Engineering topics

Huang, Norden E.

Publications and source records attributed to Huang, Norden E..

At least 19 records

NASA NTRS2016

On Holo-Hilbert Spectral Analysis: A Full Informational Spectral Representation for Nonlinear and Non-Stationary Data

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert-Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time- frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and nonstationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities.

Huang, Norden E.↗

NASA NTRS2009

An Analysis of Moisture Fluxes into the Gulf of California

This study examines the nature of episodes of enhanced warm-season moisture flux into the Gulf of California. Both spatial structure and primary time scales of the fluxes are examined using the 40-yr ECMWF Re-Analysis data for the period 1980-2001. The analysis approach consists of a compositing technique that is keyed on the low-level moisture fluxes into the Gulf of California. The results show that the fluxes have a rich spectrum of temporal variability, with periods of enhanced transport over the gulf linked to African easterly waves on subweekly (3-8 day) time scales, the Madden-Julian oscillation (MJO) at intraseasonal time scales (20-90 day), and intermediate (10-15 day) time-scale disturbances that appear to originate primarily in the Caribbean Sea-western Atlantic Ocean. In the case of the MJO, enhanced low-level westerlies and large-scale rising motion provide an environment that favors large-scale cyclonic development near the west coast of Central America that, over the course of about 2 weeks, expands northward along the coast eventually reaching the mouth of the Gulf of California where it acts to enhance the southerly moisture flux in that region. On a larger scale, the development includes a northward shift in the eastern Pacific ITCZ, enhanced precipitation over much of Mexico and the southwestern United States, and enhanced southerly/southeasterly fluxes from the Gulf of Mexico into Mexico and the southwestern and central United States. In the case of the easterly waves, the systems that reach Mexico appear to redevelop/reorganize on the Pacific coast and then move rapidly to the northwest to contribute to the moisture flux into the Gulf of California. The most intense fluxes into the gulf on these time scales appear to be synchronized with a midlatitude short-wave trough over the U.S. West Coast and enhanced low-level southerly fluxes over the U.S. Great Plains. The intermediate (10-15 day) time-scale systems have zonal wavelengths roughly twice that of the easterly waves, and their initiation appears to be linked to an extratropical U.S. East Coast ridge and associated northeasterly winds that extend well into the Caribbean Sea during their development phase. The short (3-8 day) and, to a lesser extent, the intermediate (10-15 day) time-scale fluxes tend to be enhanced when the convectively active phase of the MJO is situated over the Americas.

Wu, Man-Li C.↗

NASA NTRS2008

Analyzing nonstationary financial time series via hilbert-huang transform (HHT)

An apparatus, computer program product and method of analyzing non-stationary time varying phenomena. A representation of a non-stationary time varying phenomenon is recursively sifted using Empirical Mode Decomposition (EMD) to extract intrinsic mode functions (IMFs). The representation is filtered to extract intrinsic trends by combining a number of IMFs. The intrinsic trend is inherent in the data and identifies an IMF indicating the variability of the phenomena. The trend also may be used to detrend the data.

Huang, Norden E.↗

NASA NTRS2008

System and method of analyzing vibrations and identifying failure signatures in the vibrations

An apparatus, computer program product and method of analyzing structures. Intrinsic Mode Functions (IMFs) are extracted from the data and the most energetic IMF is selected. A spline is fit to the envelope for the selected IMF. The spline derivative is determined. A stability spectrum is developed by separating the positive and negative results into two different spectra representing stable (positive) and unstable (negative) damping factors. The stability spectrum and the non-linearity indicator are applied to the data to isolate unstable vibrations.

Huang, Norden E.↗

NASA NTRS2007

Computing a Stability Spectrum by Use of the HHT

The Hilbert-Huang transform (HHT) is part of the mathematical basis of a method of calculating a stability spectrum. This method can be regarded as an extended and improved version of a prior HHT-based method of calculating a damping spectrum. In the prior method, information on positive damping (which leads to stability) and negative damping (which leads to instability) becomes mixed into a single squared damping loss factor. Hence, there is no way to distinguish between stability and instability by examining a damping spectrum. In contrast, in the present stabilityspectrum method, information on the mathematical sign of the damping is retained, making it possible to identify reThe Hilbert-Huang transform (HHT) is part of the mathematical basis of a method of calculating a stability spectrum. This method can be regarded as an extended and improved version of a prior HHT-based method of calculating a damping spectrum. In the prior method, information on positive damping (which leads to stability) and negative damping (which leads to instability) becomes mixed into a single squared damping loss factor. Hence, there is no way to distinguish between stability and instability by examining a damping spectrum. In contrast, in the present stabilityspectrum method, information on the mathematical sign of the damping is retained, making it possible to identify regions of instability in a spectrum. This method is expected to be especially useful for analyzing vibration-test data for the purpose of predicting vibrational instabilities in structures (e.g., flutter in airplane wings).

Huang, Norden E.↗

NASA NTRS2006

Computing frequency by using generalized zero-crossing applied to intrinsic mode functions

This invention presents a method for computing Instantaneous Frequency by applying Empirical Mode Decomposition to a signal and using Generalized Zero-Crossing (GZC) and Extrema Sifting. The GZC approach is the most direct, local, and also the most accurate in the mean. Furthermore, this approach will also give a statistical measure of the scattering of the frequency value. For most practical applications, this mean frequency localized down to quarter of a wave period is already a well-accepted result. As this method physically measures the period, or part of it, the values obtained can serve as the best local mean over the period to which it applies. Through Extrema Sifting, instead of the cubic spline fitting, this invention constructs the upper envelope and the lower envelope by connecting local maxima points and local minima points of the signal with straight lines, respectively, when extracting a collection of Intrinsic Mode Functions (IMFs) from a signal under consideration.

Huang, Norden E.↗

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 NTRS2005

Computing Instantaneous Frequency by normalizing Hilbert Transform

This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.

Huang, Norden E.↗

NASA NTRS2005

Empirical mode decomposition for analyzing acoustical signals

The present invention discloses a computer implemented signal analysis method through the Hilbert-Huang Transformation (HHT) for analyzing acoustical signals, which are assumed to be nonlinear and nonstationary. The Empirical Decomposition Method (EMD) and the Hilbert Spectral Analysis (HSA) are used to obtain the HHT. Essentially, the acoustical signal will be decomposed into the Intrinsic Mode Function Components (IMFs). Once the invention decomposes the acoustic signal into its constituting components, all operations such as analyzing, identifying, and removing unwanted signals can be performed on these components. Upon transforming the IMFs into Hilbert spectrum, the acoustical signal may be compared with other acoustical signals.

Huang, Norden E.↗

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 NTRS2004

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.

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 NTRS2003

Acoustical Applications of the HHT Method

A document discusses applications of a method based on the Huang-Hilbert transform (HHT). The method was described, without the HHT name, in Analyzing Time Series Using EMD and Hilbert Spectra (GSC-13817), NASA Tech Briefs, Vol. 24, No. 10 (October 2000), page 63. To recapitulate: The method is especially suitable for analyzing time-series data that represent nonstationary and nonlinear physical phenomena. The method involves the empirical mode decomposition (EMD), in which a complicated signal is decomposed into a finite number of functions, called intrinsic mode functions (IMFs), that admit well-behaved Hilbert transforms. The HHT consists of the combination of EMD and Hilbert spectral analysis.

Huang, Norden E.↗

NASA NTRS2003

Update on EMD and Hilbert-Spectra Analysis of Time Series

This method is especially well suited for analyzing time-series data that represent nonstationary and nonlinear physical phenomena. The method is based principally on the concept of empirical mode decomposition (EMD), according to which any complicated signal (as represented by digital samples) can be decomposed into a finite number of functions, called "intrinsic mode functions" (IMFs), that admit well-behaved Hilbert transforms. The local energies and the instantaneous frequencies derived from the IMFs through Hilbert transforms can be used to construct an energy-frequency-time distribution, denoted a Hilbert spectrum.

Huang, Norden E.↗

NASA NTRS2003

On the Hilbert-Huang Transform Data Processing System Development

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). The Fourier view of nonlinear mechanics that had existed for a long time, and the associated FFT (fairly recent development), carry strong a-priori assumptions about the source data, such as linearity and of being stationary. Natural phenomena measurements are essentially nonlinear and nonstationary. A very 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 the Empirical Mode Decomposition (EMD) followed by the Hilbert Transform of the empirical decomposition data (HT), the HHT allows spectrum analysis of nonlinear and nonstationary data by using an engineering a-posteriori data processing, based on the EMD algorithm. This results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF) that can be further analyzed for spectrum interpretation by the classical Hilbert Transform. This paper describes phase one of the development of a new engineering tool, the HHT Data Processing System (HHTDPS). The HHTDPS allows applying the "T to a data vector in a fashion similar to the heritage FFT. It is a generic, low cost, high performance personal computer (PC) based system that implements the HHT computational algorithms in a user friendly, file driven environment. This paper also presents a quantitative analysis for a complex waveform data sample, a summary of technology commercialization efforts and the lessons learned from this new technology development.

Kizhner, Semion↗

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 NTRS2002

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

Huang, Norden E.↗

NASA NTRS2001

Computer implemented empirical mode decomposition method, apparatus, and article of manufacture for two-dimensional signals

A computer implemented method of processing two-dimensional physical signals includes five basic components and the associated presentation techniques of the results. The first component decomposes the two-dimensional signal into one-dimensional profiles. The second component is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF's) from each profile based on local extrema and/or curvature extrema. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the profiles. In the third component, the IMF's of each profile are then subjected to a Hilbert Transform. The fourth component collates the Hilbert transformed IMF's of the profiles to form a two-dimensional Hilbert Spectrum. A fifth component manipulates the IMF's by, for example, filtering the two-dimensional signal by reconstructing the two-dimensional signal from selected IMF(s).

Huang, Norden E.↗