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

Abstract

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.

A 22:1 Compression Ratio Ammonia-Hydrogen HCCI Engine: Combustion, Load, and Emission Performances

“…To assess the ammonia-hydrogen blend operating conditions, performances, and emissions, we operated the HCCI test bench of UCLouvain. This test bench has already been described in previous studies (Bhaduri et al, 2017;Pochet et al, 2019b) and is displayed in Figure 1, together with its engine specifications.…”

“…The acquired raw data needs several post-processing steps before being suited for the engine performance analysis. The whole postprocessing process used is described in details in Pochet et al (2019b), but is summarized here. For each operating condition, 100 consecutive cycles are registered, with a resolution of 0.1 CAD.…”

“…We obtained the uncertainties on the engine inputs and outputs of interest following the whole methodology derived by the authors in Pochet et al (2019b), except for the uncertainties on the NH 3 , NO, and NO 2 exhaust concentrations that are derived in the Supplementary Materials. The computed maximal and minimal uncertainties of the engine inputs and outputs (encompassing sensor calibrations, the acquisition system, the post-processing methods, and the statistical analysis data) encountered during the whole UCLouvain study are reported in Table 2.…”

Experimental and numerical investigation of methane combustion in a HCCI engine under enriched oxygen conditions

“…The adopted methodology for uncertainty analysis has been extensively explained in [34]. In Table 3 the average uncertainties on the most significant quantities are reported.…”

Emission Measurement of Buses Fueled with Biodiesel Blends during On-Road Testing

“…Considering that these 6 (or 7 for NOx emissions) measurements are uncorrelated and that the second order derivative factor is negligible, the global uncertainty of the physical quantity E gkm = f(W 1 ,...,W 6/7 ) is expressed with Equation (4) [27]. A normal distribution is considered for the rate of emission per kilometre E gkm of one SORT cycle.…”