High Frequency Intrinsic Mode Functions Research Articles

A New Hybrid Short Term Solar Irradiation Forecasting Method Based on CEEMDAN Decomposition Approach and BiLSTM Deep Learning Network with Grid Search Algorithm

An accurate and efficient forecasting of solar energy is necessary for managing the electricity generation and distribution in today’s electricity supply system. However, due to its random character in its time series, accurate forecasting of solar irradiation is a difficult task; but it is important for grid management, scheduling and its balancing. To fully utilize the solar energy in order to balance the generation and consumption, this paper proposed an ensemble approach using CEEMDAN-BiLSTM combination to forecast short term solar irradiation. In this, Complete Ensemble Empirical Mode Decomposition with adaptive noise (CEEMDAN) extract the inherent characteristics of time series data by decomposing it into low and high frequency Intrinsic Mode Functions (IMF’s) and Bidirectional Long Short Term Memory (BiLSTM) used as a forecasting tool to forecast the solar Global Horizontal Irradiance (GHI). Furthermore, using extensive experimental analysis, the research minimizes the number of IMF’s by integrating the CEEMDAN decomposed component (IMF1–IMF14) in order to increase the prediction accuracy. Then, for each IMF subseries, the trained standalone BiLSTM network are assigned to carry out the forecasting. In last stage, the forecasted results of each BiLSTM network are aggregate to compile final results. Two year data (2012–13) of Delhi, India from National Solar Radiation Database (NSRDB) has been used for training while one year data (2014) used for testing purpose for the same location. The proposed model performance is measured in terms of root mean square error (RMSE), mean absolute percentage error (MAPE), Correlation coefficient (R22) and forecast skill (FS). For the comparative analysis of proposed model, several others models: persistence model, unidirectional deep learning models: long short term memory (LSTM), gated recurrent unit (GRU), BiLSTM and two CEEMDAN based BiLSTM models are developed. The proposed model achieved lowest annual average RMSE (18.86 W/m22, 22.24 W/m22, 26.25 W/m22) and MAPE (2.19%, 4.81%, 6.77%) among the other developed models for 1-hr, 2-hr and 3-hr ahead solar GHI forecasting respectively. The maximum correlation coefficient (R22) obtained by the proposed model is 96.4 for 1-hr ahead respectively; on the other hand, forecast skill (%) of 89% with reference to benchmark model. Various test such as: Diebold Mariano Hypothesis test (DMH) and directional change in forecasting (DC) are used to analyze the sensitivity with reference to the difference in forecasted and observed value.

Nonlinear frequency analysis of COVID-19 spread in Tokyo using empirical mode decomposition

Empirical mode decomposition (EMD) was adopted to decompose daily COVID-19 infections in Tokyo from February 28, 2020, to July 12, 2021. Daily COVID-19 infections were nonlinearly decomposed into several monochromatic waves, intrinsic mode functions (IMFs), corresponding to their periodic meanings from high frequency to low frequency. High-frequency IMFs represent variabilities of random factors and variations in the number of daily PCR and antigen inspections, which can be nonlinearly denoised using EMD. Compared with a moving average and Fourier transform, EMD provides better performance in denoising and analyzing COVID-19 spread. After variabilities of daily inspections were weekly denoised by EMD, one low-frequency IMF reveals that the average period of external influences (public health and social measures) to stop COVID-19 spread was 19 days, corresponding to the measures response duration based on the incubation period. By monitoring this nonlinear wave, public health and social measures for stopping COVID-19 spread can be evaluated and visualized quantitatively in the instantaneous frequency domain. Moreover, another low-frequency IMF revealed that the period of the COVID-19 outbreak and retreat was 57 days on average. This nonlinear wave can be used as a reference for setting the timeframe for state of emergency declarations. Thus, decomposing daily infections in the instantaneous frequency domain using EMD represents a useful tool to improve public health and social measures for stopping COVID-19 spread.

Carbon price combination prediction model based on improved variational mode decomposition

Carbon price is one of the core factors in the carbon trading process, so it is of great significance to establish a carbon price prediction model for guiding the carbon trading market to make scientific and reasonable decision. In order to improve the accuracy of carbon price prediction, a carbon price combination prediction model with variational mode decomposition based on seagull optimization algorithm (SVMD), fluctuation-based dispersion entropy (FDE), extreme learning machine (ELM) and kernel extreme learning machine (KELM) optimized by JAYA algorithm (JAYA-KELM), named SVMD-FDE-ELM-JAYA-KELM, is proposed. To solve the selection of mode number K and the penalty factor α of VMD, SVMD is proposed, which realizes adaptive determination of the parameter K and α. The idea of the SVMD-FDE-ELM-JAYA-KELM is roughly as follows. Firstly, SVMD decomposes carbon price into a series of intrinsic mode functions (IMFs). According to the FDE value, these IMFs are divided into high frequency IMFs or low frequency IMFs. Secondly, JAYA-KELM is established for high frequency IMFs and ELM is established for low frequency IMFs. Finally, the predicted value of carbon price is reconstructed to complete the prediction. The experimental results show that the proposed model has best prediction accuracy, and provides a new method for carbon price prediction.

Time‐dependent intrinsic correlation analysis of crude oil and the US dollar based on CEEMDAN

AbstractIn this article, we analyze the dynamic linkage between crude oil price and the US dollar at multi‐scale frequencies using time‐dependent intrinsic correlation analysis based on the complete ensemble empirical mode decomposition with adaptive noise. After applying a refined method to extract the trend, we reveal that the overall correlation and the long‐term trend correlation exhibit very similar patterns. The correlation coefficients between crude oil and the US dollar are negative at most of the time; however, the coefficients become positive in certain periods, such as 2013–2014 and 2017–2018. Furthermore, the negative correlations in high frequency intrinsic mode functions (IMFs), with a shorter time horizon, are weaker and display time‐varying characteristics, whereas the correlation in low frequency IMFs, with a longer time horizon, are stronger and more static. The findings of this article may have important implications for investors to construct optimal portfolio diversification.

Revealing stroke survivor gait deficits during rehabilitation using ensemble empirical mode decomposition of surface electromyography signals

In this paper, an attempt is made to explain the stroke survivor gait recovery mechanism using Ensemble Empirical Mode Decomposition (EEMD) of surface electromyography signals (sEMG). The existing gait functionality indices could describe the gait recovery through the improvement of gait parameters such as stride length, heel clearance, stance and swing time etc. However these indices reveal little information related to the kinesiology status. To address this knowledge gap, we propose an approach to decompose the sEMG signals acquired during the rehabilitation treatment using EEMD so as to reveal gait deficits in the perspective of motor unit recruitment and its firing patterns. 15 stroke survivors were recruited and their sEMG signals acquired from Gastrocnemius Lateral (GL) and Tibialis Anterior (TA) muscles were further decomposed into different intrinsic mode functions (IMF) using EEMD. Each IMF contains superimposed motor unit action potential (MUAP) with its specific frequency range. The evolvement of IMFs over three recovery stages was observed. Results show that foot drop can be caused by lack of high frequency IMF components in TA during the swing phase. Besides that, spasticity was observed in all IMF components from GL muscle that leads to counteract with TA muscle. Lack of high frequency IMF components in GL during the stance phase would increase the stance time. Co-activation from TA during the stance phase could contribute to this effect as well. In conclusion, the proposed approach could reveal additional information at kinesiology level to explain how well a stroke survivor recovers.

A Novel Decomposition-Ensemble Based Carbon Price Forecasting Model Integrated with Local Polynomial Prediction

Abstract This study proposes a decomposition-ensemble based carbon price forecasting model, which integrates ensemble empirical mode decomposition (EEMD) with local polynomial prediction (LPP). The EEMD method is used to decompose carbon price time series into several components, including some intrinsic mode functions (IMFs) and one residue. Motivated by the fully local characteristics of a time series decomposed by EEMD, we adopt the traditional LPP and regularized LPP (RLPP) to forecast each component. This led to two forecasting models, called the EEMD-LPP and EEMD-RLPP, respectively. Based on the fine-to-coarse reconstruction principle, an auto regressive integrated moving average (ARIMA) approach is used to forecast the high frequency IMFs, and LPP and RLPP is applied to forecast the low frequency IMFs and the residue. The study also proposes two other forecasting models, called the EEMD-ARIMA-LPP and EEMD-ARIMA-RLPP. The empirical study results showed that the EEMD-LPP and EEMD-ARIMA-LPP outperform the two other models. Furthermore, we examine the robustness and effects of parameter settings in the proposed model. Compared with existing state-of-art approaches, the results demonstrate that EEMD-ARIMA-LPP and EEMD-LPP can achieve higher level and directional predictions and higher robustness. The EEMD-LPP and EEMD-ARIMA-LPP are promising approaches for carbon price forecasting.

Multi-step wind speed forecasting based on a hybrid decomposition technique and an improved back-propagation neural network

Abstract Precise and reliable wind-speed prediction is vital for wind-farm operational planning. However, wind speed series usually have complex features, such as non-linearity and volatility, which makes the wind energy forecasting highly difficult. Aimed at this challenge, this paper proposes a forecasting architecture based on a new hybrid decomposition technique (HDT) and an improved flower-pollination algorithm (FPA)-back propagation (BP) neural network prediction algorithm. The proposed HDT combines the complete ensemble empirical mode decomposition adaptive noise (CEEMDAN) and the empirical wavelet transform (EWT), which is unique, since the EWT is specifically employed to further decompose the high frequency intrinsic mode functions (IMFs) generated by CEEMDAN to reduce prediction complexity. And then an improved BPNN with the flower-pollination algorithm is applied to forecast all of the decomposed IMFs and modes. To investigate the forecasting ability of the proposed model, the wind speed data collected from two different wind farms in Shandong, China were used for multi-step ahead forecasting. The experimental results show that the proposed model performs remarkably better than all of the other considered models in one-step to five-step wind speed forecasting, which indicates that the proposed model is highly suitable for non-stationary multi-step wind speed forecasting.

A novel multiscale nonlinear ensemble leaning paradigm for carbon price forecasting

In this study, a novel multiscale nonlinear ensemble leaning paradigm incorporating empirical mode decomposition (EMD) and least square support vector machine (LSSVM) with kernel function prototype is proposed for carbon price forecasting. The EMD algorithm is used to decompose the carbon price into simple intrinsic mode functions (IMFs) and one residue, which are identified as the components of high frequency, low frequency and trend by using the Lempel-Ziv complexity algorithm. The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is used to forecast the high frequency IMFs with ARCH effects. The LSSVM model with kernel function prototype is employed to forecast the high frequency IMFs without ARCH effects, the low frequency and trend components. The forecasting values of all the components are aggregated into the ones of original carbon price by the LSSVM with kernel function prototype-based nonlinear ensemble approach. Furthermore, particle swarm optimization is used for model selections of the LSSVM with kernel function prototype. Taking the popular prediction methods as benchmarks, the empirical analysis demonstrates that the proposed model can achieve higher level and directional predictions and higher robustness. The findings show that the proposed model seems an advanced approach for predicting the high nonstationary, nonlinear and irregular carbon price.

ECG Signal De-noising and Baseline Wander Correction Based on CEEMDAN and Wavelet Threshold.

A novel electrocardiogram (ECG) signal de-noising and baseline wander correction method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and wavelet threshold is proposed. Although CEEMDAN is based on empirical mode decomposition (EMD), it represents a significant improvement of the original EMD by overcoming the mode-mixing problem. However, there has been no previous study on using CEEMDAN to de-noise ECG signals, to the authors’ best knowledge. In the proposed method, the original noisy ECG signal is decomposed into a series of intrinsic mode functions (IMFs) sorted from high to low frequency by CEEMDAN. Each IMF is then analyzed by the autocorrelation method to find out the first few high frequency IMFs containing random noise, and these IMFs should be de-noised by the wavelet threshold. The zero-crossing rate (ZCR) of all IMFs, including final residue, are computed, and the IMFs with ZCR less than a certain value are removed. Finally, the remaining IMFs are reconstructed to obtain the clean ECG signal. The proposed algorithm is validated through experiments using the MIT–BIH ECG databases, and the results show that the random noise in the ECG signal can be effectively suppressed, and at the same time the baseline wander can be corrected efficiently.

Multi-step ahead electricity price forecasting using a hybrid model based on two-layer decomposition technique and BP neural network optimized by firefly algorithm

In the deregulated competitive electricity market, the price which reflects the relationship between electricity supply and demand is one of the most important elements, making it crucial for all market participants to precisely forecast the electricity price. However, electricity price series usually has complex features such as non-linearity, non-stationarity and volatility, which makes the price forecasting turn out to be very difficult. In order to improve the accuracy of electricity price forecasting, this paper first proposes a two-layer decomposition technique and then develops a hybrid model based on fast ensemble empirical mode decomposition (FEEMD), variational mode decomposition (VMD) and back propagation (BP) neural network optimized by firefly algorithm (FA). The proposed model is unique in the sense that VMD is specifically applied to further decompose the high frequency intrinsic mode functions (IMFs) generated by FEEMD into a number of modes in order to improve the forecast accuracy. To validate the effectiveness and accuracy of the proposed model, three electricity price series respectively collected from the real-world electricity markets of Australia and France are adopted to conduct the empirical study. The results indicate that the proposed model outperforms the other considered models over horizons of one-step, two-step, four-step and six-step ahead forecasting, which shows that the proposed model has superior performances for both one-step and multi-step ahead forecasting of electricity price.

A novel hybrid model for air quality index forecasting based on two-phase decomposition technique and modified extreme learning machine.

The randomness, non-stationarity and irregularity of air quality index (AQI) series bring the difficulty of AQI forecasting. To enhance forecast accuracy, a novel hybrid forecasting model combining two-phase decomposition technique and extreme learning machine (ELM) optimized by differential evolution (DE) algorithm is developed for AQI forecasting in this paper. In phase I, the complementary ensemble empirical mode decomposition (CEEMD) is utilized to decompose the AQI series into a set of intrinsic mode functions (IMFs) with different frequencies; in phase II, in order to further handle the high frequency IMFs which will increase the forecast difficulty, variational mode decomposition (VMD) is employed to decompose the high frequency IMFs into a number of variational modes (VMs). Then, the ELM model optimized by DE algorithm is applied to forecast all the IMFs and VMs. Finally, the forecast value of each high frequency IMF is obtained through adding up the forecast results of all corresponding VMs, and the forecast series of AQI is obtained by aggregating the forecast results of all IMFs. To verify and validate the proposed model, two daily AQI series from July 1, 2014 to June 30, 2016 collected from Beijing and Shanghai located in China are taken as the test cases to conduct the empirical study. The experimental results show that the proposed hybrid model based on two-phase decomposition technique is remarkably superior to all other considered models for its higher forecast accuracy.

High and low frequency unfolded partial least squares regression based on empirical mode decomposition for quantitative analysis of fuel oil samples

Accurate prediction of the model is fundamental to the successful analysis of complex samples. To utilize abundant information embedded over frequency and time domains, a novel regression model is presented for quantitative analysis of hydrocarbon contents in the fuel oil samples. The proposed method named as high and low frequency unfolded PLSR (HLUPLSR), which integrates empirical mode decomposition (EMD) and unfolded strategy with partial least squares regression (PLSR). In the proposed method, the original signals are firstly decomposed into a finite number of intrinsic mode functions (IMFs) and a residue by EMD. Secondly, the former high frequency IMFs are summed as a high frequency matrix and the latter IMFs and residue are summed as a low frequency matrix. Finally, the two matrices are unfolded to an extended matrix in variable dimension, and then the PLSR model is built between the extended matrix and the target values. Coupled with Ultraviolet (UV) spectroscopy, HLUPLSR has been applied to determine hydrocarbon contents of light gas oil and diesel fuels samples. Comparing with single PLSR and other signal processing techniques, the proposed method shows superiority in prediction ability and better model interpretation. Therefore, HLUPLSR method provides a promising tool for quantitative analysis of complex samples.

Random Noise Reduction Based on Ensemble Empirical Mode Decomposition and Wavelet Threshold Filtering

This paper presents a random noise reduction method based on ensemble empirical mode decomposition (EEMD) and wavelet threshold filtering. Firstly, we have conducted spectrum analysis and analyzed the frequency band range of effective signals and noise. Secondly, we make use of EEMD method on seismic signals to obtain intrinsic mode functions (IMFs) of each trace. Then, wavelet threshold noise reduction method is used on the high frequency IMFs of each trace to obtain new high frequency IMFs. Finally, reconstruct the desired signal by adding the new high frequency IMFs on the low frequency IMFs and the trend item together. When applying our method on synthetic seismic record and field data we can get good results.