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All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Application of Hilbert-Huang Transform for Improved Defect Detection in Terahertz NDE of Shuttle Tiles

Terahertz NDE is being examined as a method to inspect the adhesive bond-line of Space Shuttle tiles for defects. Terahertz signals are generated and detected, using optical excitation of biased semiconductors with femtosecond laser pulses. Shuttle tile samples were manufactured with defects that included repair regions unbond regions, and other conditions that occur in Shuttle structures. These samples were inspected with a commercial terahertz NDE system that scanned a tile and generated a data set of RF signals. The signals were post processed to generate C-scan type images that are typically seen in ultrasonic NDE. To improve defect visualization the Hilbert-Huang Transform, a transform that decomposes a signal into oscillating components called intrinsic mode functions, was applied to test signals identified as being in and out of the defect regions and then on a complete data set. As expected with this transform, the results showed that the decomposed low-order modes correspond to signal noise while the high-order modes correspond to low frequency oscillations in the signal and mid-order modes correspond to local signal oscillations. The local oscillations compare well with various reflection interfaces and the defect locations in the original signal.

Anastasi, Robert F.↗
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

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 NTRS2013

Advanced Signal Processing for High Temperatures Health Monitoring of Condensed Water Height in Steam Pipes

An advanced signal processing methodology is being developed to monitor the height of condensed water thru the wall of a steel pipe while operating at temperatures as high as 250deg. Using existing techniques, previous study indicated that, when the water height is low or there is disturbance in the environment, the predicted water height may not be accurate. In recent years, the use of the autocorrelation and envelope techniques in the signal processing has been demonstrated to be a very useful tool for practical applications. In this paper, various signal processing techniques including the auto correlation, Hilbert transform, and the Shannon Energy Envelope methods were studied and implemented to determine the water height in the steam pipe. The results have shown that the developed method provides a good capability for monitoring the height in the regular conditions. An alternative solution for shallow water or no water conditions based on a developed hybrid method based on Hilbert transform (HT) with a high pass filter and using the optimized windowing technique is suggested. Further development of the reported methods would provide a powerful tool for the identification of the disturbances of water height inside the pipe.

health monitoring↗
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 NTRS2001

A New Method for Nonlinear and Nonstationary Time Series Analysis: The Empirical Mode Decomposition Method

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. Classical nonlinear system models are used to illustrate the roles played by the nonlinear and nonstationary effects in the energy-frequency-time distribution.

Huang, Norden E.↗
NASA NTRS2001

On the Application of Hilbert Spectral Analysis for Climate Studies

The Hilbert spectral analysis (Huang et al, 1998, Proceedings of the Royal Society of London, A 454, pp 903-995) consisted of two steps: First, the data has to be reduced into a finite number of Intrinsic Mode Function by the Empirical Mode Decomposition method, then the resulting Intrinsic Mode Functions are converted to time-frequency-energy distribution through Hilbert transform. In this approach, the Empirical Mode Functions served as the basis functions with which the data is expanded. This basis function is adaptive, and the decomposition is nonlinear. Furthermore, as the Hilbert transform is a singular transform, it retains a high degree of local information. The instantaneous frequency is determined by differentiation of the phase function; therefore, there is no restriction of the 'uncertainty principle' for all the time-frequency analysis resulting from a priori basis approach. With the adaptive basis and the instantaneous frequency, the Hilbert Spectral analysis can represent data from nonlinear and nonstationary processes without resorting to the harmonics. Another advantage of using instantaneous frequency is the ability to find out frequency from limited length of data, which is a critical problem in climate studies. As the processes driving the climate changes could be both nonlinear and nonstationary, the Hilbert Spectral Analysis could be of great use in examining the underlying mechanisms. A preliminary study based on the length of day data will be presented as example for the application of the Hilbert Spectral Analysis for climate study.

Huang, Norden E.↗
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 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 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 NTRS2004

Acoustic Emission Analysis of Shuttle Thermal Protection System

Acoustic emission (AE) signals generated from projectile impacts on reinforced and advanced carbon/carbon (RCC and ACC) panels, fired from a compressed-gas gun, identify the type and severity of damage sustained by the target. This type of testing is vital in providing the required "return to flight" (RTF) data needed to ensure continued and safe operation of NASA's Space Shuttle fleet. The gas gun at Kennedy Space Center is capable of propelling 12-inch by 3-inch cylinders of external tank (ET) foam at exit velocities exceeding 1,000 feet per second. Conventional AE analysis techniques require time domain processing of impulse data, along with amplitude distribution analysis. It is well known that identical source excitations can produce a wide range of AE signals amplitudes. In order to satisfy RTF goals, it is necessary to identify impact energy levels above and below damage thresholds. Spectral analysis techniques involving joint time frequency analysis (JTFA) are used to reinforce time domain AE analysis. JTFA analysis of the AE signals consists of short-time Fourier transforms (STFT) and the Huang-Hilbert transform (HHT). The HHT provides a very good measure of the instantaneous frequency of impulse events dominated by a single component. Identifying failure modes and cracking of fibers from flexural and/or extensional mode acoustic signals will help support in-flight as well as postflight impact analysis.

Lane, John↗
NASA NTRS1972

Approximations to the plasma dispersion function

Linear wave propagation in hot collisionless plasmas is described by the linearized Vlasov and Maxwell equations. In uniform media, the utilization of spatial and temporal transforms of those equations leads to the consideration of integrals of the Hilbert transform type. Analysis and comparison of two simple approximations are provided based on the utilization of resonance velocity distributions. Application is then made to the Landau and whistler waves, along with a discussion of the results, and commentary on possible improvements.

Brinca, A. L.↗
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 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 NTRS1998

Empirical Mode Decomposition and Hilbert Spectral Analysis

The difficult facing data analysis is the lack of method to handle nonlinear and nonstationary time series. Traditional Fourier-based analyses simply could not be applied here. 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. Examples from the numerical results of the classical nonlinear equation systems and data representing natural phenomena are given to demonstrate the power of this new method. The classical nonlinear system data are especially interesting, for they serve to illustrate the roles played by the nonlinear and nonstationary effects in the energy-frequency-time distribution.

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 NTRS1997

Frictionless Contact of Multilayered Composite Half Planes Containing Layers With Complex Eigenvalues

A previously developed local-global stiffness matrix methodology for the response of a composite half plane, arbitrarily layered with isotropic, orthotropic or monoclinic plies, to indentation by a rigid parabolic punch is further extended to accommodate the presence of layers with complex eigenvalues (e.g., honeycomb or piezoelectric layers). First, a generalized plane deformation solution for the displacement field in an orthotropic layer or half plane characterized by complex eigenvalues is obtained using Fourier transforms. A local stiffness matrix in the transform domain is subsequently constructed for this class of layers and half planes, which is then assembled into a global stiffness matrix for the entire multilayered half plane by enforcing continuity conditions along the interfaces. Application of the mixed boundary condition on the top surface of the half plane indented by a rigid punch results in an integral equation for the unknown pressure in the contact region. The integral possesses a divergent kernel which is decomposed into Cauchy-type and regular parts using the asymptotic properties of the local stiffness matrix and a relationship between Fourier and finite Hilbert transform of the contact pressure. The solution of the resulting singular integral equation is obtained using a collocation technique based on the properties of orthogonal polynomials developed by Erdogan and Gupta. Examples are presented that illustrate the important influence of low transverse properties of layers with complex eigenvalues, such as those exhibited by honeycomb, on the load versus contact length response and contact pressure distributions for half planes containing typical composite materials.

Zhang, Wang↗