Spectral Observations of PM10 Fluctuations in the Hilbert Space

During the last 20 years, many megacities have experienced air pollution leading to negative impacts on human health. In the Caribbean region, air quality is widely affected by African dust which causes several diseases, particularly, respiratory diseases. This is why it is crucial to improve the understanding of PM10 fluctuations in order to elaborate strategies and construct tools to predict dust events. A first step consists to characterize the dynamical properties of PM10 fluctuations, for instance, to highlight possible scaling in PM10 density power spectrum. For that, the scale-invariant properties of PM10 daily time series during 6 years are investigated through the theoretical Hilbert frame. Thereafter, the Hilbert spectrum in time-frequency domain is considered. The choice of theoretical frame must be relevant. A comparative analysis is also provided between the results achieved in the Hilbert and Fourier spaces

−5/3 Kolmogorov Turbulent Behaviour and Intermittent Sustainable Energies

The massive integration of sustainable energies into electrical grids (non-interconnected or connected) is a major problem due to their stochastic character revealed by strong fluctuations at all scales. In this paper, the scaling behaviour or power law correlations and the nature of scaling behaviour of sustainable resource data such as flow velocity, atmospheric wind speed, solar global solar radiation and sustainable energy such as, wind power output, are highlighted. For the first time, Fourier power spectral densities are estimated for each dataset. We show that the power spectrum densities obtained are close to the 5/3 Kolmogorov spectrum. Furthermore, the multifractal and intermittent properties of sustainable resource and energy data have been revealed by the concavity of the scaling exponent function. The proposed analysis frame allows a full description of fluctuations of processes considered. A good knowledge of the dynamic of fluctuations is crucial to management of the integration of sustainable energies into a grid

Scaling forecast models for wind turbulence and wind turbine power intermittency

The intermittency of the wind turbine power remains an important issue for the massive development of this renewable energy. The power variability of the produced electricity are inherent to the wind variations, thus the turbulence. The energy peaks injected in the electric grid produce a supplementary difficulty in the energy distribution management. Hence, a correct forecast of the wind power in the short and middle term is needed due to the high unpredictability of the intermittency phenomenon. We consider a statistical approach through the analysis and characterization of stochastic fluctuations. The theoretical framework is the multifractal energy cascades. The tools and methods aim to study the influence of the fully developed turbulence on a horizontal three-blade wind turbine. Here, we consider simultaneous input/output data coming from three wind turbines, two of which have direct drive technology. Those turbines are producing energy in real exploitation conditions and allow to test our forecast models of power production at a different time horizons. Two forecast models were developed based on two physical principles observed in the wind and the power time series: the scaling properties on the one hand and the intermittency in the wind power increments on the other. The first tool is related to the intermittency through a multifractal lognormal fit of the power fluctuations. The second tool is based on an analogy of the power scaling properties with a fractional brownian motion. Indeed, an inner long-term memory is found in both time series. Both models show encouraging results since a correct tendency of the signal is respected over different time scales. Those tools are first steps to a search of efficient forecasting approaches for grid adaptation facing the wind energy fluctuations

Multifractal characterisation of particulate matter (PM10) time series in the Caribbean basin using visibility graphs

Datos de investigación disponibles en: http://www.gwadair.frA good knowledge of pollutant time series behavior is fundamental to elaborate strategies and construct tools to protect human health. In Caribbean area, air quality is frequently deteriorated by the transport of African dust. In the literature, it is well known that exposure to particulate matter with an aerodynamic diameter of 10 μm or less (PM10) have many adverse health effects as respiratory and cardiovascular diseases. To our knowledge, no study has yet performed an analysis of PM10 time series using complex network framework. In this study, the so-called Visibility Graph (VG) method is used to describe PM10 dynamics in Guadeloupe archipelago with a database of 11 years. Firstly, the fractal nature of PM10 time series is highlighted using degree distribution for all data, low dust season (October to April) and high dust season (May to September). Thereafter, a profound description of PM10 time series dynamics is made using multifractal analysis through two approaches, i.e. Rényi and singularity spectra. Achieved results are consistent with PM10 behavior in the Caribbean basin. Both methods showed a higher multifractality degree during the low dust season. In addition, multifractal parameters exhibited that the low dust season has the higher recurrence and the lower uniformity degrees. Lastly, centrality measures (degree, closeness and betweenness) highlighted PM10 dynamics through the year with a decay of centrality values during the high dust season. To conclude, all these results clearly showed that VG is a robust tool to describe times series properties

Stochastic Simulation of Wind Atmospheric using continuous cascade

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PDF models and synthetic model for the wind speed fluctuations based on the resolution of Langevin equation

International audienceWind energy production is very sensitive to turbulent wind speed. Thus rapid variation of wind speed due to changes in the local meteorological conditions can lead to electrical power variations of the order of the nominal power output, in particular when wind power variations on very short time scales, range at few seconds to 1 h, are considered. In small grid as they exist on islands (Guadeloupean Archipelago: French West Indies) such fluctuations can cause instabilities in case of intermediate power shortages. The developed analysis in [14] reveals three main classes of time series for the wind speed fluctuations. In this work, Probability Density Functions (PDFs) are proposed to fit the wind speed fluctuations distributions in each class. After, to simulate wind speed fluctuations sequences, we use a stochastic differential equation, the Langevin equation considering Gaussian turbulence PDF (class I), Gram–Charlier PDF (class II) and a mixture of gaussian PDF (class III). The statistical and dynamical properties of simulated wind sequences are close to those of measured wind sequences, for each clas

Classification of daily solar radiation distributions using a mixture of Dirichlet distribution

International audienceIn order to qualify the fluctuating nature of solar radiation under tropical climate, we classify daily distributions of the clearness index kt by estimating a finite mixture of Dirichlet distributions without assuming any parametric hypothesis on these daily distributions. The method is applied to solar radiation measurements performed in Guadeloupe (16°2 N, 61 W) where important fluctuations can be observed even within a short period of a few minutes. The results put in evidence four distinct classes of distributions corresponding to different types of days. The sequence of such classes can be of interest for prediction

Characterization and stochastic modelling of wind speed sequences

International audienc

Is there a causal relationship between Particulate Matter ( P M 10 ) and air Temperature data? An analysis based on the Liang–Kleeman information transfer theory

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