M.Sc. Thesis Abstract

Monitoring and Reconstruction of the Engine Speed and Cylinder Pressure Using Chaos Theory

By A. H. Haji

In recent decades the chaos theory approach to various phenomena has developed new insights in our realization of nature as well as in application fields.

In this project the attractors of engine speed and cylinder pressure of an internal combustion engine are reconstructed using embedding technique which is one of the main contributions of the chaos theory to the application fields. The reconstruction of these attractors besides providing the ability for prediction (which is accomplished in this project) and control of some features of cyclic variations can also manifest complexities and ability of the chaos theory to describe a real phenomenon.

In chapter one the phenomenon of cyclic variations in engine is introduced through brief representation of some related projects also the theoretical and empirical goals of this project are titled at the end of chapter one .

The reconstruction of time series requires acquiring data in computer, so a data acquisition board has been made and used. In chapter two specifications of this board, the engine and sensors are described.

Chapters 3 to 5 has focused on theoretical foundations required. A brief introduction to fractal geometry and its applications especially fractal dimensions some of which should be computed in reconstruction technique, is presented in chapter 3.

Chapter 4 is devoted to study some required topics of the dynamical systems and chaos theory like Poincare sections and Poincare maps, Lyapunov exponents and some routes to chaos.

In chapter 5 fundamentals of reconstruction (Takens theorems) and algorithms used in reconstruction and prediction are presented.

Finally, the results of reconstruction of engine attractors are demonstrated and discussed in chapter 6.

The results include some applicable as well as some theoretical aspects. Applicable outcomes like efficacy of Locally Constant Models in prediction of the Top Dead Center (TDC) and TDC pressure time series and theoretical results such as discussion about type of the route to Chaos based on the results of auto - mutual information function and Lyapunov exponents, consistency between low level uncertainty and relatively small Embedding dimensions, and effect of data lengths and attractor dimensions on reconstruction are remarkable. Also suggestions for further works related to this project are made at the end of this chapter.

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