Grey Prediction Methods and Their Applications

This book introduces the grey prediction model methodology and its applications as a professional book. It involves the key concepts, data characteristics of modelling objects and the latest research achievements in grey system. The grey prediction models for homogeneous and non-homogeneous exponential sequences, saturated S-shaped sequences and special sequences have been introduced. This book combines the classical models and the latest models, case studies and model applications, modelling methods, and MATLAB programs in grey system. It is a guidebook for both new learners and professionals of grey prediction models. Series Preface Foreword by Yong Long Lv Foreword by Sifeng Liu Foreword by Le’an Yu Preface Introduction Contents 1 Basic Concepts of Grey System Theory 1.1 Appearance and Growth of Grey System Theory 1.2 Grey System and Grey Numbers 1.3 Degree of Greyness and Kernel of an Interval Grey Number 1.3.1 Possibility Function 1.3.2 Degree of Greyness 1.3.3 Kernel 1.4 Theoretical Framework 1.5 Chapter Summary 2 Grey Accumulating Operators and Smoothing Operators 2.1 Basic Concepts of Grey Accumulating Generation Operators and Inverse Accumulating Generation Operators 2.2 Unification of Accumulating Generation Operators and Inverse Accumulating Generation Operators 2.3 Smoothing Operators 2.4 Adjacent Generation Operators 2.5 Chapter Summary Appendix 1: MATLAB Program Used to Extend the Value Range of Gamma Function Appendix 2: MATLAB Program Used to Calculate r-RGO 3 Grey Buffer Operators 3.1 Weakening and Strengthening Buffer Operators 3.2 Intelligent Buffer Operators 3.2.1 Definition and Type of Intelligent Grey Buffer Operators 3.2.2 The Relationship Between the Power Exponent and Buffer Strength of Intelligent Grey Buffer Operator 3.2.3 Numerical Examples 3.3 Case Study: Prediction of Wind Power Generation in China 3.4 Chapter Summary Appendix 1: Proof of Theorem 3.2.1 Appendix 2: Proof of Theorem 3.2.2 Appendices 3 and 4: The MATLAB Program for IGBO Calculation and Chart Drawing 4 Whitenization Univariate Grey Prediction Model 4.1 Overview of Univariate Grey Prediction Models 4.2 Whitenization Univariate Grey Prediction Model GM (1,1) 4.3 Three-Parameter Whitenization Grey Models—TWGM (1,1) 4.4 Performance Testing Methods of the GM (1,1) Model 4.5 Case Study: Post-evaluation of Expressway Economic Benefits 4.6 Chapter Summary 5 Discrete Univariate Grey Prediction Model 5.1 Discrete Univariate Grey Prediction Model-DGM (1,1) 5.2 Three-Parameter Discrete Univariate Grey Prediction Model—TDGM (1,1) 5.3 Comparative Analysis of the Four Univariate Grey Prediction Models 5.4 Case Study: Prediction of China Natural Gas Demand 5.5 Chapter Summary 6 Grey Prediction Model for Saturated S-Shaped Sequences 6.1 Traditional Grey Verhulst Model 6.2 New Grey Verhulst Model 6.3 Case Study: Prediction of China’s Tight Gas Production 6.4 Chapter Summary 7 Multivariate Grey Prediction Model 7.1 Traditional Multivariate Grey Prediction Model 7.2 Structural Optimization of Multivariate Grey Prediction Model 7.3 Case Study: Prediction of Concrete Bending Strength 7.4 Chapter Summary 8 Parameter Optimization Methods for Grey Prediction Models 8.1 Optimization Method for the Initial Value of the TDGM (1,1) Model 8.2 Optimization Method for the Background Value in the TDGM (1,1) Model 8.3 Extension and Optimization of the Real Number Field for the Accumulative Order of Grey Prediction Models 8.4 Case Study: Radar Transmitter Fault Prediction Based on Parameter Combination Optimization 8.5 Chapter Summary Appendix: The MATLAB Program for TDGM (1,1) with Parameter Combination Optimization 9 Grey Prediction Models for Special Sequences 9.1 Interval Grey Number Prediction Model Based on Grey Number Band and Grey Number Layer 9.2 Grey Heterogeneous Data Prediction Model Based on Kernel and Degree of Greyness 9.3 Grey Prediction Model for Small Data Fluctuation Sequence Based on Smoothing Operator 9.4 Interval Prediction Model for Small Data Oscillating Sequences Based on Enveloping Lines 9.5 Case Study: Interval Prediction of the Concentration of SO2 in Beijing 9.6 Chapter Summary