Uncertainty Forecasting in Engineering (eBook)

Univ.-Prof. Dr.-Ing. habil. Bernd Möller (*1941) studied civil engineering. From 1994 –1996 he was professor for Numerical Methods and Computer Science in Engineering at the University of Braunschweig, and from 1996 – 2006 professor for Solid and Structural Mechanics at the University of Technology in Dresden, Germany. Professor Möller has been retired since 2006. Dr.-Ing. Uwe Reuter (*1979) studied civil engineering. From 2003 – 2007 he was research associate at the Institute of Statics and Dynamics of Structures at the University of Technology in Dresden, Germany. Today he is head of the Computing Center at the Faculty of Civil Engineering at the University of Technology in Dresden.

Preface 5
Contents 7
Abbreviations 9
1 Introduction 14
1.1 Application of Time Series for Forecasting in Engineering 14
1.2 Data Uncertainty and Fuzzy Time Series 18
1.3 Examples of Fuzzy Time Series 20
2 Mathematical Description of Uncertain Data 22
2.1 Fuzzy Variables 22
2.2 Fuzzy Random Variables 38
2.3 Fuzzy Random Processes 66
3 Analysis of Time Series Comprised of Uncertain Data 71
3.1 Plot of Fuzzy Time Series 71
3.2 Fuzzy Component Model 75
3.3 Stationary Fuzzy Time Series 81
3.4 Transformation of Fuzzy Time Series Using Filters 86
3.5 Modeling on the Basis of Specific Fuzzy Random Processes 91
3.6 Modeling on the Basis of Artificial Neural Networks 118
4 Forecasting of Time Series Comprised of Uncertain Data 142
4.1 Underlying Concept 142
4.2 Forecasting on the Basis of Specific Fuzzy Random Processes 145
4.3 Forecasting on the Basis of Artificial Neural Networks 155
5 Uncertain Forecasting in Engineering and Environmental Science 164
5.1 Model-Free Forecasting 164
5.2 Model-Based Forecasting 166
5.3 Applications 174
References 203
Index 208