The Hilbert–Huang Transform (HHT) represents a desperate attempt to break the suffocating hold on the field of data analysis by the twin assumptions of linearity and stationarity. Unlike spectrograms, wavelet analysis, or the Wigner–Ville Distribution, HHT is truly a time-frequency analysis, but it does not require an a priori functional basis and, therefore, the convolution computation of frequency. The method provides a magnifying glass to examine the data, and also offers a different view of data from nonlinear processes, with the results no longer shackled by spurious harmonics — the artifacts of imposing a linearity property on a nonlinear system or of limiting by the uncertainty principle, and a consequence of Fourier transform pairs in data analysis. This is the first HHT book containing papers covering a wide variety of interests. The chapters are divided into mathematical aspects and applications, with the applications further grouped into geophysics, structural safety and visualization.
Author(s): Norden E. Huang, Samuel S. Shen
Series: Interdisciplinary Mathematical Sciences
Publisher: World Scientific Publishing Company
Year: 2005
Language: English
Pages: 324
CONTENTS......Page 8
Preface......Page 6
1.1 Introduction......Page 14
1.2 The Hilbert-Huang transform......Page 15
1.2.1 The empirical mode decomposition method (the sifting process)......Page 17
1.2.2 The Hilbert spectral analysis......Page 25
1.3 Recent developments......Page 27
1.3.1 Normalized Hilbert transform......Page 28
1.3.2 Confidence limit......Page 30
1.4 Mathematical problems related to the HHT......Page 31
1.4.2 Nonlinear system identification......Page 32
1.4.3 The prediction problem for nonstationary processes (the end effects of EMD)......Page 33
1.4.4 Spline problems (the best spline implementation for HHT, convergence and 2-D)......Page 34
1.4.5 The optimization problem (the best IMF selection and uniqueness mode mixing)......Page 35
1.4.6 Approximation problems (the Hilbert transform and quadrature)......Page 36
1.5 Conclusion......Page 37
References......Page 38
2.1 Introduction......Page 40
2.2 A B-spline algorithm for empirical mode decomposition......Page 42
2.3 Some related mathematical results......Page 46
2.4 Performance analysis of BS-EMD......Page 52
2.5 Application examples......Page 58
2.6 Conclusion and future research topics......Page 64
References......Page 66
3.1 Introduction......Page 70
3.2.1 Model and simulations......Page 71
3.2.2 Equivalent transfer functions......Page 72
3.3.2 Equivalent impulse responses......Page 76
3.4.1 EMD-based estimation of scaling exponents......Page 77
3.4.2 EMD as a data-driven spectrum analyzer......Page 81
3.4.3 Denoising and detrending with EMD......Page 82
References......Page 86
4.1 Introduction......Page 88
4.2 Objectives of HHT sifting......Page 90
4.2.1 Restrictions on amplitude and phase functions......Page 91
4.3 Huang’s sifting algorithm......Page 94
4.4 Incremental, real-time HHT sifting......Page 95
4.4.1 Testing for iteration convergence......Page 96
4.4.2 Time-warp analysis......Page 97
4.4.3 Calculating warped filter characteristics......Page 98
4.4.4 Separating amplitude and phase......Page 99
4.5 Filtering in standard time......Page 100
4.6.1 Simple reference example......Page 102
4.6.2 Amplitude modulated example......Page 103
4.6.3 Frequency modulated example......Page 105
4.6.4 Amplitude step example......Page 108
4.6.5 Frequency shift example......Page 112
4.7.1 Summary of case study findings......Page 115
4.7.2 Research directions......Page 116
References......Page 117
5.1 Introduction......Page 120
5.2 Characteristics of Gaussian white noise in EMD......Page 122
5.2.2 Mean periods of IMFs......Page 123
5.2.3 The Fourier spectra of IMFs......Page 124
5.2.4 Probability distributions of IMFs and their energy......Page 126
5.3 Spread functions of mean energy density......Page 129
5.4 Examples of a statistical significance test of noisy data......Page 132
5.4.1 Testing of the IMFs of the NAOI......Page 133
5.4.2 Testing of the IMFs of the SOI......Page 135
5.4.3 Testing of the IMFs of the GASTA......Page 136
5.5 Summary and discussion......Page 138
References......Page 139
6.1 Introduction......Page 142
6.2 Procedure......Page 144
6.3.1 Sea level heights......Page 149
6.3.2 Solar radiation......Page 152
6.3.3 Barographic observations......Page 155
Acknowledgments......Page 158
References......Page 159
7.1 Introduction......Page 162
7.2 Data......Page 163
7.3 Methodology......Page 165
7.4 Statistical tests of confidence......Page 167
7.5 Results and physical interpretations......Page 170
7.5.1 Annual cycle......Page 171
7.5.3 ENSO-like mode......Page 172
7.5.4 Solar cycle signal in the stratosphere......Page 173
7.5.5 Fifth mode......Page 174
7.6 Conclusions......Page 175
References......Page 176
8.1 Introduction......Page 180
8.2 Processing of NDVI imagery......Page 182
8.3 Empirical mode decomposition......Page 185
8.4 Impact of orbital drift on NDVI and EMD-SZA filtering......Page 186
8.5 Results and discussion......Page 189
8.6 Extension to 8-km data......Page 193
8.7 Integration of NOAA-16 data......Page 194
8.8 Conclusions......Page 196
References......Page 197
9.1 Introduction......Page 200
9.2 Analysis method and computational algorithms......Page 204
9.3 Data......Page 207
9.4.1 Examples of the TAC and the NAC......Page 208
9.4.2 Temporal resolution of data......Page 210
9.4.3.2 Robustness with respect to data length......Page 213
9.5.1 Hilbert spectra of NAC......Page 215
9.5.2 Variances of anomalies with respect to the NAC and TAC......Page 217
9.5.3 Spectral power of the anomalies with respect to the NAC and TAC......Page 218
9.6 Conclusions and discussion......Page 220
References......Page 221
10.1 Introduction......Page 224
10.2 The Hilbert-Huang spectral analysis......Page 225
10.3 Spectrum of wind-generated waves......Page 229
10.4 Statistical properties and group structure......Page 232
10.5 Summary......Page 235
Acknowledgements......Page 236
References......Page 237
11.1 Introduction to structural health monitoring......Page 240
11.2.1 Instantaneous phase......Page 243
11.2.2 EMD and HHT......Page 244
11.2.3 Extracting an instantaneous phase from measured data......Page 246
11.3 Damage detection application......Page 247
11.3.1 One-dimensional structures......Page 249
11.3.2 Experimental validations......Page 252
11.3.3 Instantaneous phase detection......Page 255
11.4 Frame structure with multiple damage......Page 256
11.4.1 Frame experiment......Page 257
11.4.2 Detecting damage by using the HHT spectrum......Page 260
11.4.3 Detecting damage by using instantaneous phase features......Page 262
11.4.4 Auto-regressive modeling and prediction error......Page 265
11.4.5 Chaotic-attractor-based prediction error......Page 268
11.5 Summary and conclusions......Page 271
References......Page 272
12.1 Introduction......Page 276
12.2 A review of the present state-of-the-art methods......Page 278
12.2.1 Data-processing methods......Page 279
12.2.2 Loading conditions......Page 281
12.2.3 The transient load......Page 283
12.3 The Hilbert-Huang transform......Page 284
12.4 Damage-detection criteria......Page 285
12.5 Case study of damage detection......Page 287
12.6 Conclusions......Page 293
References......Page 295
13.1 Introduction......Page 302
13.2 Overview......Page 303
13.3.1 The NASA laboratory......Page 304
13.3.2 The digital camera and set-up......Page 305
13.3.5 The digital camera and set-up......Page 306
13.3.5.1 Volume computations and isosurface visualization......Page 309
13.3.5.2 Use of EMD/HHT in image decomposition......Page 313
13.4 Summary......Page 316
References......Page 317
Index......Page 320
