Matthias Waechter

Stochastic analysis of different rough surfaces

Abstract.This paper shows in detail the application of a new stochastic approach for the characterization of surface height profiles, which is based on the theory of Markov processes. With this analysis we achieve a characterization of the scale dependent complexity of surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method is applied to several surfaces with different properties, for the purpose of showing the utility of this method in more detail. In particular we show evidence of the Markov properties, and we estimate the parameters of the Fokker-Planck equation by pure, parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction of the conditional probability density functions. The results are compared with those from the analysis of multi-affine and extended multi-affine scaling properties which is often used for surface topographies. The different surface structures analysed here show in detail the advantages and disadvantages of these methods.

A Multibody Model for the Simulation of Bicycle Suspension Systems

The paper describes a two-dimensional mathematical model for the motion of a bicycle-rider system with wheel suspensions. It focusses on the prediction of vibrational stress on the rider due to uneven track. The model was evaluated by comparing its predictions with measuring data concerning weighted accelerations on the human body, depending on various bicycle designs and road surfaces. For the intended purpose the predictions for vibrational stress and vibrational behaviour are sufficiently precise, and the model turns out to be adequate for designing and developing bicycle suspensions.

The footprint of atmospheric turbulence in power grid frequency measurements

Fluctuating wind energy makes a stable grid operation challenging. Due to the direct contact with atmospheric turbulence, intermittent short-term variations in the wind speed are converted to power fluctuations that cause transient imbalances in the grid. We investigate the impact of wind energy feed-in on short-term fluctuations in the frequency of the public power grid, which we have measured in our local distribution grid. By conditioning on wind power production data, provided by the ENTSO-E transparency platform, we demonstrate that wind energy feed-in has a measurable effect on frequency increment statistics for short time scales (< 1 sec) that are below the activation time of frequency control. Our results are in accordance with previous numerical studies of self-organized synchronization in power grids under intermittent perturbation and rise new challenges for a stable operation of future power grids fed by a high share of renewable generation.