题目：OnHolo-Hilbert Spectral Analysis

报告人：NordenE. Huang

               Innovation Center

               First Institute of Oceanography and

       Center for Nonlinear Sciences,

       Qingdao National Laboratory for Marine Scienceand Technology

地点： 教十二-201

时间： 10月25日，周四，15:00-16:00

Abstract

Traditionally, spectral analysis is definedas transform the time domain data to frequency domain. It is achieved throughintegral transforms based on additive expansions of a priori determinedbasis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequencymodulations generated by intra-wave and inter-wave interactions involving bothadditive and nonlinear multiplicative processes. Under such conditions, theadditive expansion could not fully represent the physical processes resultingfrom multiplicative interactions. Unfortunately, all existing spectral analysismethods are based on additive expansions, based either on a priori oradaptive bases. While the adaptive Hilbert spectral analysis could accommodatethe intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanismsthat include cross-scale coupling and phase lock modulations are leftuntreated. To resolve the multiplicative processes, we propose a full informationalspectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which wouldaccommodate all the processes: additive and multiplicative, intra-mode andinter-mode, stationary and non-stationary, linear and nonlinear interactions,through additional dimensions in the spectrum to account for both thevariations in frequency and amplitude modulations (FM and AM) simultaneously.Applications to wave-turbulence interactions to brain electric waves will bepresented to demonstrate the usefulness of this new spectral representation.

References

NordenE Huang, Kun Hu, Albert CC Yang, Hsing-Chih Chang, Deng Jia, Wei-KuangLiang, Jia Rong Yeh, Chu-Lan Kao, Chi-Hung Juan, Chung Kang Peng, JohannaH Meijer, Yung-Hung Wang, Steven R Long, Zhauhua Wu, 2016: On Holo-Hilbertspectral analysis: a full informational spectral representation for nonlinearand non-stationary data. Phil. Trans. R. Soc. A 374 (2065),20150206, 2016

报告人简介：

    Dr.Norden Huang holds a BS Engineering Degree from National Taiwan University(19690) and a PhD in fluid mechanics and mathematics from the Johns HopkinsUniversity (1967). Currently, he is the founding directors for the InnovationCenter and the Data Analysis Laboratory at the First Oceanographic Institute,SOA, Qingdao.  He was also the foundingdirectors of the Research Center for Adaptive Data Analysis and Research Centerfor Dynamical Biomarkers and Translational Medicine at the National CentralUniversity, Zhongli, Taiwan, China (2006-2017). Most of his career is in NASA (1975-2006), where he had developed theadaptive Hilbert-Huang Transform (HHT), designed to analyze nonstationary andnonlinear data. For this invention, he was awarded the 1998 NASA Special SpaceAct Award with the citation, ‘[Dr. Huang’s new method] is one of the mostimportant discoveries in the field of applied mathematics in NASAhistory.’  ‘For contributions to theanalysis of nonlinear stochastic signals and related mathematical applicationsin engineering, biology, and other sciences (NAE Citation),’ he was elected asmembers of the National Academy of Engineering, 2000; Academia Sinica, 2004;and a Foreign Member of the Chinese Academy of Engineering, 2006.

    Recently, he has developed the Holo-HilbertSpectral Analysis (HHSA) and Intrinsic Probability Density distribution, whichreveal new information on inter-wave interactions for nonlinear andnonstationary phenomena. Applications of HHSA on EEG and turbulence data arethe areas of his active research, with the collaboration with Oxford UniversityCenter for Human Brain Activity and Harvard and Stanford Medical School.

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