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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Turbulent Statistics from Time-Resolved PIV Measurements of a Jet Using Empirical Mode Decomposition

Empirical mode decomposition is an adaptive signal processing method that when applied to a broadband signal, such as that generated by turbulence, acts as a set of band-pass filters. This process was applied to data from time-resolved, particle image velocimetry measurements of subsonic jets prior to computing the second-order, two-point, space-time correlations from which turbulent phase velocities and length and time scales could be determined. The application of this method to large sets of simultaneous time histories is new. In this initial study, the results are relevant to acoustic analogy source models for jet noise prediction. The high frequency portion of the results could provide the turbulent values for subgrid scale models for noise that is missed in large-eddy simulations. The results are also used to infer that the cross-correlations between different components of the decomposed signals at two points in space, neglected in this initial study, are important.

Dahl, Milo D.↗
NASA NTRS2012

Turbulent Statistics from Time-Resolved PIV Measurements of a Jet Using Empirical Mode Decomposition

Empirical mode decomposition is an adaptive signal processing method that when applied to a broadband signal, such as that generated by turbulence, acts as a set of band-pass filters. This process was applied to data from time-resolved, particle image velocimetry measurements of subsonic jets prior to computing the second-order, two-point, space-time correlations from which turbulent phase velocities and length and time scales could be determined. The application of this method to large sets of simultaneous time histories is new. In this initial study, the results are relevant to acoustic analogy source models for jet noise prediction. The high frequency portion of the results could provide the turbulent values for subgrid scale models for noise that is missed in large-eddy simulations. The results are also used to infer that the cross-correlations between different components of the decomposed signals at two points in space, neglected in this initial study, are important.

Dahl, Milo D.↗
NASA NTRS2013

Turbulent Statistics From Time-Resolved PIV Measurements of a Jet Using Empirical Mode Decomposition

Empirical mode decomposition is an adaptive signal processing method that when applied to a broadband signal, such as that generated by turbulence, acts as a set of band-pass filters. This process was applied to data from time-resolved, particle image velocimetry measurements of subsonic jets prior to computing the second-order, two-point, space-time correlations from which turbulent phase velocities and length and time scales could be determined. The application of this method to large sets of simultaneous time histories is new. In this initial study, the results are relevant to acoustic analogy source models for jet noise prediction. The high frequency portion of the results could provide the turbulent values for subgrid scale models for noise that is missed in large-eddy simulations. The results are also used to infer that the cross-correlations between different components of the decomposed signals at two points in space, neglected in this initial study, are important.

Dahl, Milo D.↗
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.↗
DOE OSTI2021

Hybrid Improved Empirical Mode Decomposition and Artificial Neural Network Model for the Prediction of Critical Heat Flux (CHF)

Three Hybrid artificial neural network (ANN) models namely radial basis function (RBF), generalized regression neural networks (GRNN), and multi-layer perceptron (MLP) combined with empirical mode decomposition (EMD) are developed for CHF predictive modelling using CHF experimental databases.First, the original experimental inputs data series are decomposed into several intrinsic mode functions (IMFs) and one residual by EMD, whose components are divided into high, medium and low components. The performance parameters of the hybrid models indicates that the root mean square error (RMSE) are 0.8831, 0.6522, and 0.4149; the mean absolute error (MAE) are 0.6697, 0.4636, and 0.1935. The values of the R-square of the developed prediction approach utilizing EMD-RBF, EMD-GRNN, and EMD-MLP models are 0.8553, 0.9302, and 0.9818, and the index of agreement are 0.9464, 0.9700, and 0.9894., The value of the R-square and the index of agreement of the proposed models are much higher than those of the simple models .The Pearson's test results show that the association strength between the measured and the predicted values of the proposed model EMD-MLP is the strongest. These results show the following: (a) compared with other related, recent studies, the prediction accuracy of the hybrid model EMD- MLP proposed in this research is the best hybrid model; (b) the proposed hybrid model (EMD-MLP) attains superior performance compared with simple models.

Djeddou, Messaoud↗
NASA NTRS2002

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

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

Three dimensional empirical mode decomposition analysis apparatus, method and article manufacture

An apparatus and method of analysis for three-dimensional (3D) physical phenomena. The physical phenomena may include any varying 3D phenomena such as time varying polar ice flows. A repesentation of the 3D phenomena is passed through a Hilbert transform to convert the data into complex form. A spatial variable is separated from the complex representation by producing a time based covariance matrix. The temporal parts of the principal components are produced by applying Singular Value Decomposition (SVD). Based on the rapidity with which the eigenvalues decay, the first 3-10 complex principal components (CPC) are selected for Empirical Mode Decomposition into intrinsic modes. The intrinsic modes produced are filtered in order to reconstruct the spatial part of the CPC. Finally, a filtered time series may be reconstructed from the first 3-10 filtered complex principal components.

Gloersen, Per↗
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

Computer implemented empirical mode decomposition method, apparatus and article of manufacture

A computer implemented physical signal analysis method is invented. This method includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract 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. The final result is the 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.

Huang, Norden E.↗
NASA NTRS2003

Computer implemented empirical mode decomposition method apparatus, and article of manufacture utilizing curvature extrema

A computer implemented physical signal analysis method is includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals based on local extrema and curvature extrema. 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. The final result is the 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.

Huang, Norden Eh↗
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.↗
DOE OSTI2025

Bias correcting regional scale Earth system model projections: novel approach using empirical mode decomposition

Bias correction is a crucial step in using Earth system model outputs for assessments, as it adjusts systematic errors by comparing the model to observations. However, standard methods – ranging from mean-based linear scaling to distribution-based quantile mapping typically treat bias correction as a single-scale process, overlooking the fact that biases can manifest differently across daily, seasonal, and annual timescales. In this study, we propose a novel, timescale-aware bias-correction approach built on Empirical Mode Decomposition. By decomposing the meteorological signal into multiple oscillatory components and aggregating them to represent distinct timescales, we apply targeted corrections to each component, thereby preserving both short- and long-term structure in the data. Experimental illustrations show that the timescale-aware EMDBC framework matches the performance of conventional quantile-delta mapping (QDM) at the native daily scale and achieves progressively larger bias reductions at bi-weekly, seasonal, and annual scales. As a result, the proposed approach offers a more robust path to accurate and reliable Earth system projections, strengthening their utility for resilience and adaptation planning.

Ganguli, Arkaprabha [Argonne National Laboratory (↗
DOE OSTI2026

Temporal Convolutional Network Using Empirical Mode Decomposition to Detect Faults in Grid Connected Systems

Grid-connected power electronic systems require timely and reliable fault detection to prevent equipment damage and reduce downtime. This paper presents a forecasting-based anomaly detection pipeline that decomposes voltage and current measurements into intrinsic mode functions (IMFs) using empirical mode decomposition (EMD), then trains a causal temporal convolutional network (TCN) on normal-operation IMF data to predict short-horizon future dynamics. Deviations between forecasts and observations are summarized as reliability-weighted residual scores and thresholded per sensor using robust statistics with temporal persistence constraints to suppress false positives. To reduce runtime, EMD is performed on downsampled signals for detection, while raw-rate EMD is applied only within a short region of interest for high-frequency interpretability near detected events. Results on a simulated grid-connected converter system demonstrate that IMF-domain forecasting improves anomaly separability relative to raw-signal forecasting and provides interpretable evidence of faults across decomposition channels.

Sutton, Elizabeth [ORNL] (ORCID:0009000078885935)↗
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.↗
DOE OSTI2021

Hybrid Data-Driven Based HVdc Ancillary Control for Multiple Frequency Data Attacks

The high voltage direct current (HVdc) intertie has been applied to provide ancillary-services for ac grids, utilizing the real-time feedback from phasor measurement units (PMUs). However, PMU data communication is vulnerable to false data injection attacks (FDIA) due to protocol defects, thus the HVdc ancillary control and system stability will be threatened. To address this issue, this article proposes a novel HVdc control strategy based on a hybrid data-driven (HDD) methodology. In this work, the HDD methodology is first proposed to detect the types and duration time of multiple frequency attacks. Specifically, the Hilbert Huang transform (HHT) is used to decompose the frequency data, using variational mode decomposition instead of the traditional empirical mode decomposition, to extract data features. Second, a multikernel support vector machine is proposed to classify the attacked data based on the designed distinctive features from HHT. Meanwhile, the attacking duration time is decided using an unsupervised technique. Third, an HDD-based HVdc ancillary control strategy is established to eliminate the effect of FDIAs on the HVdc frequency response. Comprehensive experiments of HDD-based HVdc ancillary controls under different FDIAs suggest that the proposed HDD could fast and accurately classify the FDIAs, and the HDD-based HVdc ancillary control strategy could significantly suppress the impact of the FDIAs.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2021

Moisture and Temperature Influences on Nonlinear Vegetation Trends in Serengeti National Park

While long-term vegetation greening trends have appeared across large land areas over the late 20th century, uncertainty remains in identifying and attributing finer-scale vegetation changes and trends, particularly across protected areas. Serengeti National Park (SNP) is a critical East African protected area, where seasonal vegetation cycles support vast populations of grazing herbivores and a host of ecosystem dynamics. Previous work has shown how non-climate drivers (e.g. land use) shape the SNP ecosystem, but it is still unclear to what extent changing climate conditions influence SNP vegetation, particularly at finer spatial and temporal scales. We fill this research gap by evaluating long-term (1982–2016) changes in SNP leaf area index (LAI) in relation to both temperature and moisture availability using Ensemble Empirical Mode Decomposition and Principal Component Analysis with regression techniques. We find that SNP LAI trends are nonlinear, display high sub-seasonal variation, and are influenced by lagged changes in both moisture and temperature variables and their interactions. LAI during the long rains (e.g. March) exhibits a greening-to-browning trend reversal starting in the early 2000s, partly due to antecedent precipitation declines. In contrast, LAI during the short rains (e.g. November, December) displays browning-to-greening alongside increasing moisture availability. Rising temperature trends also have important, secondary interactions with moisture variables to shape these SNP vegetation trends. Our findings show complex vegetation-climate interactions occurring at important temporal and spatial scales of the SNP, and our rigorous statistical approaches detect these complex climate-vegetation trends and interactions, while guarding against spurious vegetation signals.

Moisture↗
DOE OSTI2020

Comparison of time-frequency-analysis techniques applied in building energy data noise cancellation for building load forecasting: A real-building case study

Time-frequency analysis that disaggregates a signal in both time and frequency domain is an important supporting technique for building energy analysis such as noise cancellation in data-driven building load forecasting. There is a gap in the literature related to comparing various time–frequency-analysis techniques, especially discrete wavelet transform (DWT) and empirical mode decomposition (EMD), to guide the selection and tuning of time–frequency-analysis techniques in data-driven building load forecasting. This article provides a framework to conduct a comprehensive comparison among thirteen DWT/EMD techniques with various parameters in a load forecasting modeling task. A real campus building is used as a case study for illustration. The DWT and EMD techniques are also compared under various data-driven modeling algorithms for building load forecasting. The results in the case study show that the load forecasting models trained with noise-cancelled energy data have increased their accuracy to 9.6% on average tested under unseen data. This study also shows that the effectiveness of DWT/EMD techniques depends on the data-driven algorithms used for load forecasting modeling and the training data. Hence, DWT/EMD-based noise cancellation needs customized selection and tuning to optimize their performance for data-driven building load forecasting modeling.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗