intrinsic mode functions
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Based on the Mann-Kendall test and Sen’s slope method, this study investigates the monthly, seasonal, and annual sea surface temperature (SST) trends in the coastal area of Hai Phong (West of Tonkin Gulf) based on the measurements at Hon Dau Station from 1995 to 2020. The results show a sea surface warming trend of 0.02°C/year for the period 1995-2020 (significant level α = 0.1) and of 0.093°C/year for the period 2008-2020 (significant level α = 0.05). The monthly SSTs in June and September increased by 0.027°C/year and 0.036°C/year, respectively, for the period 1995-2020, and by 0.080°C/year and 0.047°C/year, respectively, for the period 2008-2020. SST trends in winter, summer, and other months were either different for the two periods or not significant enough. This may be due to the impact of ENSO, which caused interannual SST variability in the Hai Phong coastal with two intrinsic mode functions (IMF) signals a period of ~2 (IMF3) and ~5.2 years cycle (IMF4). A combination of these signals had a maximum correlation of 0.22 with ONI (Oceanic Niño Index) delayed by 8 months. ENSO events took ~8 months to affect SST at Hai Phong coastal area for 1995-2020 and caused a variation of SST within 1.2°C.

This research introduces a procedure for signal denoising based on linear combinations of intrinsic mode functions (IMFs) extracted using empirical mode decomposition (EMD). The method, termed component-scaled signal reconstruction, employs the standard EMD algorithm, with no enhancements to decompose the signal into a set of IMFs. The problem of mode mixing is leveraged for noise removal by constructing an optimal linear combination of the potentially mixed IMFs. The optimal linear combination is determined using an optimization routine with an objective function that maximizes and minimizes the information and noise, respectively, in the denoised signal. The method is demonstrated by applying it to a computer-generated voice sample and the displacement response of a cantilever beam with local stiffness nonlinearity. In the first application, the noise is introduced into the sample manually by adding a Gaussian white-noise signal to the signal. In the second application, the response of the entire beam is filmed using two 1-megapixel cameras, and the three-dimensional displacement field is extracted using digital image correlation. The noise in this application arises entirely from the images captured. The proposed method is compared to existing EMD, ensemble EMD, and LMD based denoising approaches and is found to perform better.

Abstract. In the last few years, wind power forecasting has established itself as an essential tool in the energy industry due to the increase of wind power penetration in the electric grid. This paper presents a wind power forecasting method based on ensemble empirical mode decomposition (EEMD) and deep learning. EEMD is employed to decompose wind power time series data into several intrinsic mode functions and a residual component. Afterwards, every intrinsic mode function is trained by means of a CNN-LSTM architecture. Finally, wind power forecast is obtained by adding the prediction of every component. Compared to the benchmark model, the proposed approach provides more accurate predictions for several time horizons. Furthermore, prediction intervals are modelled using quantile regression.

The vibration induced by blasting excavation of the subway tunnel in complex urban environments may cause harmful effects on adjacent buildings. Investigating the dynamic response of adjacent buildings is a key issue to predict and control blasting hazards. In this paper, the blasting excavation of the subway tunnel right below a building was selected as a case study, and the blast vibrations in the field were monitored. The Hilbert–Huang Transform (HHT) model was used to extract and analyze the time-frequency characteristic parameters of blasting dynamic response signals. By substituting intrinsic mode functions (IMF) component frequency and instantaneous energy for main frequency and blasting total input energy, respectively, the characteristics of time-instantaneous frequency-instantaneous energy of buildings under blasting seismic load were analyzed, and the concept of effective duration of vibration was proposed.

Rolling bearings are the key components of rotating machinery. Incipient fault diagnosis of bearing plays an increasingly important role in guaranteeing normal and safe operation of rotating machinery. However, because of the high complexity of the fault feature extraction, the incipient faults of rolling bearings are difficult to diagnose. To solve this problem, this paper presents a new incipient fault intelligent identification method of rolling bearings based on variational mode decomposition (VMD), principal component analysis (PCA), and support vector machines (SVM). In the proposed method, the bearing vibration signals are decomposed by using VMD, and a series of intrinsic mode functions (IMFs) with different frequencies are obtained. Then, the energy and kurtosis values of each IMF are calculated to reveal the intrinsic characteristics of the vibration signals in different scales. Finally, all energy and kurtosis values of IMFs are processed via PCA and subsequently fed into SVM to achieve the bearing fault identification automatically. The effectiveness of this method is verified through the experimental bearing data. The verification results indicate that the proposed method can effectively extract the bearing fault features and accurately identify the bearing incipient faults, and outperform the two compared methods obviously in identification accuracy and computation time.

AbstractIn this paper, we propose a novel hybrid model that extends prior work involving ensemble empirical mode decomposition (EEMD) by using fuzzy entropy and extreme learning machine (ELM) methods. We demonstrate this 3-stage model by applying it to forecast carbon futures prices which are characterized by chaos and complexity. First, we employ the EEMD method to decompose carbon futures prices into a couple of intrinsic mode functions (IMFs) and one residue. Second, the fuzzy entropy and K-means clustering methods are used to reconstruct the IMFs and the residue to obtain three reconstructed components, specifically a high frequency series, a low frequency series, and a trend series. Third, the ARMA model is implemented for the stationary high and low frequency series, while the extreme learning machine (ELM) model is utilized for the non-stationary trend series. Finally, all the component forecasts are aggregated to form final forecasts of the carbon price for each model. The empirical results show that the proposed reconstruction algorithm can bring more than 40% improvement in prediction accuracy compared to the traditional fine-to-coarse reconstruction algorithm under the same forecasting framework. The hybrid forecasting model proposed in this paper also well captures the direction of the price changes, with strong and robust forecasting ability, which is significantly better than the single forecasting models and the other hybrid forecasting models.

Due to the complexity and unique features of the hydroacoustic channel, ship-radiated noise (SRN) detected using a passive sonar tends mostly to distort. SRN feature extraction has been proposed to improve the detected passive sonar signal. Unfortunately, the current methods used in SRN feature extraction have many shortcomings. Considering this, in this paper we propose a new multi-stage feature extraction approach to enhance the current SRN feature extractions based on enhanced variational mode decomposition (EVMD), weighted permutation entropy (WPE), local tangent space alignment (LTSA), and particle swarm optimization-based support vector machine (PSO-SVM). In the proposed method, first, we enhance the decomposition operation of the conventional VMD by decomposing the SRN signal into a finite group of intrinsic mode functions (IMFs) and then calculate the WPE of each IMF. Then, the high-dimensional features obtained are reduced to two-dimensional ones by using the LTSA method. Finally, the feature vectors are fed into the PSO-SVM multi-class classifier to realize the classification of different types of SRN sample. The simulation and experimental results demonstrate that the recognition rate of the proposed method overcomes the conventional SRN feature extraction methods, and it has a recognition rate of up to 96.6667%.

In this paper, we propose the use of the Ensemble Empirical Mode Decomposition (EEMD) method in the analysis of trends in climate data. As compared to existing traditional methods, EEMD is simple, fast and reliable. It works by decomposing the time-series data into intrinsic mode functions until a residual component is obtained which represents the trend in the data. The dataset considered consists of satellite precipitation estimates (SPE) obtained from the Tropical Rainfall Measuring Mission (TRMM) for the tropical South-West Indian Ocean (SWIO) basin recorded during the periods January 1998 to December 2013. The SWIO basin spans from the latitudes 5° S to 35° S and the longitudes 30° E to 70° E and comprises of part of the east coast of Africa and some small island developing states (SIDS) such as Comoros, Madagascar, Mauritius and Reunion Island. The EEMD analysis is carried out for summer, winter and yearly time series of the SPE data. The results from the study are presented in terms of intrinsic mode functions (IMFs) and the trends. The analysis reveals that in summer, there is a tendency to have an increase in the amount of rainfall, whereas in winter, from 1998 to 2004 there has been an initial increase of 0.0022 mm/hr/year and from there onwards till 2013 a decrease of 0.00052 mm/hr/year was noted.  

Abstract Surface Electroencephalography (EEG) is a non-invasive technique used for monitoring and recording the electrical activity of the human brain. Typically, the raw and unprocessed EEG signals are contaminated with various types of physiological artifacts originated from eye blinks and limb moments due to long haul monitoring. The removal of such low frequency motion artifacts in preprocessing techniques could potentially improves the accuracy of diagnosis. In this viewpoint, a multi-resolution analysis such as discrete wavelet transform (DWT) with empirical mode decomposition (EMD) is presented to filter the motion artifacts from the EEG signal. Initially, the low frequency components were separated from EEG signal using DWT decomposition technique and the same are passed to EMD to find intrinsic mode functions (IMFs). Using iterative thresholding algorithm the noisy IMF’s are filtered out, and these denoised approximated components are utilized to reconstruct the motion artifact free EEG signal. The proposed technique shows 15.3218 dB of △SNR, 41.9859% of Relative root mean square error (RRMSE) and the percentage reduction in correlation coefficient (%η) of 65.8213 by using Physionet data base.