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With the rising awareness of health and wellness, accurate ultraviolet (UV) radiation forecasts have become crucial for planning and conducting outdoor activities safely, particularly in the context of global sporting events arrangement and recommendation with definite constraint on environmental conditions. The dynamic nature of UV exposure, influenced by factors such as solar zenith angles, cloud cover, and atmospheric conditions, makes accurate UV radiation data forecasting difficult and challenging. To cope with these challenges, we present an innovative approach for predicting the UV radiation levels of a certain region during a certain time period using Empirical Mode Decomposition (EMD), a robust method for analyzing non-linear and non-stationary data. Our model is specifically designed for urban areas, where outdoor events are common, and integrates meteorological data with historical UV radiation records from specific geographic regions and time periods. The EMD-based model offers precise predictions of UV levels, essential for event organizers and city planners to make informed decisions regarding the scheduling, relocation and recommendation of events to minimize health risks associated with UV exposure. At last, the effectiveness of this model is validated through various experiments across different spatial and temporal contexts based on the Urban-Air dataset (recording 2,891,393 Air Quality Index data that cover four major Chinese cities), demonstrating its adaptability and accuracy under diverse environmental conditions. [ABSTRACT FROM AUTHOR]

We present a denoising technique for inertial sensors based on Empirical Mode Decomposition (EMD). The method uses the fractional Gaussian noise (fGn) model to accurately quantify errors, addressing the complex nature of sensor noise encompassing both Gaussian white and colored components. A modified Hausdorff Distance technique is integrated with the fGn energy model to categorize the resulting Intrinsic Mode Functions (IMFs) into dominant noise, dominant information, and mixed components. The relevant signal IMFs are selectively chosen, while the mixed IMFs undergo hard thresholding before recombination for optimized signal reconstruction. Comparative assessments with conventional wavelet transform, Savitzky Golay, and Moving Average filtering methodologies validate our approach, including analysis via Allan Variance (AVAR), realistic dynamic scenario simulations, and an inertial navigation algorithm implementation. Leveraging data from Microelectromechanical System sensors, our noise removal technique outperforms the other methods in all these analyses. We observe nearly complete suppression of white noise and an approximate 5% reduction in colored noise. Additionally, a 90% decrease in mean squared error and a 10% extension in GNSS-denied navigation duration are noted relative to the original data. • Proposed method effectively denoises MEMS sensors, enhancing accuracy. • Lower RMSE in dynamic analysis showcases adaptability to abrupt changes. • Method in navigation algorithms boosts autonomy, ensuring reliability. [ABSTRACT FROM AUTHOR]

• A fast EMD method for serialized multi-dimensional signals is proposed. • Transitions are included to avoid discontinuity in the joint signals. • Time performance of multi-dimensional analysis is significantly improved. • The decomposed IMFs can achieve high accuracy in noisy face recognition scenario. Empirical mode decomposition (EMD) has developed into a prominent tool for adaptive, scale-based signal analysis in various fields like robotics, security and biomedical engineering. Since the dramatic increase in amount of data puts forward higher requirements for the capability of real-time signal analysis, it is difficult for existing EMD and its variants to trade off the growth of data dimension and the speed of signal analysis. In order to decompose multi-dimensional signals at a faster speed, we present a novel signal-serialization method (serial-EMD), which concatenates multi-variate or multi-dimensional signals into a one-dimensional signal and uses various one-dimensional EMD algorithms to decompose it. To verify the effects of the proposed method, synthetic multi-variate time series, artificial 2D images with various textures and real-world facial images are tested. Compared with existing multi-EMD algorithms, the decomposition time becomes significantly reduced. In addition, the results of facial recognition with Intrinsic Mode Functions (IMFs) extracted using our method can achieve a higher accuracy than those obtained by existing multi-EMD algorithms, which demonstrates the superior performance of our method in terms of the quality of IMFs. Furthermore, this method can provide a new perspective to optimize the existing EMD algorithms, that is, transforming the structure of the input signal rather than being constrained by developing envelope computation techniques or signal decomposition methods. In summary, the study suggests that the serial-EMD technique is a highly competitive and fast alternative for multi-dimensional signal analysis. [ABSTRACT FROM AUTHOR]

This paper presents a novel method for demagnetization fault detection in permanent magnet synchronous machine (PMSM). Demagnetization fault is a common problem existing in PMSM which deteriorates the machine performance and can lead to serious subsequential machine damages. Unlike the most popular method based on the analysis of the machine currents for detecting this type of fault, the approach proposed in this paper analyzes the voltage signal of a non-invasive search coil by means of Hilbert Huang transform. Simulations are carried out with a two dimensional finite element analysis (FEA) for different demagnetization levels to test the capability of the proposed method to detect PM demagnetization faults. [ABSTRACT FROM AUTHOR]

Multivariate or multichannel data have become ubiquitous in many modern scientific and engineering applications, e.g., biomedical engineering, owing to recent advances in sensor and computing technology. Processing these data sets is challenging owing to their large size and multidimensional nature, thus requiring specialized algorithms and efficient hardware designs for online and real time processing. In this paper, we address this issue by proposing a fully FPGA based hardware architecture of a popular multi-scale and multivariate signal processing algorithm, termed as multivariate empirical mode decomposition (MEMD). MEMD is a data-driven method that extends the functionality of standard empirical mode decomposition (EMD) algorithm to multichannel or multivariate data sets. Since its inception in 2010, the algorithm has found wide spread applications spanning different engineering related fields. Yet, no parallel FPGA based hardware design of the algorithm is available for its online and real time processing. Our proposed architecture for MEMD uses fixed-point operations and employs cubic spline interpolation (CSI) within the sifting process. Finally, examples of decomposition of multivariate synthetic and real-world biological signals are provided. [ABSTRACT FROM AUTHOR]

Brain-computer interface (BCI) provides a platform for humans to communicate using Electroencephalogram (EEG) signals by converting them into commands that can be used by the output device to perform the desired tasks. This paper focuses on the identification of vowels from EEG signals. First, a dataset of EEG signals has been created for the identification of vowels by collecting data using a 14-channel EEG device Emotiv- epoc+ from 16 subjects. Then, a deep learning-based model is proposed using a multi-headed Convolutional Neural Network for feature extraction and classification of imagined speech of vowels. Butterworth lowpass and bandpass filter of order five are implemented for denoising and sub-banding of the EEG signals which are further pre-processed using Hilbert Huang Transform. The model has achieved an average accuracy of 97.67% with a five-fold cross-validation technique using all six sub-bands of the EEG signals. The model has achieved an average precision and recall of 95.54% and 95.11% respectively. The proposed model is statistically tested using the Mann-Whitney U test and paired t-test with a p-value less than 0.05. [ABSTRACT FROM AUTHOR]

• A novel comprehensive time series prediction framework comprising a decomposition-aggregation process and outputting information granules is proposed. • Complexity is effectively used to guide modeling from two aspects. • The application of GNNs is further extended to time series prediction field. • Granular neural networks are used to capture critical patterns of the original time series. Complexity of time series has always been of significant interest to researchers; however, it is not yet effectively explored in assisting time series prediction modeling. In this study, we develop a decomposition-aggregation time series prediction framework sufficiently applying the complexity concept from two aspects. One aspect is realized during the process of allocating information granularity onto each decomposed subsequence (with comparably lower complexity). The other aspect is realized through constituting the objective function of a prediction model (a granular neural network in this paper) which is built with a subsequence individually. To capture several critical patterns of a time series, it is decomposed into several subsequences and used to train a granular neural network independently. An effective aggregation strategy is then adopted to aggregate those predicted information granules which are the outputs of local granular neural networks. The quality of the global output information granule is assessed by analyzing the relationship of coverage and specificity and keeping in mind the overall information granularity. Experimental studies show that the decomposition-aggregation strategy prediction results are better than the non-decomposed one and the complexity-aided objective function performs better than the objective function without complexity. [ABSTRACT FROM AUTHOR]

Empirical mode decomposition (EMD) is an effective tool for breaking down components (modes) of a nonlinear and non-stationary signal. Recently, a newly adaptive signal decomposition method, namely extreme-point weighted mode decomposition (EWMD), was put forward to improve the performance of EMD, in particular, to resolve the over- or undershooting issue associated with the large amplitude variations. However, similar to EMD, EWMD also suffers the mode mixing problem caused by intermittence or noisy signals. In this paper, inspired by complementary ensemble EMD (CEEMD), a noise-assisted data analysis method called partial ensemble extreme-point weighted mode decomposition (PEEWMD) is proposed to eliminate the mode mixing problem and enhance the performance of EWMD. In the proposed PEEWMD method, firstly white noises in pairs are added to the targeted signal and then the noisy signals are decomposed using the EWMD method to obtain the intrinsic mode functions (IMFs) in the first several stages. Secondly, permutation entropy is employed to detect the components that cause mode mixing. The residual signal is obtained after the identified components are separated from the original signal. Lastly, the residual signal is fully decomposed by using the EWMD method. The proposed PEEWMD method is compared with original EWMD, ensemble EWMD (EEWMD) and CEEMD using simulated signals. The results demonstrate that PEEWMD can effectively restrain the mode mixing issue and generates IMFs with much better performance. Based on that the PEEWMD and envelope power spectrum based fault diagnosis method was proposed and applied to the rubbing fault identification of rotor system and the fault diagnosis of rolling bearing with inner race. The result indicates that the proposed method of fault diagnosis gets much better effect than EMD and EWMD. • Partial ensemble extreme-point weighted mode decomposition (PEEWMD) is developed for signal mode separation. • PEEWMD is proposed to eliminate the mode mixing of extreme-point weighted mode decomposition. • PEEWMD is compared with EWMD, ensemble EWMD and CEEMD using simulated signals and experimental data. • PEEWMD is applied to the fault diagnosis of rotor system with rubbing impact. [ABSTRACT FROM AUTHOR]

Empirical mode decomposition (EMD) may generate undesirable intrinsic mode functions (IMFs) under low sampling rate, which can significantly affect the results of decomposition. In this paper, an improved EMD method using second generation wavelets interpolation is presented which can eliminate undesirable IMFs and reduce the scale mixing effectively under low sampling rate. Firstly, the original signal under low sampling rate is reconstructed by inverse process of second generation wavelets lifting algorithm. Secondly, the location algorithm of extrema using second generation wavelets is given to obtain the accurate position of extrema. Finally, five examples are demonstrated to justify the effectiveness. Numerical simulation and experimental results are attained to show the effectiveness of the proposed method in eliminating undesirable IMFs and reducing the scale mixing, thereby making the proposed improved EMD a promising method for improving the performance of EMD under low sampling rate. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this study is to reveal the lead–lag structure between international crude oil price and stock markets.Design/methodology/approach The methods used for this study are as follows: empirical mode decomposition; shift-window-based Pearson coefficient and thermal causal path method.Findings The fluctuation characteristic of Chinese stock market before 2010 is very similar to international crude oil prices. After 2010, their fluctuation patterns are significantly different from each other. The two stock markets significantly led international crude oil prices, revealing varying lead–lag orders among stock markets. During 2000 and 2004, the stock markets significantly led international crude oil prices but they are less distinct from the lead–lag orders. After 2004, the effects changed so that the leading effect of Shanghai composite index remains no longer significant, and after 2012, S&P index just significantly lagged behind the international crude oil prices.Originality/value China and the US stock markets develop different pattens to handle the crude oil prices fluctuation after finance crisis in 1998. [ABSTRACT FROM AUTHOR]

Evidence theory, as a useful uncertain reasoning method, is widely used in various fields. Nevertheless, how to quantify the divergence between the basic belief assignments in belief theory and how to apply it are still open issues. To measure the discrepancy between basic belief assignments, we first introduce belief f -divergence (BFD) in this paper. We also analyze and verify its related properties that are expected to significantly improve the performance of electroencephalogram (EEG) complexity evaluation. Then, we employ empirical mode decomposition to detrend EEG noise and reconstruct EEG signals with inherent components and develop a belief f -divergence-based complexity (BFDC) evaluation method with five different functions, including belief KL divergence, belief Hellinger divergence, belief χ 2 divergence, belief triangular divergence, and belief total variation divergence, to evaluate the complexity of the EEG signals. Based on a benchmark lane-keeping EEG driving experiment, our proposed BFDC evaluation approach can identify the differences among keep–drift events more obviously and significantly reduce the root mean squared error up to the order of 102 compared to the existing complexity measurement of fuzzy entropy. We believe that our proposed BFDC evaluation method has the potential to be a new and robust approach to precisely evaluate the dynamic complexity of physiological signals. [ABSTRACT FROM AUTHOR]

Cardiovascular diseases (CVDs) are the main cause of cardiac death worldwide. The Coronary Artery Disease (CAD) is one of the leading causes of these CVD deaths. CAD condition progresses rapidly, if not diagnosed and treated at an early stage may eventually lead to an irreversible state of heart muscle death called Myocardial Infarction (MI). Normally, the presence of these cardiac conditions is primarily reflected on the electrocardiogram (ECG) signal. However, it is challenging and requires rich experience to manually interpret the visual subtle changes occurring in the ECG waveforms. Thus, many automated diagnostic systems are developed to overcome these limitations. In this study, the performance of an automated diagnostic system developed for detection of CAD and MI using three methods such as Discrete Wavelet Transform (DWT), Empirical Mode Decomposition (EMD) and Discrete Cosine Transform (DCT) are compared. In this study, ECG signals are subjected to DCT, DWT and EMD to obtain respective coefficients. These coefficients are reduced using Locality Preserving Projection (LPP) data reduction method. Then, the LPP features are ranked using F-value. Finally, the highly ranked coefficients are fed into the K-Nearest Neighbor (KNN) classifier to achieve the best classification performance. Our proposed system yielded highest classification results of 98.5% accuracy, 99.7% sensitivity and 98.5% specificity using only seven features obtained using DCT technique. The screening system can help the cardiologists in detecting the CAD and hence presents any possible MI by prescribing suitable medications. It can be employed in routine community screening, old age homes, polyclinics and hospitals. [ABSTRACT FROM AUTHOR]

Wave attenuation is often measured using spectral techniques such as the spectral ratio method and the frequency shift method, comparing the spectral content of pairs of waveforms along the ray path. The recent introduction of novel highly-localized time–frequency transforms leads to high-resolution but discontinuous spectra. It prevents the use of these time–frequency transforms with conventional attenuation measurement methods. We show how three highly-localized time–frequency transforms, namely basis pursuit, the synchrosqueezing wavelet transform, and complete ensemble empirical mode decomposition, can still be used to estimate attenuation using the peak frequency method. Assuming a Ricker source wavelet, the decrease in peak frequency of a wave spectrum as it propagates in a given medium is used to estimate attenuation. When applied to a synthetic benchmarking signal corrupted by Gaussian white noise, the three transforms show different degrees of performance and robustness for different signal-to-noise ratios. The developed methodology is suitable for geophysical investigations, but may also find application in other fields such as biomedicine, acoustics and engineering. [ABSTRACT FROM AUTHOR]

Bidimensional Empirical Mode Decomposition (BEMD) interprets an image as a superposition of Bidimensional Intrinsic Mode Functions (BIMFs). They are extracted by a process called sifting, which encompasses two-dimensional surface interpolations connecting a set of local maxima or minima to form corresponding envelope surfaces. Existing surface interpolation schemes are computationally very demanding and often induce artifacts in the extracted modes. This paper suggests a novel method of envelope surface interpolation based on Green’s functions. Including surface tension greatly improves the stability of the new method which we call Green’s function in tension -based BEMD (GiT-BEMD). Simulation results, using toy images with various textures, facial images and functional neuroimages, demonstrate the superior performance of the new method when compared to its canonical BEMD counterpart. GiT-BEMD strongly speeds up computations and achieves a higher quality of the extracted BIMFs. Furthermore, GiT-BEMD can be extended simply to an ensemble-based variant (GiT-BEEMD), if needed. In summary, the study suggests the new variant GiT-BEMD as a highly competitive, fast and stable alternative to existing BEMD techniques for image analysis. [ABSTRACT FROM AUTHOR]

Empirical mode decomposition (EMD) is an adaptive decomposition method, which is widely used in time-frequency analysis. As a bidimensional extension of EMD, bidimensional empirical mode decomposition (BEMD) presents many useful applications in image processing and computer vision. In this paper, we define the mean points in BEMD ‘sifting’ processing as centroid point of neighbour extrema points in Delaunay triangulation and propose using mean approximation instead of envelope mean in ‘sifting’. The proposed method improves the decomposition result and reduces average computation time of ‘sifting’ processing. Furthermore, a BEMD-based image fusion approach is presented in this paper. Experimental results show our method can achieve more orthogonal and physical meaningful components and more effective result in image fusion application. [ABSTRACT FROM AUTHOR]

Hierarchical multiresolution analysis is an important tool for the analysis of signals. Since this multiresolution representation provides a pyramid like framework for representing signals, it can extract signal information effectively via levels by levels. On the other hand, a signal can be nonlinearly and adaptively represented as a sum of intrinsic mode functions (IMFs) via the empirical mode decomposition (EMD) algorithm. Nevertheless, as the IMFs are obtained only when the EMD algorithm converges, no further iterative sifting process will be performed directly when the EMD algorithm is applied to an IMF. As a result, the same IMF will be resulted and further level decompositions of the IMFs cannot be obtained directly by the EMD algorithm. In other words, the hierarchical multiresolution analysis cannot be performed via the EMD algorithm directly. This paper is to address this issue by performing a nonlinear and adaptive hierarchical multiresolution analysis based on the EMD algorithm via a frequency domain approach. In the beginning, an IMF is expressed in the frequency domain by applying discrete Fourier transform (DFT) to it. Next, zeros are inserted to the DFT sequence and a conjugate symmetric zero padded DFT sequence is obtained. Then, inverse discrete Fourier transform (IDFT) is applied to the zero padded DFT sequence and a new signal expressed in the time domain is obtained. Actually, the next level IMFs can be obtained by applying the EMD algorithm to this signal. However, the lengths of these next level IMFs are increased. To reduce these lengths, first DFT is applied to each next level IMF. Second, the DFT coefficients of each next level IMF at the positions where the zeros are inserted before are removed. Finally, by applying IDFT to the shorten DFT sequence of each next level IMF, the final set of next level IMFs are obtained. It is shown in this paper that the original IMF can be perfectly reconstructed. Moreover, computer numerical simulation results show that our proposed method can reach a component with less number of levels of decomposition compared to that of the conventional linear and nonadaptive wavelets and filter bank approaches. Also, as no filter is involved in our proposed method, there is no spectral leakage in various levels of decomposition introduced by our proposed method. Whereas there could be some significant leakage components in the various levels of decomposition introduced by the wavelets and filter bank approaches. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study on the investigation of coherent modes in chaotic time series data based on two techniques: the empirical mode decomposition and the discrete wavelet transform. We have applied these techniques to the different types of chaotic time series data obtained from a glow discharge plasma. The discrete wavelet transform and empirical mode decomposition analysis of the chaotic time series, combined with some simple statistical estimations like variance and correlation coefficient, helps in identifying the presence of coherent modes. We carried out a bicoherency analysis on the coherent modes extracted using empirical mode decomposition to detect the interactions amongst them. It is quite likely that the interactions between the different plasma modes are responsible for such turbulent nonlinear oscillations. [ABSTRACT FROM AUTHOR]

Rotating bearing degradation is a physical process that typically evolves in stages characterized by different speeds of evolution of the characteristic health indicators. Therefore, it is opportune to apply different predictive models in the different stages, with the aim of balancing accuracy and calculation complexity in light of the varying needs and constraints of the different stages. This paper proposes a condition-based adaptive trend prediction method for rotating bearings. The empirical mode decomposition–self-organizing map (EMD–SOM) method is applied to analyze vibration signals and calculate a confidence value (CV) on the bearing health state. Four different degradation stages, normal, slight degradation, severe degradation and failure, are identified by using the CV value and CV change rate. At each stage, we develop a different prediction strategy tailored to the specific degradation profile. In operation, upon recognition of the stage, the corresponding prognostics models are selected to estimate the health trend. A case study on datasets from 17 test bearings demonstrates and validates the feasibility of the proposed method. The experiment results show that the adaptive prediction method is accurate and reduces computational complexity, which can be important for online applications, especially in case of limited computing resources. [ABSTRACT FROM AUTHOR]

Signal decompositions such as wavelet and Gabor transforms have successfully been applied in denoising problems. Empirical mode decomposition (EMD) is a recently proposed method to analyze non-linear and non-stationary time series and may be used for noise elimination. Similar to other decomposition based denoising approaches, EMD based denoising requires a reliable threshold to determine which oscillations called intrinsic mode functions (IMFs) are noise components or noise free signal components. Here, we propose a metric based on detrended fluctuation analysis (DFA) to define a robust threshold. The scaling exponent of DFA is an indicator of statistical self-affinity. In our study, it is used to determine a threshold region to eliminate the noisy IMFs. The proposed DFA threshold and denoising by DFA-EMD are tested on different synthetic and real signals at various signal to noise ratios (SNR). The results are promising especially at 0 dB when signal is corrupted by white Gaussian noise (WGN). The proposed method outperforms soft and hard wavelet threshold method. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to simulate and analyze accurately the multi-scale characteristics, variation periods and trends of the annual streamflow series in the Haihe River Basin (HRB) using the Hilbert-Huang Transform (HHT). Design/methodology/approach – The Empirical Mode Decomposition (EMD) approach is adopted to decompose the original signal into intrinsic mode functions (IMFs) in multi-scales. The Hilbert spectrum is applied to each IMF component and the localized time-frequency-energy distribution. The monotonic residues obtained by EMD can be treated as the trend of the original sequence. Findings – The authors apply HHT to 14 hydrological stations in the HRB. The annual streamflow series are decomposed into four IMFs and a residual component, which exhibits the multi-scale characteristics. After the Hilbert transform, the instantaneous frequency, center frequency and mean period of the IMFs are obtained. Common multi-scale periods of the 14 series exist, e.g. 3.3a, 4∼7a, 8∼10a, 11-14a, 24∼25a and 43∼45a. The residues indicate that the annual streamflow series has exhibited a decreasing trend over the past 50 years. Research limitations/implications – The HHT method is still in its early stages of application in hydrology and needs to be further tested. Practical implications – It is helpful for the study of the complex features of streamflow. Social implications – This paper will contribute to the sustainable utilization of water resources. Originality/value – This study represents the first use of the HHT method to analyze the multi-scale characteristics of the streamflow series in the HRB. This paper provides an important theoretical support for water resources management. [ABSTRACT FROM AUTHOR]

Abstract: Condition assessment is one of the most important techniques to realize the equipment's health management and condition based maintenance (CBM). This paper introduces a preprocessing model of the bearing using wavelet packet–empirical mode decomposition (WP-EMD) for feature extraction. Then it uses self-organization mapping (SOM) for the condition assessment of the performance degradation. To verify the superiority of the proposed method, it is compared with some traditional features, such as RMS, kurtosis, crest factor and entropy. Meanwhile, seventeen datasets from the bearing run-to-failure test are used to validate the proposed method. The analysis results from the bearing's signals with multiple faults show that the proposed assessment model can effectively indicate the degradation state and help us to estimate remaining useful life (RUL) of the bearings. [Copyright &y& Elsevier]

Abstract: The problem of reconstructing a known high-resolution signal from a set of its low-resolution parts exposed to additive white Gaussian noise is addressed in this paper from the perspective of statistical multirate signal processing. To enhance the performance of the existing high-resolution signal reconstruction procedure that is based on using a set of linear periodically time-varying (LPTV) Wiener filter structures, we propose two empirical methods combining empirical mode decomposition- and least squares support vector machine regression-based noise reduction schemes with these filter structures. The methods originate from the idea of reducing the effects of white Gaussian noise present in the low-resolution observations before applying them directly to the LPTV Wiener filters. Performances of the proposed methods are evaluated over one-dimensional simulated signals and two-dimensional images. Simulation results show that, under certain conditions, considerable improvements have been achieved by the proposed methods when compared with the previous study that only uses a set of LPTV Wiener filter structures for the signal reconstruction process. [Copyright &y& Elsevier]

The tradition methods for estimating rolling period based on self-correlation and spectrum analysis often gain false period. In allusion to this problem, a new method based on the nonparametric rank variance test and empirical mode decomposition is proposed. First, the trend character of RCS sequence is extracted by the mathematical morphological closed operation. Then, the extracted RCS sequence is operated by the empirical mode decomposition. And, the periods of each intrinsic mode functions (IMF) are gained by using the spectrum analysis Finally, the rolling period can be estimated by using the nonparametric statistics theory. The experimental results for the emulational and measured data show that the proposed method can solve the false period problem effectively and improve the performance of the estimation. [ABSTRACT FROM AUTHOR]

Abstract: The problem of filtering low-frequency trend from a given time series is considered. In order to solve this problem, a nonparametric technique called empirical mode decomposition trend filtering is developed. A key assumption is that the trend is representable as the sum of intrinsic mode functions produced by the empirical mode decomposition (EMD) of the time series. Based on an empirical analysis of the EMD, an automatic procedure for selecting the requisite intrinsic mode functions is proposed. To illustrate the effectiveness of the technique, it is applied to simulated time series containing different types of trend, as well as real-world data collected from an environmental study (atmospheric carbon dioxide levels at Mauna Loa Observatory) and from a bicycle rental service (rental numbers of Grand Lyon Vélo’v). [Copyright &y& Elsevier]

Abstract: Because nonlinear responses are oftentimes transient and consist of complex amplitude and frequency modulations, linearization would inevitably obscure the temporal transition attributable to the nonlinear terms, thus also making all inherent nonlinear effects inconspicuous. It is shown that linearization of a softening Duffing oscillator underestimates the variation of the frequency response, thereby concealing the underlying evolution from bifurcation to chaos. In addition, Fourier analysis falls short of capturing the time evolution of the route-to-chaos and also misinterprets the corresponding response with fictitious frequencies. Instantaneous frequency along with the empirical mode decomposition is adopted to unravel the multi-components that underlie the bifurcation-to-chaos transition, while retaining the physical features of each component. Through considering time and frequency responses simultaneously, a better understanding of the particular Duffing oscillator is achieved. [Copyright &y& Elsevier]

Purpose – Embedding dimension determination in phase space reconstruction is difficult. The purpose of this paper is to present a new approach for embedding dimension determination based on empirical mode, showing that embedding dimensions for phase space reconstruction could be easily determined according to the number of intrinsic mode functions decomposed by empirical mode decomposition. Design/methodology/approach – Through the relation analysis of intrinsic mode functions and embedding dimensions, the approach for embedding dimension determination by the number of intrinsic mode functions is presented. First, a time series is decomposed into several intrinsic mode functions. Second, correlation analysis between intrinsic mode functions and original signals is investigated, and then false intrinsic mode functions could be eliminated by the analysis of correlation coefficient thresholds, which makes the embedding dimension precise. Finally, the method presented is applied to the Lorenz system, Chen's system, and the Duffing equation. Simulation results prove this method is feasible. Findings – A new approach for embedding dimension determination based on empirical mode decomposition is presented. Compared with G-P algorithms, this new method is effective and decreases computational complexity. Research limitations/implications – This method provides an effective qualitative criterion to the selection of embedding dimensions in phase space reconstruction. Practical implications – This method could be used to determine embedding dimensions of phase space reconstruction and degree-of-freedom of nonlinear dynamical systems. Originality/value – The paper proposes a new method of embedding dimension determination in phase space reconstruction. [ABSTRACT FROM AUTHOR]

Abstract: Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. A novel chaos control scheme is formulated by addressing the fundamental characteristics inherent of chaotic response. The proposed control scheme has its philosophical basis established in simultaneous time–frequency control, on-line system identification, and adaptive control. Physical features that embody the concept include multiresolution analysis, adaptive Finite Impulse Response (FIR) filter, and Filtered-x Least Mean Square (FXLMS) algorithm. A non-stationary Duffing oscillator is investigated to demonstrate the effectiveness of the control methodology. Results presented herein indicate that for the control of dynamic instability including chaos to be deemed viable, mitigation has to be adaptive and engaged in the time and frequency domains at the same time. [Copyright &y& Elsevier]

In order to remove noise and achieve high accuracy classification of hyperspectral images, a high-accuracy hyperspectral images classification algorithm based on wavelet threshold denoising (WTD) and empirical modal decomposition (EMD) is presented. First, high-frequency noise in hyperspectral images is removed by wavelet threshold denoising. Second, the essential characteristics of hyperspectral images are extracted through the decomposition of hyperspectral images with EMD, and the residual with low-frequency noise is removed. Finally, the hyperspectral images are classified with SVM, which have been composed by the Intrinsic Modal Function(IMF) of hyperspectral images. Experimental results of the AVIRIS data indicate that the proposed approach not only improves the classification accuracy of hyperspectral images, but also reduces the number of support vectors and improves the speed of hyperspectral images classification. [ABSTRACT FROM AUTHOR]

Abstract: Due to the strong non-linear, complexity and non-stationary characteristics of wind farm power, a hybrid prediction model with empirical mode decomposition (EMD), chaotic theory, and grey theory is constructed. The EMD is used to decompose the wind farm power into several intrinsic mode function (IMF) components and one residual component. The grey forecasting model is used to predict the residual component. For the IMF components, identify their characteristics, if it is chaotic time series use largest Lyapunov exponent prediction method to predict. If not, use grey forecasting model to predict. Prediction results of residual component and all IMF components are aggregated to produce the ultimate predicted result for wind farm power. The ultimate predicted result shows that the proposed method has good prediction accuracy, can be used for short-term prediction of wind farm power. [Copyright &y& Elsevier]

Abstract: Taking into account two types of tremor, namely essential tremor (ET) and Parkinsonʼs disease (PD), which are often misdiagnosed in clinical practice, a novel approach using singular value decomposition (SVD) to extract the features of intrinsic mode functions (IMFs) and support vector machine (SVM) is proposed to distinguish between them. The hand acceleration signals of 25 voluntary subjects with two conditions were collected and preprocessed. The empirical mode decomposition (EMD) method decomposed the signals into a number of stationary IMFs. The singular value features of the preceding four IMFs were extracted, and the features were inputted to the SVM classifier, which can recognize the two types of tremor. To comparing, we also used the singular value features of discrete wavelet transform (DWT) as input to the SVM. Cross-validation testing results indicated that the accuracy, sensitivity, and specificify of EMD-SVD features extracted are all remarkable higher than that of DWT-SVD method. Due to the accuracy, sensitivity, and specificify could arrive at 98%, 97.5% and 98.33% respectively, thus, practical guiding significance for diagnosing tremor types in clinic is provided. [Copyright &y& Elsevier]

Abstract: This paper investigates the application of the Hilbert spectrum (HS), which is a recent tool for the analysis of nonlinear and nonstationary time-series, to the study of electromyographic (EMG) signals. The HS allows for the visualization of the energy of signals through a joint time–frequency representation. In this work we illustrate the use of the HS in two distinct applications. The first is for feature extraction from EMG signals. Our results showed that the instantaneous mean frequency (IMNF) estimated from the HS is a relevant feature to clinical practice. We found that the median of the IMNF reduces when the force level of the muscle contraction increases. In the second application we investigated the use of the HS for detection of motor unit action potentials (MUAPs). The detection of MUAPs is a basic step in EMG decomposition tools, which provide relevant information about the neuromuscular system through the morphology and firing time of MUAPs. We compared, visually, how MUAP activity is perceived on the HS with visualizations provided by some traditional (e.g. scalogram, spectrogram, Wigner–Ville) time–frequency distributions. Furthermore, an alternative visualization to the HS, for detection of MUAPs, is proposed and compared to a similar approach based on the continuous wavelet transform (CWT). Our results showed that both the proposed technique and the CWT allowed for a clear visualization of MUAP activity on the time–frequency distributions, whereas results obtained with the HS were the most difficult to interpret as they were extremely affected by spurious energy activity. [Copyright &y& Elsevier]

An alternative approach to using phase plots, bifurcation diagrams, or Fourier analysis for characterizing the various responses displayed by time-delayed feedback oscillators of both autonomous and non-autonomous types is presented. The alternative employs the fundamental notion of instantaneous frequency to describe characteristics innate to periodic, quasi-periodic and chaotic motions in response to varying positive feedback and forcing parameters. Simultaneous periodicity-modal aberrations are seen to precede the birth of new modes, which explicitly signifies the inception of bifurcation. Modes thus defined in the context of instantaneous frequency are obtained using a separation scheme referred to as the empirical mode decomposition and thus, by definition, they are also an orthogonal set of intrinsic monocomponents each retaining the physical features inherent to the motions being studied. [Copyright &y& Elsevier]

The empirical mode decomposition (EMD) is a method that is commonly applied to extract the intrinsic mode functions (IMFs) of a signal by a sifting process, which requires imposing the extended extrema at both ends of the signal (i.e., the end condition). The imposition of extended extrema can cause an error, which is often presented by the changing shapes of original envelopes and distort extracted IMFs, which is described as the end effect. An important issue during the application of the EMD is restricting the end effect. This paper reveals the decisive factors that can restrict the end effect by determining the uniqueness of the envelope, and provides an interpretation of the end effect in terms of the differences between the original envelope and the extended envelope based on the cubic spline theory. Two principles that are important to the design of an end condition method are provided. The first principle is that the domain of the extended envelope needs to cover the original signal; the second is that the ordinate value of the extended local maxima is greater than or equal to that of the extended local minima. Following these two principles, a new end condition method, the cubic spline based method (CSBM), is proposed in this study. The novelty of the CSBM is that the extended envelope maintains the shape of the original envelope in their intersection domain, and the end effect can be restricted in a limited domain during the sifting process of EMD for each different input signal. Six signals are used to demonstrate the performance of the CSBM by comparing them with two other end condition methods, the extreme method and the improved slope based method (ISBM). The six signals include: a damped sinusoid signal, four monovariate signals with various amplitude modulation-frequency modulation (AM-FM) behaviors, and a one-channel functional near-infrared spectroscopy (fNIRS) signal. Results show that the CSBM in general performs better than the other two methods. [ABSTRACT FROM AUTHOR]

Chaotic time series exist in nature, such as in the field of meteorology or physics, with unpredictable features caused by their inherent high complexity and nonstationary motion. To improve the prediction effect of chaotic time series, a hybrid prediction method on the basis of the empirical mode decomposition (EMD) and neural networks (NN) is proposed. First, the original chaotic time series is decomposed into several intrinsic mode functions (IMFs) and one residual by EMD, whose components are divided into high, medium and low components by using the runs test. The high IMFs change dramatically, and the correlation among data is not high; therefore, we use the fuzzy first-order transition rules trained neural network (NN-FFOTR) model to predict the high frequency components. Autoregressive integrated moving average (ARIMA) models are applied according to the random characteristic exhibited by the medium frequency IMFs and residual. Finally, the prediction results of the two models are adaptively superimposed together to obtain the final prediction results. The proposed hybrid method is named EMD-ARIMA-NN-FFOTR for simplicity. The simulation results are verified through two typical chaotic time series including the Lorenz-63 system and Mackey-Glass time series. For the x-axis of the Lorenz-63 system, the experimental results indicates that the symmetric mean absolute percentage error (SMAPE) of the ARIMA, NN-FFOTR, ARIMA-NN-FFOTR and EMD-ARIMA-NN-FFOTR are 1.0657, 1.5281, 1.0657 and 0.0041;the root mean square error (RMSE) are 2.2591,0.6830,0.4231 and 0.0012; the mean absolute error (MAE) are 50.5149,15.2130,9.4610 and 0.0019; the sum of error squares (SSE) are 101.4,96.32,65.8300 and 21.6351; and the Theil inequality coefficient are 0.0674, 0.0741, 0.0213 and 0.0162, the proposed model's TIC are much lower than those of the comparison models. The values of the R square of the developed prediction approach utilizing ARIMA, NN-FFPTR, ARIMA-NN-FFOTR and EMD-ARIMA-NN-FFOTR method are 0.9674,0.9741, 0.9799 and 0.9963, and the index of agreement are 0.8992,0.9921,0.9845 and 0.9991, the value of the R-square and the index of agreement of the proposed model's are much higher than those of the comparison models. The Pearson's test results show that the association strength between the actual value and the predicted values of the proposed model is stronger. These results show the following: (a) compared with other related, recent studies, the prediction accuracy of the hybrid system EMD-ARIMA-NN-FFOTR proposed in this article is higher; (b) the proposed hybrid system attains superior performance compared with single models; and (c) the proposed hybrid system balances the forecast accuracy and convergence speed simultaneously during prediction. Therefore, it is feasible to apply the hybrid model to the prediction of chaotic time series. [ABSTRACT FROM AUTHOR]

In this paper an audio coding scheme based on the empirical mode decomposition in association with a psychoacoustic model is presented. The principle of the method consists in breaking down adaptively the audio signal into intrinsic oscillatory components, called Intrinsic Mode Functions (IMFs), that are fully described by their local extrema. These extrema are encoded. The coding is carried out frame by frame and no assumption is made upon the signal to be coded. The number of allocated bits varies from mode to mode and obeys to the coding error inaudibility constraint. Due to the symmetry of an IMF, only the extrema (maxima or minima) of one of its interpolating envelopes are perceptually coded. In addition, to deal with rapidly changing audio signals, a stationarity index is used and when a transient is detected, the frame is split into two overlapping sub-frames. At the decoder side, the IMFs are recovered using the associated coded maxima, and the original signal is reconstructed by IMFs summation. Performance of the proposed coding is analyzed and compared to that of MP3 and AAC codecs, and the wavelet-based coding approach. Based on the analyzed mono audio signals, the obtained results show that the proposed coding scheme outperforms the MP3 and the wavelet-based coding methods and performs slightly better than the AAC codec, showing thus the potential of the EMD for data-driven audio coding. [ABSTRACT FROM AUTHOR]

Presents a study assessing the chaotic parameters from nonstationary electrocardiogram (ECG) signals. Preservation of the 10th intrinsic mode functions of the ECG signals; Likelihood for the original ECG to have chaotic properties; Failure of the chaotic parameters to show differences among the data sets.