Innovative Second-Generation Wavelets Construction With Recurrent Neural Networks for Solar Radiation Forecasting

Solar radiation prediction is an important challenge for the electrical engineer because it is used to estimate the power developed by commercial photovoltaic modules. This paper deals with the problem of solar radiation prediction based on observed meteorological data. A 2-day forecast is obtained by using novel wavelet recurrent neural networks (WRNNs). In fact, these WRNNS are used to exploit the correlation between solar radiation and timescale-related variations of wind speed, humidity, and temperature. The input to the selected WRNN is provided by timescale-related bands of wavelet coefficients obtained from meteorological time series. The experimental setup available at the University of Catania, Italy, provided this information. The novelty of this approach is that the proposed WRNN performs the prediction in the wavelet domain and, in addition, also performs the inverse wavelet transform, giving the predicted signal as output. The obtained simulation results show a very low root-mean-square error compared to the results of the solar radiation prediction approaches obtained by hybrid neural networks reported in the recent literature

A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

A new unified modelling framework based on the superposition of additive submodels, functional components, and wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters problem, which can be solved using least-squares type methods. An efficient model structure determination approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to represent high-order and high dimensional non-linear systems

Observed flux density enhancement at submillimeter wavelengths during an X-class flare

We analyse the 30 October, 2004, X1.2/SF solar event that occurred in AR 10691 (N13 W18) at around 11:44 UT. Observations at 212 and 405 GHz of the Solar Submillimeter Telescope (SST), with high time resolution (5 ms), show an intense impulsive burst followed by a long-lasting thermal phase. EUV images from the Extreme Ultraviolet Imaging Telescope (SOHO/EIT) are used to identify the possible emitting sources. Data from the Radio Solar Telescope Network (RSTN) complement our spectral observations below 15 GHz. During the impulsive phase the turnover frequency is above 15.4 GHz. The long-lasting phase is analysed in terms of thermal emission and compared with GOES observations. From the ratio between the two GOES soft X-ray bands, we derive the temperature and emission measure, which is used to estimate the free-free submillimeter flux density. Good temporal agreement is found between the estimated and observed profiles, however the former is larger than the latter.Comment: 13 pages, 7 figure

Wavelet analysis of the LF radio signals collected by the European VLF/LF network from July 2009 to April 2011

In 2008, a radio receiver that works in very low frequency (VLF; 20-60 kHz) and LF (150-300 kHz) bands was developed by an Italian factory. The receiver can monitor 10 frequencies distributed in these bands, with the measurement for each of them of the electric field intensity. Since 2009, to date, six of these radio receivers have been installed throughout Europe to establish a ‘European VLF/LF Network’. At present, two of these are into operation in Italy, and the remaining four are located in Greece, Turkey, Portugal and Romania. For the present study, the LF radio data collected over about two years were analysed. At first, the day-time data and the night-time data were separated for each radio signal. Taking into account that the LF signals are characterized by ground-wave and sky-wave propagation modes, the day-time data are related to the ground wave and the night-time data to the sky wave. In this framework, the effects of solar activity and storm activity were defined in the different trends. Then, the earthquakes with M ≥5.0 that occurred over the same period were selected, as those located in a 300-km radius around each receiver/transmitter and within the 5th Fresnel zone related to each transmitter-receiver path. Where possible, the wavelet analysis was applied on the time series of the radio signal intensity, and some anomalies related to previous earthquakes were revealed. Except for some doubt in one case, success appears to have been obtained in all of the cases related to the 300 km circles in for the ground waves and the sky waves. For the Fresnel cases, success in two cases and one failure were seen in analysing the sky waves. The failure occurred in August/September, and might be related to the disturbed conditions of the ionosphere in summer

Short-term solar radiation forecasting by using an iterative combination of wavelet artificial neural networks

The information provided by accurate forecasts of solar energy time series are considered essential for performing an appropriate prediction of the electrical power that will be available in an electric system, as pointed out in Zhou et al. (2011). However, since the underlying data are highly non-stationary, it follows that to produce their accurate predictions is a very difficult assignment. In order to accomplish it, this paper proposes an iterative Combination of Wavelet Artificial Neural Networks (CWANN) which is aimed to produce short-term solar radiation time series forecasting. Basically, the CWANN method can be split into three stages: at first one, a decomposition of level p, defined in terms of a wavelet basis, of a given solar radiation time series is performed, generating r+1 Wavelet Components (WC); at second one, these r+1 WCs are individually modeled by the k different ANNs, where k>5, and the 5 best forecasts of each WC are combined by means of another ANN, producing the combined forecasts of WC; and, at third one, the combined forecasts WC are simply added, generating the forecasts of the underlying solar radiation data. An iterative algorithm is proposed for iteratively searching for the optimal values for the CWANN parameters, as we will see. In order to evaluate it, ten real solar radiation time series of Brazilian system were modeled here. In all statistical results, the CWANN method has achieved remarkable greater forecasting performances when compared with a traditional ANN (described in Section 2.1)

Wavelet analysis of the ionospheric response at mid-latitudes during the April 200 storm using magnetograms and vTEC from GPS

In this work we pursue the idea of computing a parameter that allows us to estimate the local ionospheric response to a geospheric event that triggers an ionospheric storm. For that, wavelet technique has been chosen because of its ability to analyze non-stationary signals. The advantage of the time-frequency analysis method called Wavelet Transform resides in providing information not only about the frequencies of the event but also about its location in the time series. Specifically, we compute the Scale Average Wavelet Power (SAWP) of two parameters that describe the local geomagnetic field variation at the Earth surface caused by a geospheric storm and ionospheric response to the storm event. In particular, we propose the time delay between the maximum values of SAWP applied to the vTEC (vertical Total Electron Content) and the horizontal component of the geomagnetic field (H) variations as parameters to characterize the local behavior of the ionospheric storm. We applied the parameter to the geomagnetic and ionospheric disturbances caused by a coronal mass ejection (CME) that took place on April 4, 2000. We used vTEC values computed from GPS observations and H at the surface of the Earth, measured in stations near to each GPS station chosen. The vTEC values used came from the GPS permanent stations belonging to the global IGS (International GNSS Service) network. We chose stations located at magnetic mid-latitudes. Moreover, three-longitude bands representing the ionospheric behavior at different local times (LT) were studied. Because the April 2000 storm has been extensively studied for many authors, the results are compared with those in the literature and we found a very good agreement as expected.En este trabajo perseguimos la idea de estimar un parámetro que nos permita calcular la respuesta ionosférica local a un evento geosférico desencadenante de una tormenta ionosférica. Para ello, se eligió la aplicación de la técnica ondeleta debido a su capacidad para analizar señales no estacionarias. La ventaja del método de análisis en tiempo y frecuencia llamada Transformada Ondeleta reside en el hecho de que provee información, no sólo acerca de las frecuencias del evento, sino también sobre su ubicación en la serie de tiempo. En concreto, se calcula el promedio por escalas de la potencia de la transformada ondeleta (SWAP, de su sigla en inglés Scale Average Wavelet Power) para dos parámetros que describen la respuesta local de la magnetosfera y la ionosfera a una tormenta. En particular, se propone el retraso de tiempo entre los valores máximos de SAWP aplicadas al vTEC (Contenido Electrónico Total en dirección Vertical) y la componente horizontal del campo geomagnético (H), como parámetros cuyas variaciones caracterizan el comportamiento local de la tormenta ionosférica. El parámetro propuesto se aplicó a las perturbaciones geomagnética e ionosférica causadas por una eyección de masa coronal (CME, Coronal Mass Ejection), que tuvo lugar el 4 de abril de 2000. Se utilizaron valores vTEC calculados a partir de las observaciones GPS y H en la superficie de la Tierra, medida en las estaciones cercanas a cada estación de GPS elegida. Los valores de vTEC utilizados provinieron de las estaciones GPS permanentes que pertenecen a la red del servicio internacional IGS (International GNSS Service). Entre todas, elegimos estaciones situadas en latitudes magnéticas medias. Por otra parte, estudiamos tres bandas de longitud que representan el comportamiento de la ionosfera a distintas horas locales (LT). Debido a que la tormenta de abril de 2000 ha sido ampliamente estudiada por muchos autores, los resultados se comparan con los de la literatura y nos encontramos con un muy buen acuerdo entre los datos publicados y nuestros resultados, tal y como se esperaba.Fil: Fernandez, Laura Isabel. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Meza, Amalia Margarita. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Van Zele, Maria Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias Geológicas; Argentin

Wavelets and their use

This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous proofs of mathematical statements are omitted, and the reader is just referred to corresponding literature. The multiresolution analysis and fast wavelet transform became a standard procedure for dealing with discrete wavelets. The proper choice of a wavelet and use of nonstandard matrix multiplication are often crucial for achievement of a goal. Analysis of various functions with the help of wavelets allows to reveal fractal structures, singularities etc. Wavelet transform of operator expressions helps solve some equations. In practical applications one deals often with the discretized functions, and the problem of stability of wavelet transform and corresponding numerical algorithms becomes important. After discussing all these topics we turn to practical applications of the wavelet machinery. They are so numerous that we have to limit ourselves by some examples only. The authors would be grateful for any comments which improve this review paper and move us closer to the goal proclaimed in the first phrase of the abstract.Comment: 63 pages with 22 ps-figures, to be published in Physics-Uspekh