy inference system. Even when dataset split ratio downs to 0.2, the relative mean absolute error can be restricted to 3.18% with the help of Gaussian distributed resampling technique.