Fatih Onur Hocaoglu (Anadolu University Eskisehir, Turkey), Ömer Nezih Gerek (Anadolu University Eskisehir, Turkey) and Mehmet Kurban (Anadolu University Eskisehir, Turkey)

DOI: 10.4018/978-1-59904-849-9.ch210

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TopThe prediction of hourly solar radiation data has important consequences in many solar applications (Markvart, Fragaki & Ross, 2006). Such data can be regarded as a time series and its prediction depends on accurate modeling of the stochastic process. The computation of the conditional expectation, which is in general non-linear, requires the knowledge of the high order distribution of the samples. Using a finite data, such distributions can only be estimated or fit into a pre-set stochastic model. Methods like Auto*-*Regressive (AR) prediction, Fourier Analysis (Dorvlo, 2000) Markov chains (Jain & Lungu, 2002) (Muselli, Poggi, Notton & Louche, 2001) and ARMA model (Mellit, Benghanem, Hadj Arab, & Guessoum, 2005) for designing the non-linear signal predictors are examples to this approach. The neural network (NN) approach also provides a good to the problem by utilizing the inherent adaptive nature (Elminir, Azzam, Younes, 2007). Since NNs can be trained to predict results from examples, they are able to deal with non*-*linear problems. Once the training is complete, the predictor can be set to a fixed value for further prediction at high speed. A number of researchers have worked on prediction of global solar radiation data (Kaplanis, 2006) (Bulut & Buyukalaca, 2007). In these works, the data is treated in its raw form as a 1-D time series, therefore the inter-day dependencies are not exploited. This article introduces a new and simple approach for hourly solar radiation forecasting. First, the data are rendered in a matrix to form a 2-D image-like model. As a first attempt to test the 2-D model efficiency, optimal linear image prediction filters (Gonzalez, 2002) are constructed. In order to take into account the adaptive nature for complex and non-stationary time series, NNs are also applied to the forecasting problem and results are discussed.

This article presents a two-dimensional model approach for the prediction of hourly solar radiation. Before proceeding with the prediction results, the following technical background is provided. Using the described tools, the approach is tested with optimal coefficient linear filters and artificial NNs (Hocaoglu, Gerek & Kurban, 2007).

The collected hourly solar radiation data is a 1-D discrete-time signal. In this work, we render this data in a 2-D matrix form as given in equation 1.

By inspecting the image version of the data in Fig. 1, it is easy to interpret daily and seasonal behavior of solar radiation. Dark regions of the image indicate that there is no sun shine on horizontal surface. The transition from black to white indicates that solar radiation fall on horizontal surface is increasing or decreasing. During winter time, the dawn to dusk period is shorter, producing a narrower protruding blob. Conversely, the white blob is wider during summer times, indicating that the day-time is longer. The width behavior of the white blob clearly indicates the seasonal changes of sun-light periods. The horizontal *and* vertical correlations within the 2-D data are quite pronounced. This implies that, given the vertical correlation among the same hours of consecutive days, it is beneficial to use 2-D prediction for hourly forecasting. The prediction efficiency of the proposed model is illustrated with 2-D optimum linear prediction filters and NNs.

Solar Radiation: Radiant energy emitted by the sun from a nuclear fusion reaction that creates electromagnetic energy.

Prediction Error: Difference between the actually measured and previously forcasted value of a time-series data. Commonly represented in terms of RMSE.

RMSE: Root-Mean-Squared Error. A quantitative error measure that defines the error between two sets of data as one-by-one differencing, squaring each difference, adding the squared terms, and finally taking the square root.

Optimal Coefficient Linear Filters: A linear predictor takes a linear combination of past values in a time series, and assigns this combination as the prediction value. While taking the linear combination, the scales of each past sample should be calculated in a way that the prediction error has minimum amount of energy. Such a set of scales are called optimal coefficients of a linear filter.

Backpropagation algorithm: Learning algorithm of ANNs, based on minimising the error obtained from the comparison between the outputs that the network gives after the application of a set of network inputs and the outputs it should give (the desired outputs).

2-D Data Representation: A matrix containing vertical and horizontal indexes can also be considered as a 2-D image. A 2-D representation does not have to correspond to an image acquired by a camera or an imaging device. Here, the representation is used for the compact visualization of the solar data.

Artificial Neural Networks: A network of many simple processors (“units” or “neurons”) that imitates a biological neural network. The units are connected by unidirectional communication channels, which carry numeric data. Neural networks can be trained to find nonlinear relationships in data, and are used in applications such as robotics, speech recognition, signal processing or medical diagnosis.

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Representing Non-Rigid Objects with Neural Networks
(pages 1363-1369)

José García-Rodríguez, Francisco Flórez-Revuelta, Juan Manuel García-Chamizo

$37.50

Chapter 201

A Roadmap on Updates
(pages 1370-1375)

Fernando Zacarías Flores, Dionicio Zacarías Flores, Rosalba Cuapa Canto, Luis Miguel Guzmán Muñoz

$37.50

Chapter 202

A Robot Model of Dynamic Appraisal and Response
(pages 1376-1382)

Carlos Herrera, Tom Ziemke, Thomas M. McGinnity

$37.50

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Chapter 206

Rule Engines and Agent-Based Systems
(pages 1404-1410)

Agostino Poggi, Michele Tomaiuolo

$37.50

Chapter 207

Sequence Processing with Recurrent Neural Networks
(pages 1411-1417)

Chun-Cheng Peng, George D. Magoulas

$37.50

Chapter 208

Shortening Automated Negotiation Threads via Neural Nets
(pages 1418-1425)

Ioanna Roussaki, Ioannis Papaioannou, Miltiades Anagnostou

$37.50

Chapter 209

Signed Formulae as a New Update Process
(pages 1426-1432)

Fernando Zacarías Flores, Dionicio Zacarías Flores, Rosalba Cuapa Canto, Luis Miguel Guzmán Muñoz

$37.50

Chapter 210

Solar Radiation Forecasting Model
(pages 1433-1438)

Fatih Onur Hocaoglu, Ömer Nezih Gerek, Mehmet Kurban

$37.50

Chapter 211

Speech-Based Clinical Diagnostic Systems
(pages 1439-1446)

Jesús Bernardino Alonso Hernández, Patricia Henríquez Rodríguez

$37.50

Chapter 212

State of the Art in Writer's Off-Line Identification
(pages 1447-1454)

Carlos M. Travieso González, Carlos F. Romero

$37.50

Chapter 213

State-of-the-Art on Video-Based Face Recognition
(pages 1455-1461)

Yan Yan, Yu-Jin Zhang

$37.50

Chapter 214

Stationary Density of Stochastic Search Processes
(pages 1462-1466)

Arturo Berrones, Dexmont Peña, Ricardo Sánchez

$37.50

Chapter 215

Statistical Modelling of Highly Inflective Languages
(pages 1467-1473)

Mirjam Sepesy Maucec, Zdravko Kacic

$37.50

Chapter 216

Statistical Simulations on Perceptron-Based Adders
(pages 1474-1481)

Snorre Aunet, Hans Kristian Otnes Berge

$37.50

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Chapter 218

Stream Processing of a Neural Classifier I
(pages 1490-1496)

M. Martínez-Zarzuela, F. J. Díaz Pernas, D. González Ortega, J. F. Díez Higuera, M. Antón Rodríguez

$37.50

Chapter 219

Stream Processing of a Neural Classifier II
(pages 1497-1503)

M. Martínez-Zarzuela, F. J. Díaz Pernas, D. González Ortega, J. F. Díez Higuera, M. Antón Rodríguez

$37.50

$37.50

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$37.50

Chapter 223

A Survey on Neural Networks in Automated Negotiations
(pages 1524-1529)

Ioannis Papaioannou, Ioanna Roussaki, Miltiades Anagnostou

$37.50

Chapter 224

Swarm Intelligence Approach for Ad-Hoc Networks
(pages 1530-1536)

Prayag Narula, Sudip Misra, Sanjay Kumar Dhurandher

$37.50

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Chapter 230

Thermal Design of Gas-Fired Cooktop Burners Through ANN
(pages 1568-1575)

T. T. Wong, C. W. Leung

$37.50

Chapter 231

A 2D Positioning Application in PET Using ANNs
(pages 1576-1582)

Fernando Mateo, Ramón J. Aliaga, Jorge D. Martínez, José Ma Monzó, Rafael Gadea

$37.50

Chapter 232

2D-PAGE Analysis Using Evolutionary Computation
(pages 1583-1588)

Pablo Mesejo, Enrique Fernández-Blanco, Diego Martínez-Feijóo, Francisco J. Blanco

$37.50

Chapter 233

Visualizing Cancer Databases Using Hybrid Spaces
(pages 1589-1595)

Julio J. Valdés, Alan J. Barton

$37.50

Chapter 234

Voltage Instability Detection Using Neural Networks
(pages 1596-1602)

Adnan Khashman, Kadri Buruncuk, Samir Jabr

$37.50

Chapter 235

Wave Reflection at Submerged Breakwaters
(pages 1603-1609)

Alberte Castro Ponte, Gregorio Iglesias, Francisco Taveira Pinto, Rodrigo Carballo

$37.50

Chapter 236

Web-Based Assessment System Applying Many-Valued Logic
(pages 1610-1614)

Sylvia Encheva, Sharil Tumin

$37.50

Chapter 237

Workflow Management Based on Mobile Agent Technology
(pages 1615-1623)

Marina Flores-Badillo, Ernesto López-Mellado

$37.50

About the Editors

Index