Nonlinear Modeling of Solar Radiation and Wind Speed Time Series (eBook)

Luigi Fortuna received the degree of electrical engineering (cum laude) from the University of Catania, Italy, in 1977. He is a Full Professor of system theory with the University Of Catania. He was the Coordinator of the courses in electronic engineering and the Head of the Dipartimento di Ingegneria Elettrica Elettronica e dei Sistemi. From 2005 to 2012, he was the Dean of the Engineering Faculty. He currently teaches complex adaptive systems and robust control. He has published more than 500 technical papers and twelve scientific books. His scientific interests include robust control, nonlinear science and complexity, chaos, cellular neural networks, soft-computing strategies for control, robotics, micronanosensor and smart devices for control, and nanocellular neural networks modeling. Dr. Fortuna was the IEEE Circuits and Systems (CAS) Chairman of the CNN Technical Committee, IEEE CAS Distinguished Lecturer from 2001 to 2002, and IEEE Chairman of the IEEE CAS Chapter Central-South Italy. Giuseppe Nunnari received the “Laurea” degree in electrical engineering (cum laudae) from the University of Catania, Catania, Italy, in 1979. He was a software engineer in private companies until 1983 and Researcher of the Italian National Research Council (CNR), from May 1983 to October 1992, where he carried out research concerning the modelling and processing of geophysical data. From November 1992 he joined with the University of Catania, Faculty of Engineering, were he has served as associate professor of System Theory and Automatic Control, till September 2001 and as a professor up to the present days. His research interests include the modelling and control of dynamic systems, signal and image processing, soft computing and modelling of environmental systems. He is author or co-author of about 230 scientific papers published in international journals, conference proceedings and books chapters. He has also co-authored 3 scientific books published by international publishers. Silvia Nunnari received the degree in computer engineering in 2010, the master degree in computer engineering in 2012 and a PhD in Systems Engineering in 2015. She has co-authored 6 papers in international journals and conference proceedings.

Preface 7
Acknowledgments 9
Contents 10
Abbreviations 13
1 Time Series Methods 14
1.1 Stationarity Analysis 14
1.2 Recurrence Plots 15
1.3 Linear Detrending 15
1.4 Noise Reduction 16
1.5 Power Spectrum 16
1.6 Autocorrelation 17
1.7 Mutual Information 17
1.8 Noise 1/f and Random Walks 18
1.9 Fractal Dimension and Hurst Exponent 18
1.9.1 The Box-Dimension 18
1.9.2 The Hurst Exponent 19
1.10 Multifractals 20
1.11 False Nearest Neighbors 21
1.12 Lyapunov Spectrum 21
1.13 Daily Patterns 21
1.14 Time Series Clustering 23
1.14.1 The Exclusive Clustering 24
1.14.2 The Overlapping Clustering 24
1.14.3 The Hierarchical Clustering 25
1.14.4 The Probabilistic Clustering 25
1.14.5 Feature Based Clustering 26
1.14.6 Choosing the Number of Clusters 26
1.15 Conclusions 27
References 28
2 Analysis of Solar Radiation Time Series 29
2.1 Energy from the Sun 29
2.2 The Solar Radiation Data Set 30
2.2.1 Stationarity Analysis 31
2.2.2 Autocorrelation and Mutual Information 32
2.2.3 Power Spectra 33
2.2.4 Hurst Exponent and Fractal Dimension 34
2.2.5 Multifractal Analysis of Solar Radiation 36
2.2.6 Estimation of the Embedding Dimension 36
2.2.7 Maximal Lyapunov Exponent 37
2.3 Conclusions 38
References 39
3 Analysis of Wind Speed Time Series 40
3.1 Energy from the Wind 40
3.2 The Wind Speed Data Set 41
3.3 Stationary Analysis 42
3.4 Autocorrelation and Mutual Information 44
3.5 Power Spectra 45
3.6 Hurst Exponent and Fractal Dimension 47
3.7 Multifractal Spectrum 49
3.8 Estimation of the Embedding Dimension 49
3.9 Lyapunov Exponents 50
3.10 Conclusions 51
References 51
4 Prediction Models for Solar Radiation and Wind Speed Time Series 52
4.1 NARX Time Series Models 52
4.2 Multistep Ahead Prediction Models 53
4.3 EPS Time Series Models 53
4.4 Mapping Approximation 54
4.4.1 The Neuro-Fuzzy Approach 55
4.4.2 The Feedforward Neural Network Approach 55
4.5 Assessing the Model Performances 56
4.5.1 Reference Models 56
4.6 Conclusions 57
References 57
5 Modeling Hourly Average Solar Radiation Time Series 58
5.1 Introduction 58
5.2 Modeling Results 59
5.2.1 Performances of the EPSNF Approach 59
5.2.2 Performances of the EPSNN Approach 64
5.2.3 A Direct Comparison Between EPSNF and EPSNN 67
5.2.4 Average Skill Index Considering the P24 Reference Model 68
5.3 Conclusions 69
References 70
6 Modeling Hourly Average Wind Speed Time Series 71
6.1 Introduction 71
6.2 Considerations on the Choice of Model Parameters 71
6.3 Performances for All the Considered Stations 74
6.4 Conclusions 76
References 76
7 Clustering Daily Solar Radiation Time Series 78
7.1 Two Features of Solar Radiation Time Series 78
7.1.1 The Area Ratio Ar Index 78
7.1.2 The GPHr Index 79
7.2 Clustering Daily Patterns of Solar Radiation 80
7.3 Daily Pattern Shapes 81
7.3.1 Weight of a Solar Radiation Class 82
7.3.2 Permanence of a Solar Radiation Class 85
7.4 Conclusions 87
References 87
8 Clustering Daily Wind Speed Time Series 88
8.1 Introduction 88
8.2 Two Features of Daily Wind Speed Time Series 88
8.3 The Wr Index 89
8.4 The Hurst Exponent of Daily Wind Speed 90
8.5 Clustering Wind Speed Daily Patterns 90
8.5.1 Stability of the Wind Speed Features Cluster Centers 93
8.6 Some Applications 94
8.6.1 Weight of a Class 95
8.6.2 Permanence of Patterns in a Class 95
8.7 Conclusions 97
References 98
9 Concluding Remarks 99
Appendix ASoftware Tools and Data 101
Index 104