Title: Application of linearised hierarchical models to indicated torque modelling for a turbocharged engine

Authors: Mark Cary; Byron Mason; Peter Schaal

Addresses: Ford Motor Company, Dunton Technical Centre, GB 15/2A-G13-C, Laindon, Basildon, Essex, SS15 6EE, UK ' Department of Aerospace and Automotive Engineering, Loughborough University, Stewart Miller Building, University Way, Loughborough, LE11 3TU, UK ' Department of Aerospace and Automotive Engineering, Loughborough University, Stewart Miller Building, University Way, Loughborough, LE11 3TU, UK

Abstract: This paper shows the application of linearised hierarchical models to the estimation of indicated torque data obtained from a large scale engine mapping experiment conducted on a turbocharged spark-ignition engine. Unlike previous studies that have utilised two-stage regression techniques for analysis, the use of linearised methods provides a framework to directly address the issues of sparseness of sweep-specific data and mixed effects modelling. In addition, spline models are presented at both levels of the model hierarchy that possess the required smoothness, are capable of capturing physical behaviour and simultaneously yield models sufficiently accurate for calibration work. The paper considers, at length, the required model fitting procedures which are founded on an iterative generalised least-squares approach. Further, a model building case study is presented addressing the issue of which factors should be modelled as fixed or mixed. This utilises information criteria to identify the most parsimonious model. Finally, the fit provided by the model to the data is demonstrated, which is seen to satisfy the engineering measure of success applicable to the application.

Keywords: linearised hierarchal models; two-stage regression; engine mapping; engine calibration; data sparseness; torque modelling; turbocharged engines; spark ignition engine; SI engines; model fitting; iterative generalised least squares.

DOI: 10.1504/IJPT.2016.081798

International Journal of Powertrains, 2016 Vol.5 No.4, pp.395 - 411

Received: 24 Nov 2014
Accepted: 30 Sep 2015
Published online: 26 Jan 2017 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article