The Hilbert-Huang transform and its applications:
Saved in:
| Other Authors: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hackensack, NJ <<[u.a.]>>
World Scientific
2005
|
| Series: | Interdisciplinary mathematical sciences
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 311 S. Ill., graph. Darst. |
| ISBN: | 9812563768 |
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MARC
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| 245 | 1 | 0 | |a The Hilbert-Huang transform and its applications |c eds.: Norden E. Huang; Samuel S P Shen |
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Record in the Search Index
| _version_ | 1804140628226867200 |
|---|---|
| adam_text | CONTENTS
Preface v
Theoretical Aspects
1 Introduction to the Hilbert—Huang Transform and Its
Related Mathematical Problems 1
Norden E. Huang
1.1 Introduction 1
1.2 The Hilbert-Huang transform 2
1.2.1 The empirical mode decomposition method (the sifting process) 4
1.2.2 The Hilbert spectral analysis 12
1.3 Recent developments 14
1.3.1 Normalized Hilbert transform 15
1.3.2 Confidence limit 17
1.3.3 Statistical significance of IMFs 18
1.4 Mathematical problems related to the HHT 18
1.4.1 Adaptive data-analysis methodology 19
1.4.2 Nonlinear system identification 19
1.4.3 The prediction problem for nonstationary processes (the end
effects of EMD) 20
1.4.4 Spline problems (the best spline implementation for HHT,
convergence and 2-D) 21
1.4.5 The optimization problem (the best IMF selection and unique¬
ness mode mixing) 22
1.4.6 Approximation problems (the Hilbert transform and quadrature) 23
1.4.7 Miscellaneous statistical questions concerning HHT 24
1.5 Conclusion 24
2 B-Spline Based Empirical Mode Decomposition 27
Sherman Riemenschneider, Bao Liu, Yuesheng Xu and Norden E. Huang
2.1 Introduction 27
2.2 A B-spline algorithm for empirical mode decomposition 29
2.3 Some related mathematical results 33
vii
viii Contents
2.4 Performance analysis of BS-EMD 39
2.5 Application examples 45
2.6 Conclusion and future research topics 51
3 EMD Equivalent Filter Banks, from Interpretation
to Applications 57
Patrick Flandrin, Paulo Goncalves and Gabriel Rilling
3.1 Introduction 57
3.2 A stochastic perspective in the frequency domain 58
3.2.1 Model and simulations 58
3.2.2 Equivalent transfer functions 59
3.3 A deterministic perspective in the time domain 63
3.3.1 Model and simulations 63
3.3.2 Equivalent impulse responses 63
3.4 Selected applications 64
3.4.1 EMD-based estimation of scaling exponents 64
3.4.2 EMD as a data-driven spectrum analyzer 68
3.4.3 Denoising and detrending with EMD 69
3.5 Concluding remarks 73
4 HHT Sifting and Filtering 75
Reginald N. Meeson
4.1 Introduction 75
4.2 Objectives of HHT sifting 77
4.2.1 Restrictions on amplitude and phase functions 78
4.2.2 End-point analysis 81
4.3 Huang s sifting algorithm 81
4.4 Incremental, real-time HHT sifting 82
4.4.1 Testing for iteration convergence 83
4.4.2 Time-warp analysis 84
4.4.3 Calculating warped filter characteristics 85
4.4.4 Separating amplitude and phase 86
4.5 Filtering in standard time 87
4.6 Case studies 89
4.6.1 Simple reference example 89
4.6.2 Amplitude modulated example 90
4.6.3 Frequency modulated example 92
4.6.4 Amplitude step example 95
4.6.5 Frequency shift example 99
4.7 Summary and conclusions 102
4.7.1 Summary of case study findings 102
4.7.2 Research directions 103
Contents ix
5 Statistical Significance Test of Intrinsic Mode Functions 107
Zhaohua Wu and Norden E. Huang
5.1 Introduction 107
5.2 Characteristics of Gaussian white noise in EMD 109
5.2.1 Numerical experiment 110
5.2.2 Mean periods of IMFs 110
5.2.3 The Fourier spectra of IMFs Ill
5.2.4 Probability distributions of IMFs and their energy 113
5.3 Spread functions of mean energy density 116
5.4 Examples of a statistical significance test of noisy data 119
5.4.1 Testing of the IMFs of the NAOI 120
5.4.2 Testing of the IMFs of the SOI 122
5.4.3 Testing of the IMFs of the GASTA 123
5.4.4 A posteriori test 125
5.5 Summary and discussion 125
Applications to Geophysics
6 The Application of Hilbert—Huang Transforms to
Meteorological Datasets 129
Dean G. Duffy
6.1 Introduction 129
6.2 Procedure 131
6.3 Applications 136
6.3.1 Sea level heights 136
6.3.2 Solar radiation 139
6.3.3 Barographic observations 142
6.4 Conclusion 145
7 Empirical Mode Decomposition and Climate Variability 149
Katie Coughlin and Ka Kit Tung
7.1 Introduction 149
7.2 Data 150
7.3 Methodology 152
7.4 Statistical tests of confidence 154
7.5 Results and physical interpretations 157
7.5.1 Annual cycle 158
7.5.2 Quasi-Biennial Oscillation (QBO) 159
7.5.3 ENSO-like mode 159
7.5.4 Solar cycle signal in the stratosphere 160
7.5.5 Fifth mode 161
x Contents
7.5.6 Trends 162
7.6 Conclusions 162
8 EMD Correction of Orbital Drift Artifacts in Satellite
Data Stream 167
Jorge E. Pinzon, Molly E. Brown and Compton J. Thicker
8.1 Introduction 167
8.2 Processing of NDVI imagery 169
8.3 Empirical mode decomposition 172
8.4 Impact of orbital drift on NDVI and EMD-SZA filtering 173
8.5 Results and discussion 176
8.6 Extension to 8-km data 180
8.7 Integration of NOAA-16 data 181
8.8 Conclusions 183
9 HHT Analysis of the Nonlinear and Non-Stationary Annual
Cycle of Daily Surface Air Temperature Data 187
Samuel S. P. Shen, Tingting Shu, Norden E. Huang, Zhaohua Wu,
Gerald R. North, Thomas R. Karl and David R. Easterling
9.1 Introduction 187
9.2 Analysis method and computational algorithms 191
9.3 Data 194
9.4 Time analysis 195
9.4.1 Examples of the TAC and the NAC 195
9.4.2 Temporal resolution of data 197
9.4.3 Robustness of the EMD method 200
9.4.3.1 EMD separation of a known signal in a synthetic
da ,aset 200
9.4.3.2 Robustness with respect to data length 200
9.4.3.3 Robustness with respect to end conditions 202
9.5 Frequency analysis 202
9.5.1 Hilbert spectra of NAC 202
9.5.2 Variances of anomalies with respect to the NAC and TAC .... 204
9.5.3 Spectral power of the anomalies with respect to the NAC and
TAC 205
9.6 Conclusions and discussion 207
10 Hilbert Spectra of Nonlinear Ocean Waves 211
Paul A. Hwang, Norden E. Huang, David W. Wang, and
Jame M. Kaihatu
10.1 Introduction 211
10.2 The Hilbert-Huang spectral analysis 212
Contents xi
10.3 Spectrum of wind-generated waves 216
10.4 Statistical properties and group structure 219
10.5 Summary 222
Applications to Structural Safety
11 EMD and Instantaneous Phase Detection of Structural
Damage 227
Liming W. Salvino, Darryll J. Pine, Michael Todd and
Jonathan M. Nichols
11.1 Introduction to structural health monitoring 227
11.2 Instantaneous phase and EMD 230
11.2.1 Instantaneous phase 230
11.2.2 EMD and HHT 231
11.2.3 Extracting an instantaneous phase from measured data .... 233
11.3 Damage detection application 234
11.3.1 One-dimensional structures 236
11.3.2 Experimental validations 239
11.3.3 Instantaneous phase detection 242
11.4 Frame structure with multiple damage 243
11.4.1 Frame experiment 244
11.4.2 Detecting damage by using the HHT spectrum 247
11.4.3 Detecting damage by using instantaneous phase features .... 249
11.4.4 Auto-regressive modeling and prediction error 252
11.4.5 Chaotic-attractor-based prediction error 255
11.5 Summary and conclusions 258
12 HHT-Based Bridge Structural Health-Monitoring Method 263
Norden E. Huang, Kang Huang and Wei-Ling Chiang
12.1 Introduction 263
12.2 A review of the present state-of-the-art methods 265
12.2.1 Data-processing methods 266
12.2.2 Loading conditions 268
12.2.3 The transient load 270
12.3 The Hilbert-Huang transform 271
12.4 Damage-detection criteria 272
12.5 Case study of damage detection 274
12.6 Conclusions 280
xii Contents
Applications to Visualization
13 Applications of HHT in Image Analysis 289
Steven R. Long
13.1 Introduction 289
13.2 Overview 290
13.3 The analysis of digital slope images 291
13.3.1 The NASA laboratory 291
13.3.2 The digital camera and set-up 292
13.3.3 Acquiring experimental images 293
13.3.4 Using EMD/HHT analysis on images 293
13.3.5 The digital camera and set-up 293
13.3.5.1 Volume computations and isosurface visualization . . 296
13.3.5.2 Use of EMD/HHT in image decomposition 300
13.4 Summary 303
Index 307
|
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| spelling | The Hilbert-Huang transform and its applications eds.: Norden E. Huang; Samuel S P Shen Hackensack, NJ <<[u.a.]>> World Scientific 2005 XII, 311 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Interdisciplinary mathematical sciences 5 Prozess (DE-588)4047577-3 gnd rswk-swf Hilbert-Transformation (DE-588)4375311-5 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Hilbert-Transformation (DE-588)4375311-5 s Prozess (DE-588)4047577-3 s Datenanalyse (DE-588)4123037-1 s 1\p DE-604 Huang, Norden E. edt Shen, Samuel S. Sonstige oth Interdisciplinary mathematical sciences 5 (DE-604)BV035420471 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018583947&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | The Hilbert-Huang transform and its applications Interdisciplinary mathematical sciences Prozess (DE-588)4047577-3 gnd Hilbert-Transformation (DE-588)4375311-5 gnd Datenanalyse (DE-588)4123037-1 gnd |
| subject_GND | (DE-588)4047577-3 (DE-588)4375311-5 (DE-588)4123037-1 |
| title | The Hilbert-Huang transform and its applications |
| title_auth | The Hilbert-Huang transform and its applications |
| title_exact_search | The Hilbert-Huang transform and its applications |
| title_full | The Hilbert-Huang transform and its applications eds.: Norden E. Huang; Samuel S P Shen |
| title_fullStr | The Hilbert-Huang transform and its applications eds.: Norden E. Huang; Samuel S P Shen |
| title_full_unstemmed | The Hilbert-Huang transform and its applications eds.: Norden E. Huang; Samuel S P Shen |
| title_short | The Hilbert-Huang transform and its applications |
| title_sort | the hilbert huang transform and its applications |
| topic | Prozess (DE-588)4047577-3 gnd Hilbert-Transformation (DE-588)4375311-5 gnd Datenanalyse (DE-588)4123037-1 gnd |
| topic_facet | Prozess Hilbert-Transformation Datenanalyse |
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