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Author: Braun, Tobias ×

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    Correlated power time series of individual wind turbines: A data driven model approach
    (Woodbury, NY : American Inst. of Physics, 2020) Braun, Tobias; Waechter, Matthias; Peinke, Joachim; Guhr, Thomas
    Wind farms can be regarded as complex systems that are, on the one hand, coupled to the nonlinear, stochastic characteristics of weather and, on the other hand, strongly influenced by supervisory control mechanisms. One crucial problem in this context today is the predictability of wind energy as an intermittent renewable resource with additional non-stationary nature. In this context, we analyze the power time series measured in an offshore wind farm for a total period of one year with a time resolution of 10 min. Applying detrended fluctuation analysis, we characterize the autocorrelation of power time series and find a Hurst exponent in the persistent regime with crossover behavior. To enrich the modeling perspective of complex large wind energy systems, we develop a stochastic reduced-form model of power time series. The observed transitions between two dominating power generation phases are reflected by a bistable deterministic component, while correlated stochastic fluctuations account for the identified persistence. The model succeeds to qualitatively reproduce several empirical characteristics such as the autocorrelation function and the bimodal probability density function. © 2020 Author(s).
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    Analysing Interlinked Frequency Dynamics of the Urban Acoustic Environment
    (Basel : MDPI AG, 2022) Haselhoff, Timo; Braun, Tobias; Hornberg, Jonas; Lawrence, Bryce T.; Ahmed, Salman; Gruehn, Dietwald; Moebus, Susanne
    As sustainable metropolitan regions require more densely built-up areas, a comprehensive understanding of the urban acoustic environment (AE) is needed. However, comprehensive datasets of the urban AE and well-established research methods for the AE are scarce. Datasets of audio recordings tend to be large and require a lot of storage space as well as computationally expensive analyses. Thus, knowledge about the long-term urban AE is limited. In recent years, however, these limitations have been steadily overcome, allowing a more comprehensive analysis of the urban AE. In this respect, the objective of this work is to contribute to a better understanding of the time-frequency domain of the urban AE, analysing automatic audio recordings from nine urban settings over ten months. We compute median power spectra as well as normalised spectrograms for all settings. Additionally, we demonstrate the use of frequency correlation matrices (FCMs) as a novel approach to access large audio datasets. Our results show site-dependent patterns in frequency dynamics. Normalised spectrograms reveal that frequency bins with low power hold relevant information and that the AE changes considerably over a year. We demonstrate that this information can be captured by using FCMs, which also unravel communities of interlinked frequency dynamics for all settings.
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    Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure
    (Dordrecht [u.a.] : Springer Science + Business Media B.V, 2021) Braun, Tobias; Unni, Vishnu R.; Sujith, R.I.; Kurths, Juergen; Marwan, Norbert
    We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogeneity in the temporal recurrence patterns at all relevant time scales. We demonstrate the potential of the proposed method when applied to empirical data, namely time series of acoustic pressure fluctuations from a turbulent combustor. Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots. Furthermore, it contributes to a better distinction between stable operation and near blowout states of combustors.
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    Recurrence flow measure of nonlinear dependence
    (Berlin ; Heidelberg : Springer, 2022) Braun, Tobias; Kraemer, K. Hauke; Marwan, Norbert
    Couplings in complex real-world systems are often nonlinear and scale dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a high-dimensional nonlinear system. We propose a recurrence-based dependence measure that quantifies the relationship between multiple time series based on the predictability of their joint evolution. The statistical analysis of recurrence plots (RPs) is a powerful framework in nonlinear time series analysis that has proven to be effective in addressing many fundamental problems, e.g., regime shift detection and identification of couplings. The recurrence flow through an RP exploits artifacts in the formation of diagonal lines, a structure in RPs that reflects periods of predictable dynamics. Using time-delayed variables of a deterministic uni-/multivariate system, lagged dependencies with potentially many time scales can be captured by the recurrence flow measure. Given an RP, no parameters are required for its computation. We showcase the scope of the method for quantifying lagged nonlinear correlations and put a focus on the delay selection problem in time-delay embedding which is often used for attractor reconstruction. The recurrence flow measure of dependence helps to identify non-uniform delays and appears as a promising foundation for a recurrence-based state space reconstruction algorithm.