Interpretation of cyclic combustion variations in internal combustion engines using recurrence quantification analysis

Dual fuel combustion is a promising solution to lowering engine emissions and enabling higher fuel flexibility. High cyclic variability is one of the main challenges of dual fuel combustion which can compromise emissions, operational stability, and drivability. Recurrence quantification analysis (RQA) is a potent tool for the quantification of cyclic variability, however the application of RQA to engine cylinder pressure data represents methodological challenges. In this work, a systematic RQA approach for cyclic pressure variations is proposed with two main contributions: (1) a methodology to determine RQA parameters to capture inter-cycle recurrences, and (2) a sliding window technique to enable real-time crank-angle-resolved analysis. This methodology was demonstrated using four firing conditions with increased cyclic variability from the most stable neat diesel case to highly unstable dual fuel cases with increasing percentage of natural gas substitution. Phase-space reconstruction enabled qualitative investigation using recurrence plots. The results showed that RQA can capture nuances in the cyclic dynamics not readily captured using averaged integrated quantities such as the indicated mean effective pressure, cumulative heat release, or combustion phasing. The median recurrence rate (RR) was shown to consistently decrease with increased cyclic variability. Determinism (DET) decreases then increases with higher cyclic variability. This finding reveals the paradox that lower repeatability (or RR) does not necessarily lead to lower predictability (or DET) as is sometimes the case with partially misfiring cycles being followed by more robust recovery cycles. These results can have significant implications for real-time cycle-by-cycle engine control.