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NASA NTRS1998

Modal Behavior of Hemispheric Sea Ice Covers

Recent papers have described 18-year trends and annual oscillations in the Arctic and Antarctic sea ice extents, areas, and enclosed open water areas based on a newly-formulated 18.2-year ice concentration time series. This time series includes data for the entire Arctic and Antarctic ice covers, as well as for previously defined subregions consisting of 5 sectors in the Antarctic and 9 regions in the Arctic. It was obtained by fine-tuning the sea ice algorithm tie points individually for each of the four sensors used to acquire the data. In this paper, we extend these analyses to an examination of the intrinsic modes of these time series, obtained by means of Empirical Mode Decomposition, with emphasis on periodicities greater than the annual cycle. Quasibiennial and quasiquadrennial oscillations observed with a different technique and reported earlier for the first 8.8 years of this time series were also observed in the present series. However, the intrinsic modes were not monochromatic; they feature frequency as well as amplitude modulation within their respective frequency bands. Modal periods of up to 18 years are observed, with important implications for the trend analyses published earlier. These results are compared with the oscillations in the Length-of-Day and North Atlantic Oscillation parameters similarly determined for the same 18.2-year period.

Gloersen, Per↗
NASA NTRS1999

A New Method for Nonlinear and Nonstationary Time Series Analysis and Its Application to the Earthquake and Building Response Records

A new method for analyzing nonlinear and nonstationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum, Example of application of this method to earthquake and building response will be given. The results indicate those low frequency components, totally missed by the Fourier analysis, are clearly identified by the new method. Comparisons with Wavelet and window Fourier analysis show the new method offers much better temporal and frequency resolutions.

Huang, Norden E.↗
NASA NTRS1999

A Critical Examination of Wind-Wave Spectral Functional Form

Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid under extremely general conditions, there are some crucial restrictions for the Fourier spectral analysis. The system must be linear, and the data must be stationary- otherwise, the resulting spectrum will make little physical sense. The stationarity requirement is also a common required criterion for most of other available data analysis methods. Nevertheless, few, if any, natural phenomena are linear and stationary. To compound these complications is the imperfection of our probes or numerical schemes the interactions of the imperfect probes even with a perfect linear system can make the final data nonlinear. Furthermore, all the available data are usually of finite duration. Under these conditions, Fourier analysis is of limited use, For lack of alternatives, however, Fourier analysis is still used to process such data. The loose application of Fourier analysis and the insouciant adoption of the stationary and linear assumptions may lead to misleading conclusions. Ocean waves are know to be nonlinear, and the wind system generating the wave field are seldom stationary- As a result, the traditional examination of the spectral form hardly made physical sense. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data, This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. The spectral forms of the ocean waves are very different. This new method offers the first physical meaningful view of the wave spectrum. Data from laboratory and field will be presented to illustrate the differences.

Huang, Norden E.↗
NASA NTRS1998

Baseline Observations of Hemispheric Sea Ice with the Nimbus 7 Scanning Multichannel Microwave Radiometer

The Scanning Multichannel Microwave Radiometer (SMMR) on board the NASA Nimbus 7 satellite was designed to obtain data for sea surface temperatures (SSTs), near-surface wind speeds, sea ice coverage and type, rainfall rates over the oceans, cloud water content, snow water equivalent, and soil moisture. In this paper, I shall emphasize the sea ice observations and mention briefly some important SST observations. A prime factor contributing to the importance of SMMR sea ice observations lies in their successful integration into a long-term time series, presently being extended by observations from the series of Special Sensor Microwave/Imager (SSMI) on board the DOD/DMSP F8, Fl1, and F12 satellites. This currently constitutes a 19-year data set. Almost half of this was provided by the SMMR. Unfortunately, the 4-year data set produced earlier by the single-channel Electrically Scanned Microwave Radiometer (ESMR) was not successfully integrated into the SMMR/SSMI data set. This resulted primarily from the lack of an overlap period to provide intersensor adjustment, but also because of the large difference between the algorithms to produce ice concentrations and large temporal gaps in the ESMR data. The lack of overlap between the SeaSat and Nimbus 7 SMMR data sets was an important consideration for also excluding the SeatSat one, but the spatial gaps especially in the Southern Hemisphere daily SeaSat observations was another. The sea ice observations will continue into the future by means of the Advanced Microwave Scanning Radiometer (AMSR) on board the ADEOS II and EOS satellites due to be launched in mid- and late-2000, respectively. Analysis of the sea ice data has been carried out by a number of different techniques. Long-term trends have been examined by means of ordinary least squares and band-limited regression. Oscillations in the data have been examined by band-limited Fourier analysis. Here, I shall present results from a novel combination of Principal Component analysis and the recently-developed Empirical Mode Decomposition (EMD). In this method, the data are first separated into spatial and temporal parts, and then the temporal parts of the first few PCs are broken into intrinsic modes by the EMD method.

Gloersen, Per↗
NASA NTRS2000

Laboratory Study of Water Surface Roughness Generation by Wave-Current Interaction

Within the framework of this project, the blocking of waves by inhomogeneous currents was studied. A laboratory experiment was conducted in collaboration with Steven R. Long at the linear wave tank of the NASA Air-Sea Interaction Facility, Wallops Island, VA during May 1999. Mechanically-generated waves were blocked approximately 3m upstream from the wave paddle by an opposing current. A false bottom was used to obtain a spatially varying flow field in the measurement section of the wave tank. We used an imaging slope gauge, which was mounted directly underneath the sloping section of the false tank bottom to observe the wave field. For a given current speed, the amplitude and the frequency of the waves was adjusted so that the blocking occurred within the observed footprint. Image sequences of up to 600 images at up 100 Hz sampling rate were recorded for an area of approximately 25cm x 25cm. Unlike previous measurements with wave wire gauges, the captured image sequences show the generation of the capillary waves at the blocking point and give detailed insight into the spatial and temporal evolution of the blocking process. The image data were used to study the wave-current interaction for currents from 5 to 25 cm/s and waves with frequencies between 1 and 3 Hz. First the images were calibrated with regard to size and slope. Then standard Fourier techniques as well the empirical mode decomposition method developed by Dr. Norden Huang and Dr. Steven R. Long were employed to quantify the wave number downshift from the gravity to the capillary regime.

Klinke, Jochen↗
NASA NTRS2000

A Bridge Health Monitoring Method Using the Hilbert-Huang Transform: A Case Study

We have developed a new method for nondestructive instrument method to monitor the health of a bridge. This new method is based on a transient test load and simple data collection. The nuclear of the method is the new invented nonstationary and nonlinear time series analysis method, the Empirical Mode Decomposition and Hilbert Spectral Analysis. The final decision on the health of the bridge structure is based on the nonlinear characteristic of the data, and on the comparison between the free and the forced vibration frequencies. Thus this alternative method enjoys many advantages: (1) no a priori data required, (2) simple data collection, and (3) minimum traffic disruption. Results from a case study of the Shing-Nan Bridge in Hou-Wei will be reported.

Huang, Norden E.↗
NASA NTRS2000

A New View of Earthquake Ground Motion Data: The Hilbert Spectral Analysis

A brief description of the newly developed Empirical Mode Decomposition (ENID) and Hilbert Spectral Analysis (HSA) method will be given. The decomposition is adaptive and can be applied to both nonlinear and nonstationary data. Example of the method applied to a sample earthquake record will be given. The results indicate those low frequency components, totally missed by the Fourier analysis, are clearly identified by the new method. Comparisons with Wavelet and window Fourier analysis show the new method offers much better temporal and frequency resolutions.

Huang, Norden↗
NASA NTRS2001

Impacts of ENSO on the South American Summer Monsoon During 1997-1999

Using the National Center for Environmental Prediction (NCEP) Reanalysis, and CPC Merged Analysis Product (CMAP) rainfall, we have compared and contrasted the anomalies of the South American Summer Monsoon (SASM) during two extreme years of 1997/98 (EI Nino) and 1998/99 (La Nina). The results are assessed against a "canonical" ENSO response (CER) pattern for the SASM obtained from empirical mode decomposition based on a previous period (1980-1995). Overall, the SASM anomalies compare well with CER, but with some important differences. Anomalies occurring in the warm phase of the 1997-98 El Nino are very significant and robust, while those occurring in 1998/99 La Nina, appear to be reversed from 1997/98, but are relatively weak and less well-defined. The most pronounced signal in DJF 1997/98 is the development of drought conditions in northern Brazil, excessive rainfall over northern Peru and Ecuador, and over Uruguay and southern Brazil. The tropical rainfall anomalies are associated with the eastward shift of the Walker circulation, which is represented by pronounced low-level anomalous westerlies over the equatorial eastern Pacific and easterlies over northern Brazil. The easterlies are deflected sharply southeastward by the steep topography of the Andes, enhancing the low-level jet (LLJ) along the eastern foothills of the Andes near 15-20 S. The LLJ penetrates deep into the extratropics, yielding rainfall anomalies further poleward compared to CER. During DJF 1997/98, the eastward expansion of the warm tropospheric temperature over the Nino-3 region causes anomalous geopotential height to develop in the upper troposphere above the Altiplano, leading to a strengthened Bolivian High. An upper-tropospheric jet anomaly maximum is found over the subtropical continent near 30 S, due to increasing meridional gradient of tropospheric temperature, as well as teleconnection patterns linking the South Pacific and the South Atlantic. Consistent with the CER, the South Pacific High is weakened, and the South Atlantic High is strengthened in DJF 1997/98. However, rather than appearing as a coherent large scale signal over the entire Atlantic as in CER, the South Atlantic High anomalies in DJF 1997/98 split into two separate high pressure centers; one located south of the Amazon basin, and another over the southeastern South Atlantic. The former is induced as a Rossby-wave response by ENSO-Induced sinking motion over nor-them and eastern Brazil, and the latter may be associated with extratropical teleconnection signals. Anomalous convection observed over equatorial western Africa may also have contributed to the different circulation response over the Atlantic in DFJ 1997/99 compared to the CER. Comparison of the evolution of the SASM anomalies in 1997-99 with their corresponding annual cycles, suggest that the anomalies are phase-locked to and represent either enhancement or reduction of the annual variations. Results suggest that, from a system perspective the SASM was strengthened during the 1997/98 El Nino and weakened, albeit to a lesser extent, during the 1998/99 La Nina.

Lau, K.-M.↗
NASA NTRS2001

Applications of the Hilbert-Huang Transform

A new method, the Hilbert-Huang Transform, has been developed for analyzing nonlinear and nonstationary data. The key part of the method is the Empirical Mode Decomposition with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An M is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies'as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. With this technique we can examine the detailed dynamics characteristics of a nonlinear system through the instantaneous frequency rather than harmonics. Thus it constitutes a new view of the nonlinear dynamics. Examples of classic nonlinear equations and other nonlinear and nonstationary data sets will be used as examples to illustrate the advantage of the application of this new data analysis method.

Huang, Norden E.↗
NASA NTRS2003

On the Confidence Limit of Hilbert Spectrum

Confidence limit is a routine requirement for Fourier spectral analysis. But this confidence limit is established based on ergodic theory: For stationary process, temporal average equals the ensemble average. Therefore, one can divide the data into n-sections and treat each section as independent realization. Most natural processes in general, and climate data in particular, are not stationary; therefore, there is a need for the Hilbert Spectral analysis for such processes. Here ergodic theory is no longer applicable. We propose to use various adjustable parameters in the shifting processes of the Empirical Mode Decomposition (EMD) method to obtain an ensemble of Intrinsic Mode Function 0 sets. Based on such an ensemble, we introduce a statistical measure in. a form of confidence limits for the Intrinsic Mode Functions, and consequently, the Hilbert spectra. The criterion of selecting the various adjustable parameters is based on the orthogonality test of the resulting M F sets. Length-of-day data from 1962 to 2001 will be used to illustrate this new approach. Its implication in climate data analysis will also be discussed.

Huang, Norden↗
NASA NTRS2003

Applications of Hilbert Spectral Analysis for Speech and Sound Signals

A new method for analyzing nonlinear and nonstationary data has been developed, and the natural applications are to speech and sound signals. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time, which give sharp identifications of imbedded structures. This method invention can be used to process all acoustic signals. Specifically, it can process the speech signals for Speech synthesis, Speaker identification and verification, Speech recognition, and Sound signal enhancement and filtering. Additionally, as the acoustical signals from machinery are essentially the way the machines are talking to us. Therefore, the acoustical signals, from the machines, either from sound through air or vibration on the machines, can tell us the operating conditions of the machines. Thus, we can use the acoustic signal to diagnosis the problems of machines.

Huang, Norden E.↗
NASA NTRS2004

On the Hilbert-Huang Transform Theoretical Foundation

The Hilbert-Huang Transform [HHT] is a novel empirical method for spectrum analysis of non-linear and non-stationary signals. The HHT is a recent development and much remains to be done to establish the theoretical foundation of the HHT algorithms. This paper develops the theoretical foundation for the convergence of the HHT sifting algorithm and it proves that the finest spectrum scale will always be the first generated by the HHT Empirical Mode Decomposition (EMD) algorithm. The theoretical foundation for cutting an extrema data points set into two parts is also developed. This then allows parallel signal processing for the HHT computationally complex sifting algorithm and its optimization in hardware.

Kizhner, Semion↗
NASA NTRS2005

Aeroelastic Flight Data Analysis with the Hilbert-Huang Algorithm

This paper investigates the utility of the Hilbert-Huang transform for the analysis of aeroelastic flight data. It is well known that the classical Hilbert transform can be used for time-frequency analysis of functions or signals. Unfortunately, the Hilbert transform can only be effectively applied to an extremely small class of signals, namely those that are characterized by a single frequency component at any instant in time. The recently-developed Hilbert-Huang algorithm addresses the limitations of the classical Hilbert transform through a process known as empirical mode decomposition. Using this approach, the data is filtered into a series of intrinsic mode functions, each of which admits a well-behaved Hilbert transform. In this manner, the Hilbert-Huang algorithm affords time-frequency analysis of a large class of signals. This powerful tool has been applied in the analysis of scientific data, structural system identification, mechanical system fault detection, and even image processing. The purpose of this paper is to demonstrate the potential applications of the Hilbert-Huang algorithm for the analysis of aeroelastic systems, with improvements such as localized/online processing. Applications for correlations between system input and output, and amongst output sensors, are discussed to characterize the time-varying amplitude and frequency correlations present in the various components of multiple data channels. Online stability analyses and modal identification are also presented. Examples are given using aeroelastic test data from the F/A-18 Active Aeroelastic Wing aircraft, an Aerostructures Test Wing, and pitch-plunge simulation.

Brenner, Marty↗
NASA NTRS2005

On the Hilbert-Huang Transform Theoretical Developments

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as linearity, of being stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposition data, the HHT allows spectrum analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a near orthogonal adaptive basis, a basis that is derived from the data. The IMFs can be further analyzed for spectrum interpretation by the classical Hilbert Transform. A new engineering spectrum analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications post additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs near orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the developments of new HHT processing options, such as real-time and 2-D processing using Field Programmable Array (FPGA) computational resources, enhanced HHT synthesis, and broaden the scope of HHT applications for signal processing.

Kizhner, Semion↗
NASA NTRS2006

On Certain Theoretical Developments Underlying the Hilbert-Huang Transform

One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real-value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a nearly orthogonal derived from the data (adaptive) basis. The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2-D processing using Field Programmable Gate Array (FPGA) computational resources,

Kizhner, Semion↗
NASA NTRS2006

Aeroelastic Flight Data Analysis with the Hilbert-Huang Algorithm

This report investigates the utility of the Hilbert Huang transform for the analysis of aeroelastic flight data. It is well known that the classical Hilbert transform can be used for time-frequency analysis of functions or signals. Unfortunately, the Hilbert transform can only be effectively applied to an extremely small class of signals, namely those that are characterized by a single frequency component at any instant in time. The recently-developed Hilbert Huang algorithm addresses the limitations of the classical Hilbert transform through a process known as empirical mode decomposition. Using this approach, the data is filtered into a series of intrinsic mode functions, each of which admits a well-behaved Hilbert transform. In this manner, the Hilbert Huang algorithm affords time-frequency analysis of a large class of signals. This powerful tool has been applied in the analysis of scientific data, structural system identification, mechanical system fault detection, and even image processing. The purpose of this report is to demonstrate the potential applications of the Hilbert Huang algorithm for the analysis of aeroelastic systems, with improvements such as localized online processing. Applications for correlations between system input and output, and amongst output sensors, are discussed to characterize the time-varying amplitude and frequency correlations present in the various components of multiple data channels. Online stability analyses and modal identification are also presented. Examples are given using aeroelastic test data from the F-18 Active Aeroelastic Wing airplane, an Aerostructures Test Wing, and pitch plunge simulation.

Brenner, Martin J.↗
NASA NTRS2006

Does The Nile Reflect Solar Variability?

Historical records of the Nile water level provide a unique opportunity to investigate the possibility that solar variability influences the Earth's climate. Particularly important are the annual records of the water level, which are uninterrupted for the years 622-1470 A.D. These records are non-stationary, so that standard spectral analyses cannot adequately characterize them. Here the Empirical Mode Decomposition technique, which is designed to deal with nonstationary, nonlinear time series, becomes useful. It allows the identification of two characteristic time scales in the water level data that can be linked to solar variability: the 88 year period and a time scale of about 200 years. These time scales are also present in the concurrent aurora data. Auroras are driven by coronal mass ejections and the rate of auroras is an excellent proxy for solar variability. Analysis of auroral data contemporaneous with the Nile data shows peaks at 88 years and about 200 years. This suggests a physical link between solar variability and the low frequency variations of the Nile water level. The link involves the influence of solar variability on the North Annual Mode of atmospheric variability and its North Atlantic and Indian Oceans patterns that affect rainfall over Eastern Equatorial Africa where the Nile originates.

statistical methods↗
NASA NTRS2006

Is Solar Variability Reflected in the Nile River?

We investigate the possibility that solar variability influences North African climate by using annual records of the water level of the Nile collected in 622-1470 A.D. The time series of these records are nonstationary, in that the amplitudes and frequencies of the quasi-periodic variations are time-dependent. We apply the Empirical Mode Decomposition technique especially designed to deal with such time series. We identify two characteristic timescales in the records that may be linked to solar variability: a period of about 88 years and one exceeding 200 years. We show that these timescales are present in the number of auroras reported per decade in the Northern Hemisphere at the same time. The 11-year cycle is seen in the Nile's high-water level variations, but it is damped in the low-water anomalies. We suggest a possible physical link between solar variability and the low-frequency variations of the Nile water level. This link involves the influence of solar variability on the atmospheric Northern Annual Mode and on its North Atlantic Ocean and Indian Ocean patterns that affect the rainfall over the sources of the Nile in eastern equatorial Africa.

solar variability↗