The use of a Bayesian weighted least-squares approach to accelerate empirical engine model generation

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An alternative to the commonly used design-of-experiments (DoE) technique based on the use of prior knowledge to speed up the model generation phase of the test programme is presented. Data are gathered in areas where the prior knowledge is least accurate and is blended into an overall empirical model using a Bayesian weighted least-squares (BWLS) approach. The work demonstrates the potential of the BWLS mechanism to reduce the test effort by the incorporation of prior knowledge from neighbouring operating points. Where the prior knowledge is a good representation of the current operating point the number of test points required to allow model convergence may be half that required by a DoE approach. Conversely, the Bayesian technique with inaccurate prior knowledge can still generate an accurate model at the expense of an increased number of test points over a standard experimental design, because the prior will incorrectly influence the model. The algorithm was tested with and without an outlier detection mechanism. This mechanism proved effective in detecting and rejecting simulated outliers and retesting the spurious data point.
Original languageEnglish
Pages (from-to)366-394
JournalProceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering
Issue numberD3
Publication statusPublished - Feb 2011


  • model-based engine calibration
  • engine modelling
  • Bayesian statistics


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