From noisy data to physical knowledge: Applications to wind energy and nanosystems
Final Report Abstract
The main goals of the cooperation, i.e. development of advanced analysis and reconstruction methods for real-world stochastic processes as well as their application to empirical data, have been achieved. The main scientific results can be divided into the fields of advanced statistics and extreme events such as gusts in wind data on the one hand (research questions Q1, Q2) and the connection of turbulence research to recent fundamental results in statistical physics (research question Q3). The statistics of atmospheric wind speeds is known to be extremely complex, namely highly nonstationary and dominated by long-range and higher-order correlations. The model derived captures important and practically relevant aspects of these statistics by a rather simple mathematical concept. These aspects are especially two-point statistics of higher orders. Moreover, the parameters of the model can be directly derived from empirical data, which facilitates its practical application. Focussing on the phenomenon of wind gusts, it is necessary to consider the statistics of more than two points. Wind gusts are multi-point structures embedded in the turbulent atmospheric flow and hence require a multi-point statistical ansatz. Current industry standards in wind energy define a wind gust as a Mexican-hat shape, which implies at least a five-point correlation. We could show evidence that these Mexican-hat structures are not a special feature of atmospheric wind, but are present with comparable (however very low) probability in surrogate data with strongly simplified statistics. This result raises the question how a more meaningful and realistic definition of a wind gust could be proposed. This question is relevant both for the more fundamental atmospheric sciences as well as for industrial applications, e.g., in wind energy and structural engineering. The work on question Q3 was investigating the statistics of turbulence rather as a fundamental problem. Previous results about the validity of the integral fluctuation theorem in turbulence could be confirmed and investigated in more detail. It was found that also another, more strict relation is partly applicable in turbulence, namely the detailed fluctuation theorem. While the integral fluctuation theorem constitutes an average relation between positive and negative entropy fluctuations, the detailed fluctuation theorem relates those fluctuations for special, fixed entropy values, rather than for the average. Moreover, it turned out that the entropy gain of turbulent fluctuations is an efficient measure to separate statistical fluctuations from coherent structures in turbulence. This aspect allows for a connection to the problem of wind gusts discussed above. In the future we want to investigate the possibility of a new understanding and definition of wind gusts based on fundamental thermodynamic concepts. This would have the advantage of both being based on first principles and being more realistic and relevant than the current concept.
Publications
- On the existence and characterization of extreme events in wind data, Proceedings of the 7. European Conf. on Renewable Energy Systems, pp 320-327 (2019)
C.A. Garcia, P.G. Lind, M. Wächter, A. Otero, J. Peinke
(See online at https://doi.org/10.1038/ncomms12466) - The Fokker-Planck Approach to Complex Spatiotemporal Disordered Systems, StatPhys 27, Buenos Aires, Argentina, 8.–12.7.2019
M. Wächter, A. Hadjihosseini, A. Fuchs, C. Behnken, M. R. R. Tabar, J. Peinke
(See online at https://doi.org/10.1146/annurev-conmatphys-033117-054252) - Wind Speed Modeling by Nested ARIMA Processes, Energies 12(1) 69 (2019)
S.-K.Sim, P.Maass, P.G.Lind
(See online at https://doi.org/10.3390/en12010069)
