Uncertainty quantification from raw measurements to post-processed data: A general methodology and its application to a homogeneous-charge compression–ignition engine

Internal combustion engines have been improved for many decades. Yet, complex phenomena are now resorted to, for which any optimum might be unstable: noise, low-temperature heat release timing, stratification, pollutant sweet spots, and so on. In order to make reliable statements on an improvement, one must specify the uncertainty related to it. Still, uncertainty quantification is generally missing in the piston engine experimental literature. Therefore, we detailed a mathematical methodology to obtain any engine parameter uncertainty and then used it to derive the uncertainty expressions of the physical quantities of the most generic homogeneous-charge compression–ignition research engine (mass-flow-induced mixture with Formula: see text fuel). We then applied those expressions on an existing hydrogen homogeneous-charge compression–ignition test bench. This includes the uncertainty propagation chain from sensor specifications, user calibrations, intake control, in-cylinder processes, and post-processing techniques. Directly measured physical quantities have uncertainties of around 1%, depending on the sensor quality (e.g. pressure, volume), but indirectly measured quantities relying on modelled parameters have uncertainties higher than 5% (e.g. wall heat losses, in-cylinder temperature, gross heat release, pressure rise rate). Other findings that such an analysis can bring relate, for example, to the physical quantities driving the uncertainty and to the ones that can be neglected. In the case of the homogeneous-charge compression–ignition engine considered, the effects of blow-by, bottle purity and air moisture content were found negligible; the post-processing for effective compression ratio, effective in-cylinder temperature, and top dead centre offset were found essential; and the pressure and volume uncertainties were found to be the main drivers to a large extent. The obtained numeric values serve the general purpose of alerting the experimenter on uncertainty order of magnitudes. The developed methodology shall be used and adapted by the experimenter willing to study the uncertainty propagation in their setup or willing to assess the adequacy of a sensor performance.