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Journal articles on the topic 'EMD (Empirical Mode Decomposition)'

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Published: 4 June 2021
Last updated: 12 February 2022

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1

TSUI, PO-HSIANG, CHIEN-CHENG CHANG, and NORDEN E. HUANG. "NOISE-MODULATED EMPIRICAL MODE DECOMPOSITION." Advances in Adaptive Data Analysis 02, no. 01 (January 2010): 25–37. http://dx.doi.org/10.1142/s1793536910000410.

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The empirical mode decomposition (EMD) is the core of the Hilbert–Huang transform (HHT). In HHT, the EMD is responsible for decomposing a signal into intrinsic mode functions (IMFs) for calculating the instantaneous frequency and eventually the Hilbert spectrum. The EMD method as originally proposed, however, has an annoying mode mixing problem caused by the signal intermittency, making the physical interpretation of each IMF component unclear. To resolve this problem, the ensemble EMD (EEMD) was subsequently developed. Unlike the conventional EMD, the EEMD defines the true IMF components as the mean of an ensemble of trials, each consisting of the signal with added white noise of finite, not infinitesimal, amplitude. In this study, we further proposed an extension and alternative to EEMD designated as the noise-modulated EMD (NEMD). NEMD does not eliminate mode but intensify and amplify mixing by suppressing the small amplitude signal but the larger signals would be preserved without waveform deformation. Thus, NEMD may serve as a new adaptive threshold amplitude filtering. The principle, algorithm, simulations, and applications are presented in this paper. Some limitations and additional considerations of using the NEMD are also discussed.
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2

NIAZY, R. K., C. F. BECKMANN, J. M. BRADY, and S. M. SMITH. "PERFORMANCE EVALUATION OF ENSEMBLE EMPIRICAL MODE DECOMPOSITION." Advances in Adaptive Data Analysis 01, no. 02 (April 2009): 231–42. http://dx.doi.org/10.1142/s1793536909000102.

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Empirical mode decomposition (EMD) is an adaptive, data-driven algorithm that decomposes any time series into its intrinsic modes of oscillation, which can then be used in the calculation of the instantaneous phase and frequency. Ensemble EMD (EEMD), where the final EMD is estimated by averaging numerous EMD runs with the addition of noise, was an advancement introduced by Wu and Huang (2008) to try increasing the robustness of EMD and alleviate some of the common problems of EMD such as mode mixing. In this work, we test the performance of EEMD as opposed to normal EMD, with emphasis on the effect of selecting different stopping criteria and noise levels. Our results indicate that EEMD, in addition to slightly increasing the accuracy of the EMD output, substantially increases the robustness of the results and the confidence in the decomposition.
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3

Chen, Zhongzhe, Baqiao Liu, Xiaogang Yan, and Hongquan Yang. "An Improved Signal Processing Approach Based on Analysis Mode Decomposition and Empirical Mode Decomposition." Energies 12, no. 16 (August 9, 2019): 3077. http://dx.doi.org/10.3390/en12163077.

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Empirical mode decomposition (EMD) is a widely used adaptive signal processing method, which has shown some shortcomings in engineering practice, such as sifting stop criteria of intrinsic mode function (IMF), mode mixing and end effect. In this paper, an improved sifting stop criterion based on the valid data segment is proposed, and is compared with the traditional one. Results show that the new sifting stop criterion avoids the influence of end effects and improves the correctness of the EMD. In addition, a novel AEMD method combining the analysis mode decomposition (AMD) and EMD is developed to solve the mode-mixing problem, in which EMD is firstly applied to dispose the original signal, and then AMD is used to decompose these mixed modes. Then, these decomposed modes are reconstituted according to a certain principle. These reconstituted components showed mode mixing phenomena alleviated. Model comparison was conducted between the proposed method with the ensemble empirical mode decomposition (EEMD), which is the mainstream method improved based on EMD. Results indicated that the AEMD and EEMD can effectively restrain the mode mixing, but the AEMD has a shorter execution time than that of EEMD.
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Zhou, Xiaohang, Deshan Shan, and Qiao Li. "Morphological Filter-Assisted Ensemble Empirical Mode Decomposition." Mathematical Problems in Engineering 2018 (September 17, 2018): 1–12. http://dx.doi.org/10.1155/2018/5976589.

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In the ensemble empirical mode decomposition (EEMD) algorithm, different realizations of white noise are added to the original signal as dyadic filter banks to overcome the mode mixing problems of empirical mode decomposition (EMD). However, not all the components in white noise are necessary, and the superfluous components will introduce additional mode mixing problems. To address this problem, morphological filter-assisted ensemble empirical mode decomposition (MF-EEMD) was proposed in this paper. First, a new method for determining the structuring element shape and size was proposed to improve the adaptive ability of morphological filter (MF). Then, the adaptive MF was introduced into EMD to remove the superfluous white noise components to improve the decomposition results. Based on the contributions of MF in a single EMD process, the MF-EEMD was proposed by combining EEMD with MF to suppress the mode mixing problems. Finally, an analog signal and a measured signal were used to verify the feasibility of MF-EEMD. The results show that MF-EEMD significantly mitigates the mode mixing problems and achieves a higher decomposition efficiency compared to that of EEMD.
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5

MHAMDI, FAROUK, JEAN-MICHEL POGGI, and MÉRIEM JAÏDANE. "TREND EXTRACTION FOR SEASONAL TIME SERIES USING ENSEMBLE EMPIRICAL MODE DECOMPOSITION." Advances in Adaptive Data Analysis 03, no. 03 (July 2011): 363–83. http://dx.doi.org/10.1142/s1793536911000696.

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In this paper, we investigate eligibility of trend extraction through the empirical mode decomposition (EMD) and performance improvement of applying the ensemble EMD (EEMD) instead of the EMD for trend extraction from seasonal time series. The proposed method is an approach that can be applied on any time series with any time scales fluctuations. In order to evaluate our algorithm, experimental comparisons with three other trend extraction methods: EMD-energy-ratio approach, EEMD-energy-ratio approach, and the Hodrick–Prescott filter are conducted.
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6

HUANG, JIANFENG, and LIHUA YANG. "A PIECEWISE MONOTONOUS MODEL FOR EMPIRICAL MODE DECOMPOSITION." Advances in Adaptive Data Analysis 05, no. 04 (October 2013): 1350019. http://dx.doi.org/10.1142/s1793536913500192.

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Empirical mode decomposition (EMD) lacks theoretical support. We propose a piecewise monotonous model for EMD, and prove that the trend-subtracting iteration converges and IMF-separating procedure ends up in finite steps under mild conditions. Experiments are implemented and compared with the classical EMD.
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7

BEKKA, RAÏS EL'HADI, and YAAKOUB BERROUCHE. "IMPROVEMENT OF ENSEMBLE EMPIRICAL MODE DECOMPOSITION BY OVER-SAMPLING." Advances in Adaptive Data Analysis 05, no. 03 (July 2013): 1350012. http://dx.doi.org/10.1142/s179353691350012x.

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The empirical mode decomposition (EMD) is a useful method for the analysis of nonlinear and nonstationary signals and found immediate applications in diverse areas of signal processing. However, the major inconvenience of EMD is the mode mixing. The ensemble EMD (EEMD) was proposed to solve the problem of mode-mixing with the assistance of added noises producing the residue noise in the signal reconstructed. The residue noise in the IMFs can be reduced with a large number of ensemble trials at the expense of the increase of computational time. Improving the computing time of the EEMD by reducing the number of ensemble trials was thus proposed in this paper by over-sampling the signal to be decomposed. Numerical simulations were conducted to demonstrate proposed approach.
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8

FALTERMEIER, R., A. ZEILER, A. M. TOMÉ, A. BRAWANSKI, and E. W. LANG. "WEIGHTED SLIDING EMPIRICAL MODE DECOMPOSITION." Advances in Adaptive Data Analysis 03, no. 04 (October 2011): 509–26. http://dx.doi.org/10.1142/s1793536911000891.

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The analysis of nonlinear and nonstationary time series is still a challenge, as most classical time series analysis techniques are restricted to data that is, at least, stationary. Empirical mode decomposition (EMD) in combination with a Hilbert spectral transform, together called Hilbert-Huang transform (HHT), alleviates this problem in a purely data-driven manner. EMD adaptively and locally decomposes such time series into a sum of oscillatory modes, called Intrinsic mode functions (IMF) and a nonstationary component called residuum. In this contribution, we propose an EMD-based method, called Sliding empirical mode decomposition (SEMD), which, with a reasonable computational effort, extends the application area of EMD to a true on-line analysis of time series comprising a huge amount of data if recorded with a high sampling rate. Using nonlinear and nonstationary toy data, we demonstrate the good performance of the proposed algorithm. We also show that the new method extracts component signals that fulfill all criteria of an IMF very well and that it exhibits excellent reconstruction quality. The method itself will be refined further by a weighted version, called weighted sliding empirical mode decomposition (wSEMD), which reduces the computational effort even more while preserving the reconstruction quality.
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9

WU, ZHAOHUA, and NORDEN E. HUANG. "ON THE FILTERING PROPERTIES OF THE EMPIRICAL MODE DECOMPOSITION." Advances in Adaptive Data Analysis 02, no. 04 (October 2010): 397–414. http://dx.doi.org/10.1142/s1793536910000604.

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The empirical mode decomposition (EMD) based time-frequency analysis has been used in many scientific and engineering fields. The mathematical expression of EMD in the time-frequency-energy domain appears to be a generalization of the Fourier transform (FT), which leads to the speculation that the latter may be a special case of the former. On the other hand, the EMD is also known to behave like a dyadic filter bank when used to decompose white noise. These two observations seem to contradict each other. In this paper, we study the filtering properties of EMD, as its sifting number changes. Based on numerical results of the decompositions using EMD of a delta function and white noise, we conjecture that, as the (pre-assigned and fixed) sifting number is changed from a small number to infinity, the EMD corresponds to filter banks with a filtering ratio that changes accordingly from 2 (dyadic) to 1; the filter window does not narrow accordingly, as the sifting number increases. It is also demonstrated that the components of a delta function resulted from EMD with any prescribed sifting number can be rescaled to a single shape, a result similar to that from wavelet decomposition, although the shape changes, as the sifting number changes. These results will lead to further understandings of the relations of EMD to wavelet decomposition and FT.
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10

Du, Wei, and Quan Liu. "A Novel Empirical Mode Decomposition Denoising Scheme." Advanced Materials Research 143-144 (October 2010): 527–32. http://dx.doi.org/10.4028/www.scientific.net/amr.143-144.527.

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This paper presents a novel and fast scheme for signal denoising by using Empirical mode decomposition (EMD). The EMD involves the adaptive decomposition of signal into a series of oscillating components, Intrinsic mode functions(IMFs), by means of a decomposition process called sifting algorithm. The basic principle of the method is to reconstruct the signal with IMFs previously selected and thresholded. The denoising method is applied to four simulated signals with different noise levels and the results compared to Wavelets, EMD-Hard and EMD-Soft methods.
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11

XIE, QIWEI, BO XUAN, SILONG PENG, JIANPING LI, WEIXUAN XU, and HUA HAN. "BANDWIDTH EMPIRICAL MODE DECOMPOSITION AND ITS APPLICATION." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 06 (November 2008): 777–98. http://dx.doi.org/10.1142/s0219691308002689.

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There are some methods to decompose a signal into different components such as: Fourier decomposition and wavelet decomposition. But they have limitations in some aspects. Recently, there is a new signal decomposition algorithm called the Empirical Mode Decomposition (EMD) Algorithm which provides a powerful tool for adaptive multiscale analysis of nonstationary signals. Recent works have demonstrated that EMD has remarkable effect in time series decomposition, but EMD also has several problems such as scale mixture and convergence property. This paper proposes two key points to design Bandwidth EMD to improve on the empirical mode decomposition algorithm. By analyzing the simulated and actual signals, it is confirmed that the Intrinsic Mode Functions (IMFs) obtained by the bandwidth criterion can approach the real components and reflect the intrinsic information of the analyzed signal. In this paper, we use Bandwidth EMD to decompose electricity consumption data into cycles and trend which help us recognize the structure rule of the electricity consumption series.
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12

MOHGUEN, WAHIBA, and RAÏS EL’HADI BEKKA. "Fast Ensemble Empirical Mode Decomposition Using the Savitzky Golay filter." Algerian Journal of Signals and Systems 1, no. 1 (February 2, 2021): 79–86. http://dx.doi.org/10.51485/ajss.v1i1.21.

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Empirical mode decomposition (EMD) is a powerful algorithm proposed to analysis of nonlinear and non-stationary signals. The phenomenon of mode mixing is one of the major disadvantages of the EMD. The Ensemble EMD (EEMD) was introduced to eliminate the mode-mixing effect. The principle of EEMD is to add additional white noise into the signal with many trials. The noise in each trial is different; and the added noise can be completely cancelled out on average, if the number of trials is very high. The number of trials is a high computational load. The improvement on computational efficiency of EEMD is therefore required. In this paper, an improvement on the computing time of the EEMD was proposed by replacing white noise with white noise filtered using Savitzky-Golay (SG) filter. Numerical simulations were performed to demonstrate that such replacement has effectively reduced the number of trials to obtain a noise-free reconstructed signal.
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13

Ge, Hengqing, Guibin Chen, Haichun Yu, Huabao Chen, and Fengping An. "Theoretical Analysis of Empirical Mode Decomposition." Symmetry 10, no. 11 (November 10, 2018): 623. http://dx.doi.org/10.3390/sym10110623.

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This work suggests a theoretical principle about the oscillation signal decomposition, which is based on the requirement of a pure oscillation component, in which the mean zero is extracted from the signal. Using this principle, the validity and robustness of the empirical mode decomposition (EMD) method are first proved mathematically. This work also presents a modified version of EMD by the interpolation solution, which is able to improve the frequency decomposition of the signal. The result shows that it can provide a primary theoretical basis for the development of EMD. The simulation signal verifies the effectiveness of the EMD algorithm. At the same time, compared with the existing denoising algorithm, it has achieved good results in the denoising of rolling bearing fault signals. It contributes to the development and improvement of adaptive signal processing theory in the field of fault diagnosis. It provides practical value research results for the rapid development of adaptive technology in the field of fault diagnosis.
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14

Rehman, N., and D. P. Mandic. "Multivariate empirical mode decomposition." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2117 (December 23, 2009): 1291–302. http://dx.doi.org/10.1098/rspa.2009.0502.

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Despite empirical mode decomposition (EMD) becoming a de facto standard for time-frequency analysis of nonlinear and non-stationary signals, its multivariate extensions are only emerging; yet, they are a prerequisite for direct multichannel data analysis. An important step in this direction is the computation of the local mean, as the concept of local extrema is not well defined for multivariate signals. To this end, we propose to use real-valued projections along multiple directions on hyperspheres ( n -spheres) in order to calculate the envelopes and the local mean of multivariate signals, leading to multivariate extension of EMD. To generate a suitable set of direction vectors, unit hyperspheres ( n -spheres) are sampled based on both uniform angular sampling methods and quasi-Monte Carlo-based low-discrepancy sequences. The potential of the proposed algorithm to find common oscillatory modes within multivariate data is demonstrated by simulations performed on both hexavariate synthetic and real-world human motion signals.
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15

Zhu, Licheng, and Abdollah Malekjafarian. "On the Use of Ensemble Empirical Mode Decomposition for the Identification of Bridge Frequency from the Responses Measured in a Passing Vehicle." Infrastructures 4, no. 2 (June 4, 2019): 32. http://dx.doi.org/10.3390/infrastructures4020032.

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In this paper, ensemble empirical mode decomposition (EEMD) and empirical mode decomposition (EMD) methods are used for the effective identification of bridge natural frequencies from drive-by measurements. A vehicle bridge interaction (VBI) model is created using the finite element (FE) method in Matlab. The EMD is employed to decompose the signals measured on the vehicle to their main components. It is shown that the bridge component of the response measured on the vehicle can be extracted using the EMD method. The influence of some factors, such as the road roughness profile and measurement noise, on the results are investigated. The results suggest that the EMD shows good performance under those conditions, but the accuracy of the results may still need to be improved. It is shown that in some cases, the EMD may not be able to decompose the signal effectively and includes mode mixing. This results in inaccuracies in the identification of bridge frequencies. The use of the ensemble empirical mode decomposition (EEMD) method is proposed to overcome the mode mixing problem. The influence of factors such as road profile, measurement noise and vehicle velocity are investigated. It is numerically demonstrated that employing the EEMD improves the results compared to the EMD.
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16

Zhang, Xin, and Xiu Li Du. "Frequency Modulated Empirical Mode Decomposition Method." Advanced Materials Research 433-440 (January 2012): 4776–81. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.4776.

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Frequency modulation procedure is proposed to overcome the mode-mixing problem associated with the EMD method when processing signals with closely spaced frequencies. This procedure also provides the flexibility to start the realization of IMFs either from the high frequency end as does the original EMD or from the low frequency end when the signal contains unwanted high frequency components. The EMD procedure, under the circumstances, may behave as high pass, low pass or band pass/stop filters. The proposed method, assisted by the Hilbert-Huang transform on the governing equations, identifies the instantaneous stiffness and damping coefficients as functions of vibration amplitude of a nonlinear system. The effectiveness of the proposed method is verified by numerical simulation.
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Bejček, Michal, and Josef Kokeš. "Empirical Mode Decomposition and Quantization Effects." International Journal of Engineering Research in Africa 18 (October 2015): 175–83. http://dx.doi.org/10.4028/www.scientific.net/jera.18.175.

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The article deals with phenomena that arise when trying to apply EMD decomposition of signals with quantization noise. It explains the basic procedures of EMD as a part of Hilbert-Huang transform and shows how it can be affected by quantization. A simple method to suppress these phenomena is proposed and examples to illustrate the functionality of this method are shown.
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18

Jiang, Xiu Shan, Rui Feng Zhang, and Liang Pan. "Short-Time Fluctuation Characteristic and Combined Forecasting of High-Speed Railway Passenger Flow Based on EEMD." Applied Mechanics and Materials 409-410 (September 2013): 1071–74. http://dx.doi.org/10.4028/www.scientific.net/amm.409-410.1071.

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Take Wuhan-Guangzhou high-speed railway for example. By adopting the empirical mode decomposition (EMD) attempt to analyze mode from the perspective of volatility of high speed railway passenger flow fluctuation signal. Constructed the ensemble empirical mode decomposition-gray support vector machine (EEMD-GSVM) short-term forecasting model which fuse the gray generation and support vector machine with the ensemble empirical mode decomposition (EEMD). Finally, by the accuracy of predicted results, explains the EEMD-GSVM model has the better adaptability.
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19

Niu, Xiao-dong, Li-rong Lu, Jian Wang, Xing-cheng Han, Xuan Li, and Li-ming Wang. "An Improved Empirical Mode Decomposition Based on Local Integral Mean and Its Application in Signal Processing." Mathematical Problems in Engineering 2021 (February 1, 2021): 1–30. http://dx.doi.org/10.1155/2021/8891217.

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Empirical mode decomposition (EMD) is an effective method to deal with nonlinear nonstationary data, but the lack of orthogonal decomposition theory and mode-mixing are the main problems that limit the application of EMD. In order to solve these two problems, we propose an improved method of EMD. The most important part of this improved method is to change the mean value by envelopes of signal in EMD to the mean value by the definite integral, which enables the mean value to be mathematically expressed strictly. Firstly, we prove that the signal is orthogonally decomposed by the improved method. Secondly, the Monte Carlo method of white noise is used to explain that the improved method can effectively alleviate mode-mixing. In addition, the improved method is adaptive and does not need any input parameters, and the intrinsic mode functions (IMFs) generated from it is robust to sifting. We have carried out experiments on a series of artificial and real data, the results show that the improved method is the orthogonal decomposition method and can effectively alleviate mode-mixing, and it has better decomposition performance and physical meaning than EMD, ensemble EMD (EEMD), and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). In addition, the improved method is generally more time-consuming than EMD, but far less than EEMD and CEEMDAN.
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20

Sadhu, Ayan. "An integrated multivariate empirical mode decomposition method towards modal identification of structures." Journal of Vibration and Control 23, no. 17 (December 9, 2015): 2727–41. http://dx.doi.org/10.1177/1077546315621207.

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In this paper, a hybrid empirical mode decomposition (EMD) method is proposed to undertake ambient modal identification of civil structures. Unlike univariate EMD that uses single channel measurement independently, multivariate EMD (MEMD) is employed to estimate the joint information of multichannel vibration measurements of structural systems. The mode mixing in the resulting modal responses from MEMD is then circumvented using ensemble EMD (EEMD). The proposed hybrid MEMD method is validated using a suite of numerical models and experimental studies including the presence of low energy modes, closely-spaced frequencies, measurement noise and reduced sensor densities. The results show the improved performance of the proposed method over the traditional EMD method and reveal the potential of MEMD as a possible candidate for the ambient modal identification method.
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21

Yu, Jian Ming, and Ze Zhang. "Research on Feature Extraction for Ultrasonic Echo Signal Based on EEMD Approach." Applied Mechanics and Materials 321-324 (June 2013): 1311–16. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.1311.

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The bonding quality of composite materials have a critical influence on the quality of the product in modern industry, while the current technology can only make judgments on bonding and de-bonding instead of quantitative evaluation of different de-bonding degrees. We present HHT method to extract features of echo signals used for quantitative recognition of bonding quality of thin plates. For the non-stationary characteristic of the ultrasonic echo signal, empirical mode decomposition(EMD) and ensemble empirical mode decomposition(EEMD) are put forward to decompose the signal and calculate its energy torque. The HHT method highlights the time-frequency performance of echo signals effectively. The simulated signals verify that EEMD has more excellent decomposition performance than EMD, that is, EEMD diminishes the mode mixing to some extent generated from EMD decomposition.
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Hu, Hong Ying, Wen Long Li, and Feng Qiang Zhao. "Fully Nonparametric Regression Estimation Based on Empirical Mode Decomposition." Applied Mechanics and Materials 271-272 (December 2012): 932–35. http://dx.doi.org/10.4028/www.scientific.net/amm.271-272.932.

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Empirical Mode Decomposition (EMD) is a non-stationary signal processing method developed recently. It has been applied in many engineering fields. EMD has many similarities with wavelet decomposition. But EMD Decomposition has its own characteristics, especially in accurate trend extracting. Therefore the paper firstly proposes an algorithm of extracting slow-varying trend based on EMD. Then, according to wavelet regression estimation method, a new regression function estimation method based on EMD is presented. The simulation proves the advantages of the approach with easy computation and more accurate result.
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Zhang, Jian, Ru Qiang Yan, and Robert X. Gao. "Ensemble Empirical Mode Decomposition for Machine Health Diagnosis." Key Engineering Materials 413-414 (June 2009): 167–74. http://dx.doi.org/10.4028/www.scientific.net/kem.413-414.167.

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Ensemble Empirical Mode Decomposition (EEMD) is a new signal processing technique aimed at solving the problem of mode mixing present in the original Empirical Mode Decomposition (EMD) algorithm. This paper investigates its utility for machine health monitoring and defect diagnosis. The mechanism of EEMD is first introduced. Parameters that affect effectiveness of the EEMD are then discussed with the assistance of a simulated signal in which the mode mixing exists. Experimental study on bearing vibration signal analysis verified its effectiveness of EEMD for machine health monitoring and defect diagnosis.
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Feng, Wei, Xiaojun Zhou, Xiang Zeng, and Chenlong Yang. "Ultrasonic Flaw Echo Enhancement Based on Empirical Mode Decomposition." Sensors 19, no. 2 (January 9, 2019): 236. http://dx.doi.org/10.3390/s19020236.

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The detection of flaw echoes in backscattered signals in ultrasonic nondestructive testing can be challenging due to the existence of backscattering noise and electronic noise. In this article, an empirical mode decomposition (EMD) methodology is proposed for flaw echo enhancement. The backscattered signal was first decomposed into several intrinsic mode functions (IMFs) using EMD or ensemble EMD (EEMD). The sample entropies (SampEn) of all IMFs were used to select the relevant modes. Otsu’s method was used for interval thresholding of the first relevant mode, and a window was used to separate the flaw echoes in the relevant modes. The flaw echo was reconstructed by adding the residue and the separated flaw echoes. The established methodology was successfully employed for simulated signal and experimental signal processing. For the simulated signals, an improvement of 9.42 dB in the signal-to-noise ratio (SNR) and an improvement of 0.0099 in the modified correlation coefficient (MCC) were achieved. For experimental signals obtained from two cracks at different depths, the flaw echoes were also significantly enhanced.
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Xu, Y., B. Liu, J. Liu, and S. Riemenschneider. "Two-dimensional empirical mode decomposition by finite elements." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2074 (May 5, 2006): 3081–96. http://dx.doi.org/10.1098/rspa.2006.1700.

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Empirical mode decomposition (EMD) is a powerful tool for analysis of non-stationary and nonlinear signals, and has drawn significant attention in various engineering application areas. This paper presents a finite element-based EMD method for two-dimensional data analysis. Specifically, we represent the local mean surface of the data, a key step in EMD, as a linear combination of a set of two-dimensional linear basis functions smoothed with bi-cubic spline interpolation. The coefficients of the basis functions in the linear combination are obtained from the local extrema of the data using a generalized low-pass filter. By taking advantage of the principle of finite-element analysis, we develop a fast algorithm for implementation of the EMD. The proposed method provides an effective approach to overcome several challenging difficulties in extending the original one-dimensional EMD to the two-dimensional EMD. Numerical experiments using both simulated and practical texture images show that the proposed method works well.
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26

WU, QIN, and SHERMAN D. RIEMENSCHNEIDER. "BOUNDARY EXTENSION AND STOP CRITERIA FOR EMPIRICAL MODE DECOMPOSITION." Advances in Adaptive Data Analysis 02, no. 02 (April 2010): 157–69. http://dx.doi.org/10.1142/s1793536910000434.

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In this paper, a new idea about the boundary extension has been introduced and applied to the Empirical Mode Decomposition (EMD) algorithm. Instead of the traditional mirror extension on the boundary, we propose a ratio extension on the boundary. We also adopt the stop criteria by Rilling et al. for B-Spline based EMD algorithm. Numerical experiments are used for empirically assessing performance of the modified EMD algorithm. The examples indicate that the ratio boundary extension indeed improves the result of the original EMD.
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RILLING, GABRIEL, and PATRICK FLANDRIN. "SAMPLING EFFECTS ON THE EMPIRICAL MODE DECOMPOSITION." Advances in Adaptive Data Analysis 01, no. 01 (January 2009): 43–59. http://dx.doi.org/10.1142/s1793536909000023.

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Standard exposition of Empirical Mode Decomposition (EMD) is usually done within a continuous-time setting whereas, in practice, the effective implementation always operates in discrete-time. The purpose of this contribution is to summarize a number of results aimed at quantifying the influence of sampling on EMD. The idealized case of a sampled pure tone is first considered in detail and a theoretical model is proposed for upper bounding the approximation error due to finite sampling rates. A more general approach is then discussed, based on the analysis of the nonlinear operator that underlies the EMD (one step) sifting process. New explicit, yet looser, bounds are obtained this way, whose parameters can be estimated directly from the analyzed signal. Theoretical predictions are compared to simulation results in a number of well-controlled numerical experiments.
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28

Germán-Salló, Zoltán. "Empirical Mode Decomposition in Discrete Time Signals Denoising." Acta Marisiensis. Seria Technologica 16, no. 1 (June 1, 2019): 10–13. http://dx.doi.org/10.2478/amset-2019-0002.

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Abstract This study explores the data-driven properties of the empirical mode decomposition (EMD) for signal denoising. EMD is an acknowledged procedure which has been widely used for non-stationary and nonlinear signal processing. The main idea of the EMD method is to decompose the analyzed signal into components without using expansion functions. This is a signal dependent representation and provides intrinsic mode functions (IMFs) as components. These are analyzed, through their Hurst exponent and if they are found being noisy components they will be partially or integrally eliminated. This study presents an EMD decomposition-based filtering procedure applied to test signals, the results are evaluated through signal to noise ratio (SNR) and mean square error (MSE). The obtained results are compared with discrete wavelet transform based filtering results.
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NUNES, JEAN-CLAUDE, and ÉRIC DELÉCHELLE. "EMPIRICAL MODE DECOMPOSITION: APPLICATIONS ON SIGNAL AND IMAGE PROCESSING." Advances in Adaptive Data Analysis 01, no. 01 (January 2009): 125–75. http://dx.doi.org/10.1142/s1793536909000059.

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In this paper, we propose some recent works on data analysis and synthesis based on Empirical Mode Decomposition (EMD). Firstly, a direct 2D extension of original Huang EMD algorithm with application to texture analysis, and fractional Brownian motion synthesis. Secondly, an analytical version of EMD based on PDE in 1D-space is presented. We proposed an extension in 2D-case of the so-called "sifting process" used in the original Huang's EMD. The 2D-sifting process is performed in two steps: extrema detection (by neighboring window or morphological operators) and surface interpolation by splines (thin plate splines or multigrid B-splines). We propose a multiscale segmentation approach by using the zero-crossings from each 2D-intrinsic mode function (IMF) obtained by 2D-EMD. We apply the Hilbert–Huang transform (which consists of two parts: (a) Empirical mode decomposition, and (b) the Hilbert spectral analysis) to texture analysis. We analyze each 2D-IMF obtained by 2D-EMD by studying local properties (amplitude, phase, isotropy, and orientation) extracted from the monogenic signal of each one of them. The monogenic signal proposed by Felsberg et al. is a 2D-generalization of the analytic signal, where the Riesz transform replaces the Hilbert transform. These local properties are obtained by the structure multivector such as proposed by Felsberg and Sommer. We present numerical simulations of fractional Brownian textures. Recent works published by Flandrin et al. relate that, in the case of fractional Gaussian noise (fGn), EMD acts essentially as a dyadic filter bank that can be compared to wavelet decompositions. Moreover, in the context of fGn identification, Flandrin et al. show that variance progression across IMFs is related to Hurst exponent H through a scaling law. Starting with these results, we proposed an algorithm to generate fGn, and fractional Brownian motion (fBm) of Hurst exponent H from IMFs obtained from EMD of a White noise, i.e., ordinary Gaussian noise (fGn with H = 1/2). Deléchelle et al. proposed an analytical approach (formulated as a partial differential equation (PDE)) for sifting process. This PDE-based approach is applied on signals. The analytical approach has a behavior similar to that of the EMD proposed by Huang.
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Li, Zhi Bin, Bao Xing Wu, and Yun Hui Xu. "The Applied Research of the Hilbert-Huang Transform and Wavelet Transform in the Fault Location of Transmission Line." Applied Mechanics and Materials 291-294 (February 2013): 2432–36. http://dx.doi.org/10.4028/www.scientific.net/amm.291-294.2432.

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In the process of the Hilbert-Huang transform, empirical mode decomposition (EMD) may result in the end effect and modal aliasing when processing data, so proposing Ensemble Empirical Mode Decomposition (EEMD) instead of EMD, and assessing the accuracy of the two decomposition processes according to the total energy of the signal before and after the decomposition. Take a comparison between the Hilbert-Huang transform and the wavelet transform, the localization showed that the Hilbert-Huang transform is better than wavelet transform in the fault location of transmission line.
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Hu, Hong Ying, and Chun Ming Kan. "Fully Nonparametric Probability Density Function Estimation Based on Empirical Mode Decomposition." Advanced Materials Research 460 (February 2012): 189–92. http://dx.doi.org/10.4028/www.scientific.net/amr.460.189.

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Empirical Mode Decomposition (EMD) is a non-stationary signal processing method developed recently. It has been applied in many engineering fields. EMD has many similarities with wavelet decomposition. But EMD Decomposition has its own characteristics, especially in accurate rend extracting. Therefore the paper firstly proposes an algorithm of extracting slow-varying trend based on EMD. Then, according to wavelet probability density function estimation method, a new density estimation method based on EMD is presented. The simulations of Gaussian single and mixture model density estimation prove the advantages of the approach with easy computation and more accurate result
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SHEN, ZHIYUAN, NAIZHANG FENG, and YI SHEN. "RIDGE REGRESSION MODEL-BASED ENSEMBLE EMPIRICAL MODE DECOMPOSITION FOR ULTRASOUND CLUTTER REJECTION." Advances in Adaptive Data Analysis 04, no. 01n02 (April 2012): 1250013. http://dx.doi.org/10.1142/s1793536912500136.

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Ensemble empirical mode decomposition (EEMD) is a noise-assisted adaptive data analysis method to solve the problem of mode mixing caused by empirical mode decomposition (EMD). It is shown that the decomposition error tends to zero, as ensemble number increases to infinity in EEMD. In this paper, a novel EEMD-based ridge regression model (REEMD) is proposed, which solves the problem of mode mixing and achieves less decomposition error compared with the EEMD. When the ensemble number is small, the weights of outliers are constraint to zero to reduce the decomposition error in REEMD and the result of REEMD is asymptotic to that of EEMD, as the ensemble number increases. The proposed REEMD is suitable for tissue clutter rejection in color flow imaging system. Simulation shows that reasonable flow-frequency estimations can be achieved by REEMD and the estimation error limits to zero, as the flow frequency increases.
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B Shankar, B., and D. Jayadevappa. "Ensemble EMD based Time-Frequency Analysis of Continuous Adventitious Signal Processing." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 896. http://dx.doi.org/10.14419/ijet.v7i4.10.26783.

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The importance of lung sound analyses is increasing day by day very rapidly. In this paper, we present a new method for analysis of two classes of lung signals namely wheezes and crackles. The procedure used in this article is based on improved Empirical Mode Decomposition (EMD) called Ensemble Empirical Mode Decomposition (EEMD) to analyze and compare continuous and discontinuous adventitious sounds with EMD. These two proposed procedures decompose the lung signals into a set of instantaneous frequency components. Function (IMF). The continuous and discontinuous adventitious sounds are present in an asthmatic patient, produces a non-stationary and nonlinear signal pattern. The empirical mode decomposition (EMD) decomposes such characteristic signals. The instantaneous frequency and spectral analysis related to dual techniques specified above are utilized by IMF to investigate and present the outcome in the time-frequency distribution to investigate the qualities of inbuilt properties of lung sound waves. The Hilbert marginal spectrum has been used to represent total amplitude and energy contribution from every frequency value. Finally, the resultant EEMD analysis is better for wheezes that solves mode mixing issues and improvisation is seen over the EMD method.
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Chen, Ye Qu, Wen Zheng, and Xie Ben Wei. "Application of EMD to Integrated Signal Trend Extraction." Advanced Materials Research 591-593 (November 2012): 2072–76. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.2072.

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Huang’s data-driven technique of Empirical Mode Decomposition (EMD) is presented, and issues related to its effective implementation are discussed. Integrating signal directly will produce a trend, it will cause distortion and interfere with the calculation results. This paper discusses the reasons that cause the integrated signal trend, compares the different methods for extracting trend. The traditional steps use the linear fitting and a high-pass filter to remove low frequency signal to extract trend. This paper uses Empirical Mode Decomposition (EMD) method to extract integrated signals trend, discussed the advantages of Empirical Mode Decomposition (EMD) method in this case, proves that Empirical Mode Decomposition (EMD) has a good application in integrated signal trend extraction.
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Li, Yifan, Jianxin Liu, and Yan Wang. "Railway Wheel Flat Detection Based on Improved Empirical Mode Decomposition." Shock and Vibration 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/4879283.

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This study explores the capacity of the improved empirical mode decomposition (EMD) in railway wheel flat detection. Aiming at the mode mixing problem of EMD, an EMD energy conservation theory and an intrinsic mode function (IMF) superposition theory are presented and derived, respectively. Based on the above two theories, an improved EMD method is further proposed. The advantage of the improved EMD is evaluated by a simulated vibration signal. Then this method is applied to study the axle box vibration response caused by wheel flats, considering the influence of both track irregularity and vehicle running speed on diagnosis results. Finally, the effectiveness of the proposed method is verified by a test rig experiment. Research results demonstrate that the improved EMD can inhibit mode mixing phenomenon and extract the wheel fault characteristic effectively.
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Huang, Shi Qi, Bei He Wang, Yi Hong Li, and Bei Ge. "SAR Target Detection Method Based on Empirical Mode Decomposition." Advanced Engineering Forum 6-7 (September 2012): 496–500. http://dx.doi.org/10.4028/www.scientific.net/aef.6-7.496.

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Empirical mode decomposition (EMD) is a new signal processing theory, and it is very much fitting for non-stationary signal processing, such as radar signal. So this paper proposes the new synthetic aperture radar (SAR) image target detection algorithm after analyzing the characteristics of EMD and SAR images. The proposed method performs the EMD operation, feature extraction, election and fusion, which can reduce the affection of speckle. Experimental results show that the proposed method is very effective.
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McDonald, A. J., A. J. G. Baumgaertner, G. J. Fraser, S. E. George, and S. Marsh. "Empirical Mode Decomposition of the atmospheric wave field." Annales Geophysicae 25, no. 2 (March 8, 2007): 375–84. http://dx.doi.org/10.5194/angeo-25-375-2007.

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Abstract. This study examines the utility of the Empirical Mode Decomposition (EMD) time-series analysis technique to separate the horizontal wind field observed by the Scott Base MF radar (78° S, 167° E) into its constituent parts made up of the mean wind, gravity waves, tides, planetary waves and instrumental noise. Analysis suggests that EMD effectively separates the wind field into a set of Intrinsic Mode Functions (IMFs) which can be related to atmospheric waves with different temporal scales. The Intrinsic Mode Functions resultant from application of the EMD technique to Monte-Carlo simulations of white- and red-noise processes are compared to those obtained from the measurements and are shown to be significantly different statistically. Thus, application of the EMD technique to the MF radar horizontal wind data can be used to prove that this data contains information on internal gravity waves, tides and planetary wave motions. Examination also suggests that the EMD technique has the ability to highlight amplitude and frequency modulations in these signals. Closer examination of one of these regions of amplitude modulation associated with dominant periods close to 12 h is suggested to be related to a wave-wave interaction between the semi-diurnal tide and a planetary wave. Application of the Hilbert transform to the IMFs forms a Hilbert-Huang spectrum which provides a way of viewing the data in a similar manner to the analysis from a continuous wavelet transform. However, the fact that the basis function of EMD is data-driven and does not need to be selected a priori is a major advantage. In addition, the skeleton diagrams, produced from the results of the Hilbert-Huang spectrum, provide a method of presentation which allows quantitative information on the instantaneous period and amplitude squared to be displayed as a function of time. Thus, it provides a novel way to view frequency and amplitude-modulated wave phenomena and potentially non-linear interactions. It also has the significant advantage that the results obtained are more quantitative than those resultant from the continuous wavelet transform.
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Xiao, Feng, Gang S. Chen, Wael Zatar, and J. Leroy Hulsey. "Quantification of Dynamic Properties of Pile Using Ensemble Empirical Mode Decomposition." Advances in Civil Engineering 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/8379871.

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This paper investigated dynamical interactions between pile and frozen ground by using the ensemble empirical mode decomposition (EEMD) method. Unlike the conventional empirical mode decomposition (EMD) method, EEMD is found to be able to separate the mode patterns of pile response signals of different scales without causing mode mixing. The identified dynamic properties using the EEMD method are more accurate than those obtained from conventional methods. EEMD-based results can be used to reliably and accurately characterize pile-frozen soil interactions and help designing infrastructure foundations under permafrost condition.
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ZHANG, MIN, and YI SHEN. "ENSEMBLE EMPIRICAL MODE DECOMPOSITION FOR HYPERSPECTRAL IMAGE CLASSIFICATION." Advances in Adaptive Data Analysis 04, no. 01n02 (April 2012): 1250003. http://dx.doi.org/10.1142/s1793536912500033.

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Ensemble empirical mode decomposition (EEMD) is a novel adaptive time-frequency analysis method, which is particularly suitable for extracting useful information from noisy nonlinear or nonstationary data. This paper presents the utilization of EEMD for hyperspectral images to extract signals from them, generated in noisy nonlinear and nonstationary processes. First, EEMD is applied to each hyperspectral image band and defines the true intrinsic mode function (IMF) components as the mean of an ensemble of trials, each consisting of the signal plus a white noise of finite amplitude. After EEMD is performed to each band, new bands are reconstructed as the sum of IMFs and the trend, and classification is executed over these new bands. Finally, the hyperspectral image with new bands was classified with support vector machine (SVM) to show the classification performance of the proposed approach. Experimental results show that the utilization of the EEMD significantly increases the classification accuracy compared to the dataset processed by empirical mode decomposition (EMD) and the original dataset.
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Zhang, Pan, Tai Yong Wang, Lu Liu, Lu Yang Jin, and Jin Xiang Fang. "Approach to Weak Signal Extraction Based on Empirical Mode Decomposition and Stochastic Resonance." Advanced Materials Research 819 (September 2013): 216–21. http://dx.doi.org/10.4028/www.scientific.net/amr.819.216.

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The empirical mode decomposition (EMD) of weak signals submerged in a heavy noise was conducted and a method of stochastic resonance (SR) used for noisy EMD was presented. This method used SR as pre-treatment of EMD to remove noise and detect weak signals. The experiment result prove that this method, compared with that using EMD directly, not only improve SNR, enhance weak signals, but also improve the decomposition performance and reduce the decomposition layers.
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41

Qin, Shiqiang, Qiuping Wang, and Juntao Kang. "Output-Only Modal Analysis Based on Improved Empirical Mode Decomposition Method." Advances in Materials Science and Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/945862.

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The output-only modal analysis for bridge structures based on improved empirical mode decomposition (EMD) is investigated in this study. First, a bandwidth restricted EMD is proposed for decomposing nonstationary output measurements with close frequency components. The advantage of bandwidth restricted EMD to standard EMD is illustrated by a numerical simulation. Next, the modal parameters are extracted from intrinsic mode function obtained from the improved EMD by both random decrement technique and stochastic subspace identification. Finally, output-only modal analysis of a railway bridge is presented. The study demonstrates the mode mixing issues of standard EMD can be restrained by introducing bandwidth restricted signal. Further, with the improved EMD method, band-pass filter is no longer needed for separating the closely spaced frequency components. The modal parameters extracted based on the improved EMD method show good agreement with those extracted by conventional modal identification algorithms.
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FLANDRIN, PATRICK, and PAULO GONÇALVÈS. "EMPIRICAL MODE DECOMPOSITIONS AS DATA-DRIVEN WAVELET-LIKE EXPANSIONS." International Journal of Wavelets, Multiresolution and Information Processing 02, no. 04 (December 2004): 477–96. http://dx.doi.org/10.1142/s0219691304000561.

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Huang's data-driven technique of Empirical Mode Decomposition (EMD) is applied to the versatile, broadband, model of fractional Gaussian noise (fGn). The experimental spectral analysis and statistical characterization of the obtained modes reveal an equivalent filter bank structure which shares most properties of a wavelet decomposition in the same context, in terms of self-similarity, quasi-decorrelation and variance progression. Furthermore, the spontaneous adaptation of EMD to "natural" dyadic scales is shown, rationalizing the method as an alternative way for estimating the fGn Hurst exponent.
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Liu, Xiaohan, Guangfeng Shi, and Weina Liu. "An Improved Empirical Mode Decomposition Method for Vibration Signal." Wireless Communications and Mobile Computing 2021 (April 27, 2021): 1–8. http://dx.doi.org/10.1155/2021/5525270.

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With the development of electronic measurement and signal processing technology, nonstationary and nonlinear signal characteristics are widely used in the fields of error diagnosis, system recognition, and biomedical instruments. Whether these features can be extracted effectively usually affects the performance of the entire system. Based on the above background, the research purpose of this paper is an improved vibration empirical mode decomposition method. This article introduces a method of blasting vibration signal processing—Differential Empirical Mode Decomposition (DEMD), combined with phosphate rock engineering blasting vibration monitoring test, and Empirical Mode Decomposition (EMD) to compare and analyze the frequency screening of blasting vibration signals, the aliasing distortion, and the power spectrum characteristics of the decomposed signal. The results show that compared with EMD, DEMD effectively suppresses signal aliasing and distortion, and from the characteristics of signal power spectrum changes, DEMD extracts different dominant frequency components, and the frequency screening effect of blasting vibration signals is superior to EMD. It can bring about an obvious improvement in accuracy, and the calculation time is about 4 times that of the EMD method. Based on the ground analysis of ground motion signals, this paper uses the EMD algorithm to analyze measured ground blast motion signals and study its velocity characteristics and differential time, which provides a new way of studying motion signals.
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Lei, Zhufeng, Wenbin Su, and Qiao Hu. "Multimode Decomposition and Wavelet Threshold Denoising of Mold Level Based on Mutual Information Entropy." Entropy 21, no. 2 (February 21, 2019): 202. http://dx.doi.org/10.3390/e21020202.

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The continuous casting process is a continuous, complex phase transition process. The noise components of the continuous casting process are complex, the model is difficult to establish, and it is difficult to separate the noise and clear signals effectively. Owing to these demerits, a hybrid algorithm combining Variational Mode Decomposition (VMD) and Wavelet Threshold denoising (WTD) is proposed, which involves multiscale resolution and adaptive features. First of all, the original signal is decomposed into several Intrinsic Mode Functions (IMFs) by Empirical Mode Decomposition (EMD), and the model parameter K of the VMD is obtained by analyzing the EMD results. Then, the original signal is decomposed by VMD based on the number of IMFs K, and the Mutual Information Entropy (MIE) between IMFs is calculated to identify the noise dominant component and the information dominant component. Next, the noise dominant component is denoised by WTD. Finally, the denoised noise dominant component and all information dominant components are reconstructed to obtain the denoised signal. In this paper, a comprehensive comparative analysis of EMD, Ensemble Empirical Mode Decomposition (EEMD), Complementary Empirical Mode Decomposition (CEEMD), EMD-WTD, Empirical Wavelet Transform (EWT), WTD, VMD, and VMD-WTD is carried out, and the denoising performance of the various methods is evaluated from four perspectives. The experimental results show that the hybrid algorithm proposed in this paper has a better denoising effect than traditional methods and can effectively separate noise and clear signals. The proposed denoising algorithm is shown to be able to effectively recognize different cast speeds.
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Wu, Zhiyuan, Changbo Jiang, Mack Conde, Bin Deng, and Jie Chen. "Hybrid improved empirical mode decomposition and BP neural network model for the prediction of sea surface temperature." Ocean Science 15, no. 2 (April 5, 2019): 349–60. http://dx.doi.org/10.5194/os-15-349-2019.

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Abstract. Sea surface temperature (SST) is the major factor that affects the ocean–atmosphere interaction, and in turn the accurate prediction of SST is the key to ocean dynamic prediction. In this paper, an SST-predicting method based on empirical mode decomposition (EMD) algorithms and back-propagation neural network (BPNN) is proposed. Two different EMD algorithms have been applied extensively for analyzing time-series SST data and some nonlinear stochastic signals. The ensemble empirical mode decomposition (EEMD) algorithm and complementary ensemble empirical mode decomposition (CEEMD) algorithm are two improved algorithms of EMD, which can effectively handle the mode-mixing problem and decompose the original data into more stationary signals with different frequencies. Each intrinsic mode function (IMF) has been taken as input data to the back-propagation neural network model. The final predicted SST data are obtained by aggregating the predicted data of individual series of IMFs (IMFi). A case study of the monthly mean SST anomaly (SSTA) in the northeastern region of the North Pacific shows that the proposed hybrid CEEMD-BPNN model is much more accurate than the hybrid EEMD-BPNN model, and the prediction accuracy based on a BP neural network is improved by the CEEMD method. Statistical analysis of the case study demonstrates that applying the proposed hybrid CEEMD-BPNN model is effective for the SST prediction. Highlights include the following: Highlights. An SST-predicting method based on the hybrid EMD algorithms and BP neural network method is proposed in this paper. SST prediction results based on the hybrid EEMD-BPNN and CEEMD-BPNN models are compared and discussed. A case study of SST in the North Pacific shows that the proposed hybrid CEEMD-BPNN model can effectively predict the time-series SST.
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PAO, SUN-HUA, CHIEH-NENG YOUNG, CHIEN-LUN TSENG, and NORDEN E. HUANG. "SMOOTHING EMPIRICAL MODE DECOMPOSITION: A PATCH TO IMPROVE THE DECOMPOSED ACCURACY." Advances in Adaptive Data Analysis 02, no. 04 (October 2010): 521–43. http://dx.doi.org/10.1142/s1793536910000616.

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Hilbert-Huang Transformation (HHT) is designed especially for analyzing data from nonlinear and nonstationary processes. It consists of the Empirical Mode Decomposition (EMD) to generate Intrinsic Mode Function (IMF) components, from which the instantaneous frequency can be computed for the time-frequency Hilbert spectral Analysis. Currently, EMD, based on the cubic spline, is the most efficient and popular algorithm to implement HHT. However, EMD as implemented now suffers from dependence on the cubic spline function chosen as the basis. Furthermore, due to the various stoppage criteria, it is difficult to establish the uniqueness of the decomposition. Consequently, the interpretation of the EMD result is subject to certain degree of ambiguity. As the IMF components from the classic EMD are all approximations from the combinations of piece-wise cubic spline functions, there could also be artificial frequency modulation in addition to amplitude modulation. A novel Smoothing Empirical Mode Decomposition (SEMD) is proposed. Although SEMD is also an approximation, extensive tests on nonlinear and nonstationary data indicate that the smoothing procedure is a robust and accurate approach to eliminate the dependence of chosen spline functional forms. Thus, we have proved the uniqueness of the decomposition under the weak limitation of spline fittings. The natural signal length-of-day 1965–1985 was tested for the performance in nonstationary and nonlinear decomposition. The resulting spectrum by SEMD is quite stable and quantitatively similar to the optimization of EMD.
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47

Zhang, Shou Cheng, and Li Li Sui. "A New Denoising Method via Empirical Mode Decomposition." Applied Mechanics and Materials 651-653 (September 2014): 2090–93. http://dx.doi.org/10.4028/www.scientific.net/amm.651-653.2090.

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In non-parametric signal denoising area, empirical mode decomposition is potentially useful. In this paper, the wavelet thresholding principle is directly used in EMD-based denoising. The basic principle of the method is to reconstruct the signal with IMFs previously thresholded. A novel threshold function is proposed to improve denoising effect by exploiting the special characteristics of the hard and soft thresholding method. The denoising method is validated through experiments on the “Doppler” signal and a real ECG signal from MIT-BIH databases corrupted by additive white Gaussian random noise. The simulations show that the proposed EMD-based method provides very good results for denoising.
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Qiu, Jian, and Ji Jun Chen. "EMD in the Research and Application of Deformation Monitoring in Embankment." Applied Mechanics and Materials 501-504 (January 2014): 1868–72. http://dx.doi.org/10.4028/www.scientific.net/amm.501-504.1868.

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In this paper, the deformation monitoring of empirical mode decomposition method is applied to the embankment, and accordingly to evaluate dike reinforcement effect. Based on empirical mode decompositionof the endpoint effect makes the decomposition results of distortion, put forward to properly control point by using the window function method.effectively ensure the accuracy of the results of decomposition. Reference for peers and staff.
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Liu, Guangda, Xinlei Hu, Enhui Wang, Ge Zhou, Jing Cai, and Shang Zhang. "SVR-EEMD: An Improved EEMD Method Based on Support Vector Regression Extension in PPG Signal Denoising." Computational and Mathematical Methods in Medicine 2019 (December 12, 2019): 1–10. http://dx.doi.org/10.1155/2019/5363712.

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Photoplethysmography (PPG) has been widely used in noninvasive blood volume and blood flow detection since its first appearance. However, its noninvasiveness also makes the PPG signals vulnerable to noise interference and thus exhibits nonlinear and nonstationary characteristics, which have brought difficulties for the denoising of PPG signals. Ensemble empirical mode decomposition known as EEMD, which has made great progress in noise processing, is a noise-assisted nonlinear and nonstationary time series analysis method based on empirical mode decomposition (EMD). The EEMD method solves the “mode mixing” problem in EMD effectively, but it can do nothing about the “end effect,” another problem in the decomposition process. In response to this problem, an improved EEMD method based on support vector regression extension (SVR-EEMD) is proposed and verified by simulated data and real-world PPG data. Experiments show that the SVR-EEMD method can solve the “end effect” efficiently to get a better decomposition performance than the traditional EEMD method and bring more benefits to the noise processing of PPG signals.
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Wu, Shuen De, Chiu Wen Wu, Cha Lin Liu, Yan Hao Huang, and Kung Yen Lee. "A Novel Gaussian Window Approach for Empirical Mode Decomposition." Advanced Materials Research 457-458 (January 2012): 274–77. http://dx.doi.org/10.4028/www.scientific.net/amr.457-458.274.

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Empirical mode decomposition (EMD) is an algorithmic construction for decomposing multi-component signals into a series of intrinsic mode functions (IMFs). However, traditional EMD may encounter the difficulty of mode mixing when a signal contains intermittency. To solve the difficulty, a Gaussian window averaging method is proposed to construct the mean envelope of a given signal in each sifting process. The numerical analysis also demonstrates promising reliability with the proposed algorithm.
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