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

Ji Li, Quan Zhou, Huw Williams, Pu Xu, Hongming Xu, Guoxiang Lu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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.

Original languageEnglish
Article number118534
Number of pages13
JournalApplied Energy
Early online date25 Jan 2022
Publication statusPublished - 15 Mar 2022

Bibliographical note

Funding Information:
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The present work is supported by the project entitled AI Strategy for Hybrid Engine Development. The authors gratefully acknowledge the funding provided by BYD Auto Ltd, Shenzhen City, China (Grant No.: 1001636). The authors also would like to thank the Future Engines and Fuels Lab, University of Birmingham, UK.

Publisher Copyright:
© 2022 Elsevier Ltd


  • Data resampling
  • Data-efficient modelling
  • Dedicated hybrid engine
  • Hierarchical fuzzy inference tree
  • Volumetric efficiency

ASJC Scopus subject areas

  • Building and Construction
  • Mechanical Engineering
  • Energy(all)
  • Management, Monitoring, Policy and Law


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