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Hilbert Huang Transformand I t s App l ica t ionsEditors
Norden HuangNASA Goddard Space Flight Center USA
Samuel S P ShenUniversity of Alberta Canada
or ld cientific
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Published byWorld Scientific Publishing Co. Pte. Ltd.5 Toh Tuck Link, Singapo re 596224US o f i ce : 27 Warren Street, Suite 401-402, Hackensack, NJ 07601UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
Library of Congress Cataloging in PublicationDataTh e Hilbert-Huang transform and its applications / editors, Norden E. Huang, Sam uel S.P. Shen.
p. cm. -- (Interdisciplinary mathematical sciences ; v 5)Includes bibliographical references and index.ISBN 981-256-376-8 (alk. paper)
1. Hilbert-Huang transform. 2. Decom position (Mathema tics) I. Huang, N E. (NordenEh), 1937- 11. Shen, S am uel S. 111 Series.QA432.HS5 2005515 .723--dc22
200505 1846
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Vlll Contents2.42.52.6
3.13.2
3.3
3.4
3.54
4.14.2
4.34.4
4.54.6
4.7
Performance analysis of BS-EMD . . . . . . . . . . . . . . . . . . . . . .Application examples . . . . . . . . . . . . . . . . . . . . . . . . . . . .Conclusion and future research topics . . . . . . . . . . . . . . . . . . .EMD Equivalent Filter Banks. from Interpretationto ApplicationsPatrick Flandrin. Paulo Gonqaluts and Gabriel RillingIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A stochastic perspective in the frequency domain3.2.1 Model and simulations . . . . . . . . . . . . . . . . . . . . . . . .3.2.2 Equivalent transfer functions . . . . . . . . . . . . . . . . . . . .A deterministic perspective in the time domain . . . . . . . . . . . . . .3.3.1 Model and simulations . . . . . . . . . . . . . . . . . . . . . . . .3.3.2 Equivalent impulse responses . . . . . . . . . . . . . . . . . . . .3.4.1 EMD-based estimation of scaling exponents . . . . . . . . . . . .3 4 2 EMD as a data-driven spectrum analyzer3.4.3 Denoising and detrending with EMD . . . . . . . . . . . . . . . .
Selected applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . .HHT Sifting and FilteringReginald N MeesonIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Objectives of HHT sifting4.2.1 Restrictions on amplitude and phase functions4.2.2 End-point analysisHuangs sifting algorithm . . . . . . . . . . . . . . . . . . . . . . . . . .Incremental real-time HHT sifting . . . . . . . . . . . . . . . . . . . . .4.4.1 Testing for iteration convergence . . . . . . . . . . . . . . . . . .4.4.2 Time-warp analysis . . . . . . . . . . . . . . . . . . . . . . . . .4.4.3 Calculating warped filter characteristics . . . . . . . . . . . . . .4.4.4 Separating amplitude and phase . . . . . . . . . . . . . . . . . .Filtering in standard time . . . . . . . . . . . . . . . . . . . . . . . . . .Case studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.6.1 Simple reference example . . . . . . . . . . . . . . . . . . . . . .4.6.2 Amplitude modulated example . . . . . . . . . . . . . . . . . . .4.6.3 Frequency modulated example . . . . . . . . . . . . . . . . . . .4.6.4 Amplitude step example . . . . . . . . . . . . . . . . . . . . . . .4.6.5 Frequency shift example . . . . . . . . . . . . . . . . . . . . . . .Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . .4.7.1 Summary of case study findings . . . . . . . . . . . . . . . . . . .4.7.2 Research directions . . . . . . . . . . . . . . . . . . . . . . . . . .
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5.15.2
5.35.4
5.5
6
6.16.26.3
6.47
7.17.27.37.47.5
Statistical Significance Test of Intrinsic o d e Functions 107Zhaohua Wu and Norden E . HuangIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Characteristics of Gaussian white noise in EMD . . . . . . . . . . . . . 1095.2.1 Numerical experiment . . . . . . . . . . . . . . . . . . . . . . . . 1105.2.2 Mean periods of IMFs . . . . . . . . . . . . . . . . . . . . . . . . 1105.2.3 The Fourier spectra of IMFs . . . . . . . . . . . . . . . . . . . . 1115.2.4 Probability distributions of IMFs and their energy 113Spread functions of mean energy density . . . . . . . . . . . . . . . . . . 116Examples of a statistical significance test of noisy data . . . . . . . . . . 1195.4.1 Testing of the IMFs of the NAOI . . . . . . . . . . . . . . . . . . 1205.4.2 Testing of the IMFs of the SO1 . . . . . . . . . . . . . . . . . . . 1225.4.4 A posteriori test . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1255.4.3 Testing of the IMFs of the GASTA . . . . . . . . . . . . . . . . . 123
Applications to Geophysics
The Application of Hilbert Huang Transforms toMeteorological DatasetsDean G Duf fy 129Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Procedure 131Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1366.3.1 Sea level heights . . . . . . . . . . . . . . . . . . . . . . . . . . . 1366.3.2 Solar radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.3.3 Barographic observations . . . . . . . . . . . . . . . . . . . . . . 142Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Empirical Mode Decomposition and Climate VariabilityKatie Coughlin and Ka Kit TungIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Statistical tests of confidence . . . . . . . . . . . . . . . . . . . . . . . . 154Results and physical interpretations 1577.5.1 Annual cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1587.5.2 Quasi-Biennial Oscillation QBO) . . . . . . . . . . . . . . . . . 1597.5.3 ENSO-like mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 1597.5.4 Solar cycle signal in the stratosphere . . . . . . . . . . . . . . . . 1607.5.5 Fifth mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
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8.18.28.38.48.58.68.78.8
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9.19.29.39.4
9.5
9.6
7.5.6 Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162Conclusions 162EMD Correction of Orbital Drift Artifacts in SatelliteData Stream 167Jorge E Pinzdn Molly E . Brown and Compton J TuckerIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Processing of NDVI imagery . . . . . . . . . . . . . . . . . . . . . . . . 169Empirical mode decomposition . . . . . . . . . . . . . . . . . . . . . . . 172Impact of orbital drift on NDVI and EMD-SZA filtering . . . . . . . . . 173Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176Extension to 8-km data . . . . . . . . . . . . . . . . . . . . . . . . . . . 180Integration of NOAA-16 data . . . . . . . . . . . . . . . . . . . . . . . . 181Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183HHT Analysis of the Nonlinear and Non Stationary AnnualCycle of Daily Surface Air Temperature DataSamuel S P Shen Tingting Shu Norden E . Huang Zhaohua WuGerald R . North. Thomas R. Karl and David R EasterlingIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187Analysis method and computational algorithms . . . . . . . . . . . . . . 191Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194Time analysis 1959.4.1 Examples of the TAC and the NAC . . . . . . . . . . . . . . . . 1959.4.2 Temporal resolution of data . . . . . . . . . . . . . . . . . . . . . 1979.4.3 Robustness of the EMD method . . . . . . . . . . . . . . . . . . 200
EMD separation of a known signal in a syntheticda:aset . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
187
9.4.3.19.4.3.2 Robustness with respect to data length . . . . . . . . . 2009.4.3.3 Robustness with respect to end conditions . . . . . . . 202
Frequency analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2029.5.1 Hilbert spectra of NAC . . . . . . . . . . . . . . . . . . . . . . . 2029.5.2 2049.5.3 Spectral power of the anomalies with respect to the NAC and
TAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205Conclusions and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 207
Variances of anomalies with respect to the NAC and TAC
10 Hilbert Spectra of Nonlinear Ocean Waves 211Paul . Hwang. Norden E Huang. David W Wang. andJame M Kaihatu
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21110.2 The Hilbert-Huang spectral analysis . . . . . . . . . . . . . . . . . . . . 212
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10.3 Spectrum of wind-generated waves . . . . . . . . . . . . . . . . . . . . . 21610.4 Statistical properties and group structure . . . . . . . . . . . . . . . . . 1910.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Applications to Structural Safety
11 EMD and Instantaneous Phase Detection of StructuralDamage 227Liming W Salvino. Darryl1 J Pine. Michael Todd andJonathan M Nichols
11 1 Introduction to structural health monitoring 22711.2 Instantaneous phase and EMD . . . . . . . . . . . . . . . . . . . . . . . 230
11.2.1 Instantaneous phase . . . . . . . . . . . . . . . . . . . . . . . . 23011.2.2 EMD and HHT . . . . . . . . . . . . . . . . . . . . . . . . . . . 23111.2.3 Extracting an instantaneous phase from measured da ta 233
11.3 Damage detection application . . . . . . . . . . . . . . . . . . . . . . . 23411.3.1 One-dimensional structures . . . . . . . . . . . . . . . . . . . . . 23611.3.2 Experimental validations . . . . . . . . . . . . . . . . . . . . . . 23911.3.3 Instantaneous phase detection . . . . . . . . . . . . . . . . . . . 242
11.4 Frame structure with multiple damage . . . . . . . . . . . . . . . . . . 24311.4.1 Frame experiment . . . . . . . . . . . . . . . . . . . . . . . . . 24411.4.2 Detecting damage by using the HHT spectrum . . . . . . . . . 24711.4.3 Detecting damage by using instantaneous phase features . . . . 24911.4.4 Auto-regressive modeling and prediction error . . . . . . . . . . 25211.4.5 Chaotic-attractor-based prediction error . . . . . . . . . . . . . 255
11.5 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 25812 HHT Based Bridge Structural Health Monitoring Method 263
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26312.2 A review of the present state-of-the-art methods . . . . . . . . . . . . . 265
12.2.1 Data-processing methods . . . . . . . . . . . . . . . . . . . . . 26612.2.2 Loading conditions . . . . . . . . . . . . . . . . . . . . . . . . . 26812.2.3 The transient load . . . . . . . . . . . . . . . . . . . . . . . . . 270
12 . 3 The Hilbert-Huang transform . . . . . . . . . . . . . . . . . . . . . . . 27112.4 Damage-detection criteria . . . . . . . . . . . . . . . . . . . . . . . . . . 27212.5 Case study of damage detection . . . . . . . . . . . . . . . . . . . . . . 27412.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
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Applications to Visualization
3 Applications of HHT in Image Analysis 28913.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28913.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29013.3 The analysis of digital slope images . . . . . . . . . . . . . . . . . . . . . 291
13.3.1 The NASA laboratory . . . . . . . . . . . . . . . . . . . . . . . 29113.3.2 The digital camera and set-up 29213.3.3 Acquiring experimental images . . . . . . . . . . . . . . . . . . . 29313.3.4 Using EMD/HHT analysis on images . . . . . . . . . . . . . . . 293
13.3.5.1 Volume computations and isosurface visua.lization 29613.3.5.2 Use of EMD/HHT in image decomposition . . . . . . 300
S t e v e n R Long
13.3.5 The digital camera and set-up . . . . . . . . . . . . . . . . . . . 93
13.4 Summary 303Index 307
