Multi-dimensional Ensemble Empirical Mode Decomposition Research Articles

Two-dimensional Hilbert-Huang transform-based thermographic data processing for non-destructive material defect detection

ABSTRACT Previous research has established the Hilbert-Huang transform (HHT) as a powerful tool for processing and analysing one-dimensional time series signals. Its extension into multi-dimensional Euclidean spaces further demonstrates its versatility. In this study, we leverage a two-dimensional (2D) HHT to enhance non-destructive testing, utilising active infrared thermographic data to improve the detection of material defects. The proposed methodology incorporates a 2D HHT, which synergises multidimensional ensemble empirical mode decomposition with the Riesz transform (RT). This combination is adept at uncovering both global (i.e. intrinsic mode functions) and local (i.e. phase angle and spatial frequency) information. In particular, RT is integrated with a Gaussian filter, which allows for a more thorough analysis of the inherent characteristics of defects through the monogenic signal produced by RT. The experimental application of this method on a mosaic sample, intentionally embedded with defects, has yielded promising results. The approach effectively distinguishes critical defect signals from the surroundings, leading to more accurate and clearer results.

Separation of ventilation and perfusion of electrical impedance tomography image streams using multi-dimensional ensemble empirical mode decomposition

Objective. In the future, thoracic electrical impedance tomography (EIT) monitoring may include continuous and simultaneous tracking of both breathing and heart activity. However, an effective way to decompose an EIT image stream into physiological processes as ventilation-related and cardiac-related signals is missing.Approach. This study analyses the potential of Multi-dimensional Ensemble Empirical Mode Decomposition by application of the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and a novel frequency-based combination criterion for detrending, denoising and source separation of EIT image streams, collected from nine healthy male test subjects with similar age and constitution.Main results. In this paper, a novel approach to estimate the lung, the heart and the perfused regions of an EIT image is proposed, which is based on the Root Mean Square Error between the index of maximal respiratory and cardiac variation to their surroundings. The summation of the indexes of the respective regions reveals physiologically meaningful time signals, separated into the physiological bandwidths of ventilation and heart activity at rest. Moreover, the respective regions were compared with the relative thorax movement and photoplethysmogram (PPG) signal. In linear regression analysis and in the Bland–Altman plot, the beat-to-beat time course of both the ventilation-related signal and the cardiac-related signal showed a high similarity with the respective reference signal.Significance. Analysis of the data reveals a fair separation of ventilatory and cardiac activity realizing the aimed source separation, with optional detrending and denoising. For all performed analyses, a feasible correlation of 0.587 to 0.905 was found between the cardiac-related signal and the PPG signal.

Responses of wildfire-induced global black carbon pollution and radiative forcing to climate change

The impacts of climate change on wildfires have been studied extensively. Along with declining emissions from fossil fuel combustion due to anthropogenic emission control, black carbon (BC) released from wildfires is expected to contribute a more significant portion to its atmospheric burden. However, from a global perspective, little is known about the BC burden and radiative forcing caused by wildfires. Here, we report the results from the long-term wildfire-induced BC concentration and direct radiative forcing (DRF) from 1981 to 2010 globally simulated by an Earth System Model using an updated wildfire BC emission inventory. We show that wildfire-induced BC concentration and DRF varied significantly spatially and temporarily, with the highest in sub-Saharan Africa, attributable to its highest level of wildfire BC emission worldwide. The temporal trends of near-surface air temperature, precipitation, and evapotranspiration and their association with wildfire-induced BC concentration are explored using the multidimensional ensemble empirical mode decomposition. A statistically significant relation between changes in climate parameters and wildfire-induced BC concentration was found for 53% of the land grid cells, explaining on average 33% of the concentration variations. The result suggests that the wildfire-induced BC DRF, with an increasing trend, would be an important contributor to climate change, especially in sub-Saharan Africa. Occurrences of wildfires in the Amazon Basin respond most strongly to climate change and play an increasingly important role in changing the global climate.

Improving GPR Imaging of the Buried Water Utility Infrastructure by Integrating the Multidimensional Nonlinear Data Decomposition Technique into the Edge Detection

Although ground-penetrating radar (GPR) is effective to detect shallow-buried objects, it still needs more effort for the application to investigate a buried water utility infrastructure. Edge detection is a well-known image processing technique that may improve the resolution of GPR images. In this study, we briefly review the theory of edge detection and discuss several popular edge detectors as examples, and then apply an enhanced edge detecting method to GPR data processing. This method integrates the multidimensional ensemble empirical mode decomposition (MDEEMD) algorithm into standard edge detecting filters. MDEEMD is implemented mainly for data reconstruction to increase the signal-to-noise ratio before edge detecting. A quantitative marginal spectrum analysis is employed to support the data reconstruction and facilitate the final data interpretation. The results of the numerical model study followed by a field example suggest that the MDEEMD edge detector is a competent method for processing and interpreting GPR data of a buried hot spring well, which cannot be efficiently handled by conventional techniques. Moreover, the proposed method should be readily considered a vital tool for processing other kinds of buried water utility infrastructures.

Multiscale Analysis of Solar Loading Thermographic Signals for Wall Structure Inspection.

Infrared thermography has been widely adopted in many applications for material structure inspection, where data analysis methods are often implemented to elaborate raw thermal data and to characterize material structural properties. Herein, a multiscale thermographic data analysis framework is proposed and applied to building structure inspection. In detail, thermograms are first collected by conducting solar loading thermography, which are then decomposed into several intrinsic mode functions under different spatial scales by multidimensional ensemble empirical mode decomposition. At each scale, principal component analysis (PCA) is implemented for feature extraction. By visualizing the loading vectors of PCA, the important building structures are highlighted. Compared with principal component thermography that applies PCA directly to raw thermal data, the proposed multiscale analysis method is able to zoom in on different types of structural features.

Long‐term evolution of global sea surface temperature trend

AbstractThe ocean plays an essential role in regulating global and regional climate, which is mainly achieved through sea surface temperature anomaly (SSTA) changes. Studies on global sea surface temperature (GSST) are primarily carried out under linear assumption, which is not capable of fully revealing the evolution characteristics of sea surface temperature (SST) due to the non‐linear and non‐stationary nature of the SST. Here, the evolution of the GSST trend in the past century is investigated by using an adaptive and local spatial–temporally multidimensional ensemble empirical mode decomposition method. The results show that the global ocean has been warming except for the subpolar North Atlantic, the equatorial central Pacific, and the Southern Ocean in the Pacific sector. The equatorial central Pacific turned from cooling to warming around the middle of the last century made it one of the fastest‐warming regions in recent decades with other regions located in the Arctic Ocean and the western‐boundary current regions and their mid‐latitude extensions in both hemispheres. The strongest warming during recent decades is found in the Arctic Ocean, east of the continents in the northern hemisphere, the entire Indian Ocean, and especially in the tropical Pacific Ocean. From a zonal average perspective, warming (>0.1 K since 1900) first took place in the subtropical regions of the Northern Hemisphere and 50°S of the Southern Hemisphere almost simultaneously around 1910, then followed by the subpolar warming in the Northern Hemisphere. The first two bands of warming both expanded equatorward leading to the fast warming of tropical oceans, especially for the Pacific Ocean.

Feature Extraction Algorithm Using a Correlation Coefficient Combined With the VMD and Its Application to the GPS and GRACE

To improve the reliability of the Global Positioning System (GPS) and Gravity Recovery and Climate Experiment (GRACE) feature extraction, this paper uses a correlation coefficient combined with the traditional variational mode decomposition (VMD), proposing a new correlation variational mode decomposition (CVMD). In contrast to previous studies, the CVMD denoises the sequences before feature extraction and it is the first time that be used in the GPS and GRACE. First, the correlation between the intrinsic mode function (IMF) and the original sequence is obtained to denoise the original sequence. Moreover, the algorithm reuses the VMD to obtain the IMF components with different frequencies. Then the Lomb Scargle (L-S) spectral analysis and energy density are used to obtain the trend-, seasonal, and residual items. Second, the features of the GPS and GRACE time series are extracted based on the CVMD and multidimensional ensemble empirical mode decomposition (MEEMD) to verify the availability of the CVMD. The results indicate that the CVMD is more superior to the MEEMD in feature extraction. Third, the CVMD is used to extract the trend- and seasonal terms of GPS and GRACE in the North China Plain (NCP). The conclusions are as follows: (1) the seasonal items of GRACE are used to correct the GPS sequences, and the average reduction of the weighted root mean square (WRMS) of each GPS station is 0.69, which demonstrates a strong consistency between the seasonal terms of the GPS sequence and GRACE sequence; (2) during 2003-2015, the mean slope of vertical displacements is 0.20 ± 0.07 mm / yr, and the uplift rate increases substantially (1.66 ± 0.62 mm / yr) after 2013. Then, the temporal and spatial relationship between rainfall and crustal load-deformation in the NCP is analyzed, and it is found that the crustal load-deformation is primarily related to rainfall, while human activities play a leading role in the southwestern regions where agricultural irrigation is relatively strong.

Evolution of NDVI secular trends and responses to climate change: A perspective from nonlinearity and nonstationarity characteristics

The evolution of vegetation patterns plays a crucial role in monitoring ecosystem dynamics in face of global warming. Notably, the time-series vegetation trends vary unevenly over time. However, conventional linear methods based on the stationarity assumption, cannot detect the implicit characteristics of nonlinear and gradual vegetation changes. Meanwhile, characterizing the inherent features of nonlinearity and nonstationarity of climatic drivers remains a challenge. This study applied multidimensional ensemble empirical mode decomposition (MEEMD) and Breaks For Additive Seasonal and Trend (BFAST) algorithm to diagnose spatiotemporal evolution and abrupt change in vegetation secular trends based on normalized difference vegetation index (NDVI) data of the Hexi Corridor during 1982–2015. Geographically and temporally weighted regression (GTWR) was used to address the spatiotemporal nonlinearity and nonstationarity of climatic drivers. A wide range of browning trends gradually evolved into greening trends from 1982 to 2015. Compared with ordinary least squares regression, MEEMD could adaptively decompose short-term trends of noise and seasonality and elucidate the entire evolutionary process of NDVI trends. Browning trends prevailed before abrupt changes, and greening trends widely expanded after 2006 due to drought before and intense precipitation during this year. GTWR addressed the nonequilibrium effect of the time dimension on climate drivers, and the R-squared achieved 0.86. The response processes between vegetation and climatic drivers showed significant spatiotemporal nonstationarity and aggregation characteristics based on three-dimensional visualization. In addition to the drivers of temperature, precipitation, solar radiation, and potential evapotranspiration, the drying effect and mechanical stimuli of wind speed on vegetation could not be underestimated. This study provides a novel framework to solve nonlinearity and nonstationarity problems related to vegetation trends and their response mechanisms and promotes the application of remote sensing to solve practical problems.

Isolating spatiotemporally local mixed Rossby-gravity waves using multi-dimensional ensemble empirical mode decomposition

Tropical waves have relatively large amplitudes in and near convective systems, attenuating as they propagate away from the area where they are generated due to the dissipative nature of the atmosphere. Traditionally, nonlocal analysis methods, such as those based on the Fourier transform, are applied to identify tropical waves. However, these methods have the potential to lead to the misidentification of local wavenumbers and spatial locations of local wave activities. To address this problem, we propose a new method for analyzing tropical waves, with particular focus placed on equatorial mixed Rossby-gravity (MRG) waves. The new tropical wave analysis method is based on the multi-dimensional ensemble empirical mode decomposition and a novel spectral representation based on spatiotemporally local wavenumber, frequency, and amplitude of waves. We first apply this new method to synthetic data to demonstrate the advantages of the method in revealing characteristics of MRG waves. We further apply the method to reanalysis data (1) to identify and isolate the spatiotemporally heterogeneous MRG waves event by event, and (2) to quantify the spatial inhomogeneity of these waves in a wavenumber-frequency-energy diagram. In this way, we reveal the climatology of spatiotemporal inhomogeneity of MRG waves and summarize it in wavenumber-frequency domain: The Indian Ocean is dominated by MRG waves in the period range of 8–12 days; the western Pacific Ocean consists of almost equal energy distribution of MRG waves in the period ranges of 3–6 and 8–12 days, respectively; and the eastern tropical Pacific Ocean and the tropical Atlantic Ocean are dominated by MRG waves in the period range of 3–6 days. The zonal wavenumbers mostly fall within the band of 4–15, with Indian Ocean has larger portion of higher wavenumber (smaller wavelength components) MRG waves.

Quantifying the shifts and intensification in the annual cycles of diurnal temperature extremes for human comfort and crop production

Any significant change in climate is known to have a significant impact on crop production and human resources, which are generally difficult to quantify. In the present study, two indices are defined: (i) refined growing season (GS) characteristics and (ii) transition period, based on the annual cycles of diurnal temperature extremes, to unravel any possible impact on these productive elements. Multi-dimensional ensemble empirical mode decomposition, a nonlinear, non-stationary approach is used to extract the annual cycles of diurnal temperature extremes. Since the adverse impact is reportedly more critical over tropical regions, the Indian region is chosen as the study area, and 1° × 1° gridded daily minimum and daily maximum temperature data are used. Results reveal earlier onset and lengthening of GS, with notable spatial variations. Further, a drastic reduction in the transition (i.e. comfortable) period is observed over the warm humid regions, majorly due to the encroachment of summer days. On the contrary, over semi-arid regions, the transition period is found to be increasing, majorly due to the shortening of winter. The quantification of these changes may aid in implementing regional adaptation strategies related to the two productive elements.

Application of MEEMD in post‐processing of dimensionality reduction methods for face recognition

Dimensionality reduction techniques are powerful tools for face recognition, because they obtain important information from a dataset. Several dimensionality reduction methods proposed in literature have been improved thanks to pre-processing approaches. However, they also require post-processing to rectify and increase the quality of projected data. This study presents a simple and new discriminative post-processing framework to make the dimensionality reduction methods robust to outliers. In detail, the proposed approach separates features according to their scale using multidimensional ensemble empirical mode decomposition (MEEMD) and then the spatial and frequency domain processing methods are employed to preserve crucial features. The performance of the proposed method is evaluated on ORL, Extended Yale B, AR, and LFW datasets by several dimensionality reduction techniques. The experimental results demonstrate that the proposed algorithm can perform very well in face recognition.

Empirical Mode Decomposition and Monogenic Signal-Based Approach for Quantification of Myocardial Infarction From MR Images.

Quantification of myocardial infarction on late Gadolinium enhancement cardiovascular magnetic resonance (LGE-CMR) images into heterogeneous infarct periphery (or gray zone) and infarct core plays an important role in cardiac diagnosis, especially in identifying patients at high risk of cardiovascular mortality. However, quantification task is challenging due to noise corrupted in cardiac MR images, the contrast variation, and limited resolution of images. In this study, we propose a novel approach for automatic myocardial infarction quantification, termed DEMPOT, which consists of three key parts: Decomposition of image into intrinsic modes, monogenic phase performing on combined dominant modes, and multilevel Otsu thresholding on the phase. In particular, inspired by the Hilbert-Huang transform, we perform the multidimensional ensemble empirical mode decomposition and 2-D generalization of the Hilbert transform known as the Riesz transform on the MR image to obtain the monogenic phase that is robust to noise and contrast variation. Then, a two-stage algorithm using multilevel Otsu thresholding is accomplished on the monogenic phase to automatically quantify the myocardium into healthy, gray zone, and infarct core regions. Experiments on LGE-CMR images with myocardial infarction from 82 patients show the superior performance of the proposed approach in terms of reproducibility, robustness, and effectiveness.

Spatial and temporal evolution of natural and anthropogenic dust events over northern China

Mineral dust interacts with radiation and cloud microphysics in East Asia can affect local and regional climate. In this study, we found that the occurrences of dust storms, blowing dust, and floating dust over northern China has decreased 76.7%, 68.5%, and 64.5% considerably since the beginning of this century. Based on a multi-dimensional ensemble empirical mode decomposition (MEEMD) method, a steady decrease in zonal maximum wind speed (up to −0.95 m/s) in the Northern Hemisphere was largely responsible for this recent decline in dust event occurrences. Then, a new detection technique that combines multi-satellite datasets with surface observations of dust events is developed to estimate the contribution of anthropogenic dust column burden from disturbed soils to the observed total dust. It is found that the percentage of the anthropogenic dust column burdens to total mineral dust is up to 76.8% by human activities during 2007–2014 in eastern China, but only less than 9.2% near desert source regions in northwestern China. However, we note that the anthropogenic effects on the dust loading for both regions are non-negligible.

A Stochastic source model for the 2015 Mw 7.9 Gorkha, Nepal, Earthquake using Multi-Dimensional Ensemble Empirical Mode Decomposition technique

The present study aims at developing a new strategy to model the spatial variability of slip on the rupture plane using multi-dimensional ensemble empirical mode decomposition (MEEMD) technique. Here, the earthquake slip distribution is split into finite number of empirical modes of oscillation called the intrinsic mode functions (IMFs). This help in identifying the fluctuation component and trend in the slip data. The trend is positive and characterizes the nonstationary mean of the slip distribution. The fluctuation component can be modelled as a stationary random field using an exponential power spectral density function. The trend can be modeled as an elliptic patch. This new technique is demonstrated for the slip distribution of the recent Nepal Earthquake, 2015. It is observed that the new model can be used to simulate the spatial complexity of slip distribution of any earthquake.

Estimation of the SST Response to Anthropogenic and External Forcing and Its Impact on the Atlantic Multidecadal Oscillation and the Pacific Decadal Oscillation

Two large ensembles (LEs) of historical climate simulations are used to compare how various statistical methods estimate the sea surface temperature (SST) changes due to anthropogenic and other external forcing, and how their removal affects the internally generated Atlantic multidecadal oscillation (AMO), Pacific decadal oscillation (PDO), and the SST footprint of the Atlantic meridional overturning circulation (AMOC). Removing the forced SST signal by subtracting the global mean SST (GM) or a linear regression on it (REGR) leads to large errors in the Pacific. Multidimensional ensemble empirical mode decomposition (MEEMD) and quadratic detrending only efficiently remove the forced SST signal in one LE, and cannot separate the short-term response to volcanic eruptions from natural SST variations. Removing a linear trend works poorly. Two methods based on linear inverse modeling (LIM), one where the leading LIM mode represents the forced signal and another using an optimal perturbation filter (LIMopt), perform consistently well. However, the first two LIM modes are sometimes needed to represent the forced signal, so the more robust LIMopt is recommended. In both LEs, the natural AMO variability seems largely driven by the AMOC in the subpolar North Atlantic, but not in the subtropics and tropics, and the scatter in the AMOC–AMO correlation is large between individual ensemble members. In three observational SST reconstructions for 1900–2015, linear and quadratic detrending, MEEMD, and GM yield somewhat different AMO behavior, and REGR yields smaller PDO amplitudes. Based on LIMopt, only about 30% of the AMO variability is internally generated, as opposed to more than 90% for the PDO. The natural SST variability contribution to global warming hiatus is discussed.

Spatiotemporal evolution of the chlorophyll a trend in the North Atlantic Ocean

Analyses of the chlorophyll a concentration (chla) from satellite ocean color products have suggested the decadal-scale variability of chla linked to the climate change. The decadal-scale variability in chla is both spatially and temporally non-uniform. We need to understand the spatiotemporal evolution of chla in decadal or multi-decadal timescales to better evaluate its linkage to climate variability. Here, the spatiotemporal evolution of the chla trend in the North Atlantic Ocean for the period 1997–2016 is analyzed using the multidimensional ensemble empirical mode decomposition method. We find that this variable trend signal of chla shows a dipole pattern between the subpolar gyre and along the Gulf Stream path, and propagation along the opposite direction of the North Atlantic Current. This propagation signal has an overlapping variability of approximately twenty years. Our findings suggest that the spatiotemporal evolution of chla during the two most recent decades is part of the multidecadal variations and possibly regulated by the changes of Atlantic Meridional Overturning Circulation, whereas the mechanisms of such evolution patterns still need to be explored.

Unravelling Diurnal Asymmetry of Surface Temperature in Different Climate Zones

Understanding the evolution of Diurnal Temperature Range (DTR), which has contradicting global and regional trends, is crucial because it influences environmental and human health. Here, we analyse the regional evolution of DTR trend over different climatic zones in India using a non-stationary approach known as the Multidimensional Ensemble Empirical Mode Decomposition (MEEMD) method, to explore the generalized influence of regional climate on DTR, if any. We report a 0.36 °C increase in overall mean of DTR till 1980, however, the rate has declined since then. Further, arid deserts and warm-temperate grasslands exhibit negative DTR trends, while the west coast and sub-tropical forest in the north-east show positive trends. This transition predominantly begins with a 0.5 °C increase from the west coast and spreads with an increase of 0.25 °C per decade. These changes are more pronounced during winter and post-monsoon, especially in the arid desert and warm-temperate grasslands, the DTR decreased up to 2 °C, where the rate of increase in minimum temperature is higher than the maximum temperature. We conclude that both maximum and minimum temperature increase in response to the global climate change, however, their rates of increase are highly local and depend on the underlying climatic zone.

Modeling study of the ionospheric responses to the quasi-biennial oscillations of the sun and stratosphere

The Quasi-biennial Oscillation (QBO) is a persistent oscillation in the zonal mean zonal winds of the low latitude middle atmosphere that is driven by breaking planetary and gravity waves with a period near two years. The atmospheric tides that dominate the dynamics of the mesosphere and lower thermosphere region (MLT, between heights of 70–120 km) are excited in the troposphere and stratosphere, and propagate through QBO-modulated zonal mean zonal wind fields. This allows the MLT tidal response to also be modulated by the QBO, with implications for ionospheric/thermospheric variability. Interannual oscillations in solar radiation can also directly drive the variations in the ionosphere with similar periodicities through the photoionization. Many studies have observed the connection between the solar activity and QBO signal in ionospheric features such as total electron content (TEC).In this research, we develop an empirical model to isolate stratospheric QBO-related tidal variability in the MLT diurnal and semidiurnal tides using values from assimilated TIMED satellite data. Migrating tidal fields corresponding to stratospheric QBO eastward and westward phases, as well as with the quasi-biennial variations in solar activity isolated by the Multi-dimensional Ensemble Empirical Mode Decomposition (MEEMD) analysis from Hilbert-Huang Transform (HHT), are then used to drive the NCAR Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM).The numerical experiment results indicate that the ionospheric QBO is mainly driven by the solar quasi-biennial variations during the solar maximum, since the solar quasi-biennial variation amplitude is directly proportionate to the solar cycle. The ionospheric QBO in the model is sensitive to both the stratospheric QBO and solar quasi-biennial variations during the solar minimum, with solar effects still playing a stronger role.

Separation of Cardiac- and Ventilation-related Signals within Electrical Impedance Tomography Data based on Multi-dimensional Ensemble Empirical Mode Decomposition

Electrical impedance tomography (EIT) is an promising imaging technology for continuous bedside monitoring of ventilation and perfusion. However, due to the spatial and frequency overlapping of ventilation and cardiac components in the heart-lung interaction system, it’s difficult to separate the components in spontaneous breathing subjects. We introduce an intuitive method based on multi-dimensional ensemble empirical mode decomposition to explore the intrinsic oscillation modes of the ventilation and cardiac components from EIT data. This study combines the spatial information with temporal information, and establishes the combination strategy for the two physiological components based on multi-scale analysis. Our study illustrates preliminary in-vivo results based on the data collected from two healthy male subjects, and qualitatively validates the efficiency of resolving the overlapping of ventilation and perfusion component. The method proposed in our study is believed to open up new possibilities for the assessment of lung ventilation and perfusion. In future work, quantitative validation for separation results of ventilation component and perfusion component will be conducted.

Post-processing of dimensionality reduction methods for face recognition

Pre-processing approaches have been widely used in face recognition to enhance images. However, a notably limited amount of research has examined the use of post-processing methods. In this paper, we propose a novel post-processing framework to improve dimensionality reduction methods for robust face recognition. The proposed method does not work on the features directly; it decomposes each feature into different components using multidimensional ensemble empirical mode decomposition and later maximizes the dependency and the dispersion among classes using a Gaussian function. The performance of the proposed algorithm is demonstrated through experiments by applying several dimensionality reduction techniques on two public databases.