Use of the Nonlinear Dynamical System Theory to Study Cycle-to-Cycle Variations from Spark Ignition Engine Pressure Data

Cycle-to-cycle variations in the pressure evolution within the cylinder of a spark ignition engine has long been recognized as a phenomenon of considerable importance. In this work, use of tools borrowed to the nonlinear dynamical system theory to investigate the time evolution of the cylinder pressure is explored. By computing a divergence rate between different pressure cycles versus crank angle, four phases during the combustion cycle are exhibited. These four phases may be identified with the four common phases evidenced by burn rate calculations [1]. Starting from phase portraits and using Poincaré sections, we also study correlations between peak pressures, IMEP and the durations from ignition to appearance of a flame kernel. Accounting for the fact that, during the ignition phase of the combustion cycle, trajectories in a plane projection of the reconstructed phase portrait associated with cycles in the case of motored engine cannot be distinguished from trajectories corresponding to combustion cycles, we estimate the duration of the ignition phase without any prior assumption on the combustion processes. Fluctuations of ignition phase lengths have been found to be correlated with IMEP standard deviations.