Tribology and nonlinear time series analysis are the main subject of my thesis. In nature, the Iinear events are the exception; few real systems follow linear laws exclusively. At the opposite, nonlinearities are involved in all natural processes (chemical reactions, mechanical engineering, economies, etc.). Systems involving dry friction are one of the most common examples, with a variety of applications. In braking systems, friction is found to cause many problems of instability. Types of instabilities addressed in this case are those of friction induced vibrations. The Modalsens method is precisely based on the exploitation of those instabilities: a sensor- a thin blade- rubs on a sample and friction induces its vibrations. Post-processing by Fourier analysis of the vibration signal can separate several components of the sample related to the relief, friction and compressibility of asperities. However, in the case of Modalsens method, Fourier analysis, which is a linear tool, acts like eyeglasses through which the signal is observed and that filters out all non-linear components. Our contribution is in this perspective: the establishment of an efficient method of nonlinear signal analysis to better understand the dynamic behavior of Modalsens and also generate new estimators for the characterization of textile surfaces. Hence, a model of contact on fibrous surface is proposed based on the obtained results.
