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

Abstract

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.

Analysis of pressure fluctuations in a natural gas engine under lean burn conditions

“…In order to develop effective control strategies for efficient combustion, it is important to understand the dynamics of cycle-to-cycle pressure variations [4][5][6]. Earlier studies on pressure fluctuations were carried out primarily in gasoline and diesel engines [7][8][9][10][11][12][13][14][15][16][17][18]. Using the methods of nonlinear dynamics and other techniques, researchers have investigated the complex dynamics of pressure fluctuations in these engines, including the possibility of chaotic oscillations [10][11][12][13][14][15][16].…”

“…Earlier studies on pressure fluctuations were carried out primarily in gasoline and diesel engines [7][8][9][10][11][12][13][14][15][16][17][18]. Using the methods of nonlinear dynamics and other techniques, researchers have investigated the complex dynamics of pressure fluctuations in these engines, including the possibility of chaotic oscillations [10][11][12][13][14][15][16]. The dynamics of pressure variations in natural gas-fired engines have also been analyzed by similar methods [19][20][21][22][23].…”

Analysis of cycle-to-cycle variation and non-uniformity of energy production: Tests on individual cylinders of a radial piston engine

“…It can be attributed not only to the cycle-to-cycle variations of each cylinder [1,2,3] but also to each cylinder's operating under different conditions. Considering the design of such engines, one can argue that following factors have an impact on the combustion process and performance of each cylinder:…”

<title>Sensor system for heart sound biomonitor</title>

“…The concept of a phase space representation of a signal is presented in Use of the Nonlinear Dynamical System Theory to Study Cycle to Cycle Variations from Spark Ignition Engine Pressure Data [7]. Theoretically, the phase space diagram of a signal is a plot of the rate of change (time derivative) of the signal against the original signal.…”