Decomposition Technique Research Articles

Research on information leakage in time series prediction based on empirical mode decomposition.

Time series analysis predicts the future based on existing historical data and has a wide range of applications in finance, economics, meteorology, biology, engineering, and other fields. Although the combination of decomposition techniques and machine learning algorithms can effectively solve the problem of predicting nonstationary sequences, this kind of decomposition-integration-prediction strategy of the prediction method has serious defects. After the decomposition of the division of the training set and the test set, the information of the test set in the process of decomposition of the information leakage ultimately shows a high accuracy of the prediction of the illusionary. This paper proposes three improvement strategies for this type of "information leakage" problem: sliding window decomposition (SW-EMD), single training and multiple decomposition (STMP-EMD), and multiple training and multiple decomposition (MTMP-EMD). They are combined with a bidirectional multiscale temporal convolutional network (MSBTCN), bidirectional long- and short-term memory network (BiLSTM), and attention mechanism (DMAttention), which introduces a dependency matrix based on cosine similarity to be applied to water quality prediction. The experimental results show that the model achieves good performance in the prediction of three water quality indicators (pH, DO and KMnO4), and the accuracies of the three models proposed in this paper are improved by 1.958% and 0.853% in terms of the RMSE and MAPE, respectively, compared with those of the mainstream LSTM models. The key contributions of this study include the following: (1) three methods are proposed to improve the class EMD decomposition, which can effectively solve the problem of "information leakage" that exists in the current models via class EMD decomposition; (2) the CEEMDAN-MSBTCN-BiLSTM-DMAttention model structure is innovated by combining improved class EMD decomposition methods; and (3) the three improved decomposition methods proposed in this paper can effectively solve the problem of "information leakage" and optimize the prediction model at the same time. This study provides an effective experimental method for water quality prediction and can effectively address the problem of "overfitting" models via class EMD decompositions during model training and testing.

Finite-field Cholesky decomposed coupled-cluster techniques (ff-CD-CC): theory and application to pressure broadening of Mg by a He atmosphere and a strong magnetic field.

For the interpretation of spectra of magnetic stellar objects such as magnetic white dwarfs (WDs), highly accurate quantum chemical predictions for atoms and molecules in finite magnetic field are required. Especially the accurate description of electronically excited states and their properties requires established methods such as those from coupled-cluster (CC) theory. However, respective calculations are computationally challenging even for medium-sized systems. Cholesky decomposition (CD) techniques may be used to alleviate memory bottlenecks. In finite magnetic field computations, the latter are increased due to the reduction of permutational symmetry within the electron-repulsion-integrals (ERIs) as well as the need for complex-valued data types. CD enables a memory-efficient, approximate description of the ERIs with rigorous error control and thus the treatment of larger systems at the CC level becomes feasible. In order to treat molecules in a finite magnetic field, we present in this work the working equations of the left and right-hand side equations for finite field (ff)-EOM-CD-CCSD for various EOM flavours as well as for the approximate ff-EOM-CD-CC2 method. The methods are applied to the study of the modification of the spectral lines of a magnesium transition by a helium atmosphere that can be found on magnetic WD stars.

Development of Four Component Scattering Power Decomposition Technique for Dual Polarization SAR Data

AbstractThe increasing availability of dual-polarimetric synthetic aperture radar (PolSAR) data has led to a significant rise in its applications over the past few decades. Model-based decompositions combined with polarimetric information extraction from PolSAR data play a crucial role in target identification and classification. In this context, the covariance matrix [C], composed of four independent parameters, was used as the input for dual-pol four-component scattering power decomposition (DP-4SD). A novel 4SD model was tested using dual polarimetric SAR data from the spaceborne ALOS-2/PALSAR-2, and its performance was evaluated against existing scattering power decomposition methods. The performance of the proposed 4SD model was assessed using dual-polarization data from the Haldwani Forest and San Francisco to evaluate its classification capabilities within a single class (forest) and across various land use and land cover classes in San Francisco. The overall classification accuracy achieved was 85.69% for the Haldwani forest and 93.66% for San Francisco, with fewer unclassified samples compared with the existing model. The 4SD model demonstrates superior classification accuracy and enhances the interpretation of polarimetric information, indicating its potential to significantly improve land-use and land-cover mapping using dual PolSAR data.

Advancing Non-Linear PDE’s Solutions: Modified Yang Transform Method with Caputo-Fabrizio Fractional Operator

Abstract In many physical processes, nonlinear PDEs have a crucial role. This paper presents a novel approach named as Modified Yang Transform (MYT) that combines an integral transform with the decomposition technique. This approach uses Yang transform and Adomian decomposition method to solve nonlinear fractional order PDEs. Nonlinear PDEs of fractional order are considered in the Caputo-Fabrizio sense. This work presents Convergence analysis of the modified Yang transform to nonlinear fractional order PDEs. Additionally, a solution framework to solve the nonlinear PDEs is carried out and some examples are provided to highlight the application of the current method.
To illustrate how the solution operates for various fractional orders, 2D and 3D graphs are plotted. After each example, the results and discussion section is included to explain the graphs and their results.

Advanced reference crop evapotranspiration prediction: a novel framework combining neural nets, bee optimization algorithm, and mode decomposition

AbstractVarious critical applications, spanning from watershed management to agricultural planning and ecological sustainability, hinge upon the accurate prediction of reference evapotranspiration (ETo). In this context, our study aimed to enhance the accuracy of ETo prediction models by combining a variety of signal decomposition techniques with an Artificial Bee Colony (ABC)–artificial neural network (ANN) (codename: ABC–ANN). To this end, historical (1979–2014) daily climate variables, including maximum temperature, minimum temperature, mean temperature, wind speed, relative humidity, solar radiation, and precipitation from four arid and semi-arid regions in Egypt: Al-Qalyubiyah, Cairo, Damietta, and Port Said, were used. Six techniques, namely, Empirical Mode Decomposition, Variational Mode Decomposition, Ensemble Empirical Mode Decomposition, Local Mean Decomposition, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, and Empirical Wavelet Transform were used to evaluate signal decomposition efficiency in ETo prediction. Our results showed that the highest ETo prediction accuracy was obtained with ABC-ANN (Train R2: 0.990 and Test R2: 0.989), (Train R2: 0.986 and Test R2: 0.986), (Train R2: 0.991 and Test R2: 0.989) and (Train R2: 0.988 and Test R2: 0.987) for Al-Qalyubiyah, Cairo, Damietta, and Port Said, respectively. The impressive results of our hybrid model attest to its importance as a powerful tool for tackling the problems associated with ETo prediction.

An Ultra‐Short‐Term Multi‐Step Prediction Model for Wind Power Based on Sparrow Search Algorithm, Variational Mode Decomposition, Gated Recurrent Unit, and Support Vector Regression

ABSTRACTAccurate ultra‐short‐term wind power prediction techniques are crucial for ensuring the efficient and safe operation of wind farms and power systems. Combined models based on data decomposition‐prediction techniques have shown excellent performance in ultra‐short‐term wind power forecasting. This study introduces a novel ultra‐short‐term multi‐step prediction model for wind power, which integrates the sparrow search algorithm (SSA), variational mode decomposition (VMD), gated recurrent unit (GRU), and support vector regression (SVR). An optimization variational mode decomposition technique is developed by adaptively determining VMD hyperparameters using SSA. The optimization VMD decomposes the original wind power sequence into sub‐modes, and the resulting sequence of decomposed sub‐modes calculates permutation entropy (PE) values. Sub‐modes with similar PE values are combined, reorganized, and categorized into high‐frequency and low‐frequency. High‐frequency sub‐modes data with high complexity and non‐stationarity are predicted by the GRU neural network. Low‐frequency sub‐modes data with low complexity and strong nonlinearity are predicted with SVR. The proposed model was evaluated against seven others using three error metrics: MAE, RMSE, and R2, along with their corresponding enhancement percentages. Experimental results indicate that the proposed model extracts detailed and trend information from the wind power series more effectively and stably than the comparison models. It also demonstrates superior multi‐step prediction performance, offering significant value for practical engineering applications.

Slow motion in corona times: Modeling cyclists’ spatial choice behavior using real-time probe data

The recent COVID-19 pandemic has provided a renewed impetus for empirical research on slow and active modes of transportation, specifically bicycling and walking. Changes in modal choice appear to be sensitive to the actual quality of the environment, the attractive land use and built environment conditions, and the ultimate destination choice. This study examines and models the influence of cyclists’ health concerns during the pandemic on their spatial destination and route choices. Using a large real-time dataset on the individual daily mobility of cyclists in the province of Utrecht, the Netherlands, collected through GPS-linked sensors on bikes (VGI, or volunteered geographical information), the analysis employs spatial regression models, Shapley decomposition techniques, and spatial autocorrelation methods to unveil the backgrounds of changes in spatial behavior. The results reveal that the perceived wellbeing benefits of bicycling in green areas during the pandemic have significantly influenced cyclists’ choice behavior, in particular route and destination choice.

Galvanic distortion decomposition of magnetotelluric impedance tensors in 1-D electrical anisotropic media

SUMMARY The electromagnetic (EM) local distortion of the transfer function due to shallow small-scale inhomogeneities hinders the accurate interpretation of magnetotelluric (MT) data. Under the assumption that regional subsurface structures are electrically isotropic, decomposition techniques of the MT impedance tensor that focus on the galvanic distortion of the electric field have been well developed. In this paper, we present a decomposition method of MT impedance tensors over a regional 1-D conductivity anisotropic Earth, in which the galvanic distortion of both the electric and the associated magnetic fields are taken into account. An eigenparameter analysis is introduced to evaluate the intrinsic indeterminacy of magnetic distortion parameters. Regional anisotropic responses and EM distortion parameters are resolved by using a modified BFGS (Broyden–Fletcher–Goldfarb–Shanno) quasi-Newton algorithm combined with phase tensor analysis and the trust region method. In the presence of near-surface anisotropic inhomogeneities, synthetic 2-D data show an accentuated magnetic galvanic effect in the response tensors especially in the diagonal components probably due to the infinite extension in the strike direction. However, the magnetic galvanic distortion is not significant in synthetic 3-D models. The decomposition scheme is also applied to the analysis of the BC87 data set collected in southeastern British Columbia to investigate both the electric and magnetic field galvanic distortion.

Disentangling the gender-differentiated determinants of home-based self-employment choices in Nigeria

Abstract Understanding gender disparities in home-based self-employment (HBS) and their links to homeownership and socioeconomic factors is crucial for advancing sustainable development goals (SDGs) in Sub-Saharan Africa, especially Nigeria. This study uses data from the 2010/2011, 2012/13, 2015/16, and 2018/19 waves of the Nigerian General Household Survey (GHS). It employs random effect probit regression, the LASSO method for identifying predictors, and the Blinder–Oaxaca decomposition technique to analyse gender differences in nonlinear binary outcomes. The results show that female business owners are more likely to engage in HBS compared to males, highlighting the importance of gender equality (SDG 5) and decent work (SDG 8). While male entrepreneurs are mainly driven by profit, females prioritise balancing paid and unpaid work, reflecting motivations beyond profit within heterodox economics. Significant gender-differentiated impacts are observed in relation to monthly rent, post-secondary education, dwelling space, energy, and regional locations. Notably, the presence of children significantly increases female involvement in HBS, a trend not seen among males. Marriage also influences female participation, suggesting that marital circumstances and economic benefits play a role. These findings highlight the need for policies addressing gender-specific constraints, challenging traditional gender roles, and promoting inclusive human development within the SDG framework.

AI-Powered Decomposition Techniques for Economic Forecasting

AI-Powered Decomposition Techniques for Economic Forecasting

Study on the accurate detection method of full‐polarimetric ground‐penetrating radar faults in mines based on modified Yamaguchi decomposition

AbstractObtaining information on tectonic tendencies is a prerequisite for intelligent and accurate mining in mines. In the special mine environment, the co‐polarized ground‐penetrating radar can only identify the spatial location of faults, and it is difficult to analyse the inclination information of fault structures. This paper proposes a mine full‐polarimetric ground‐penetrating radar fault tendency detection method based on this. First, based on the stacking characteristics of the coal depositional, this paper analyses the propagation law of the pulse electromagnetic wave in the coal seam and puts forward the assumption of the overlapping echo reflection of the fault structure. The reasonableness of the fault reflection assumption is verified through a numerical simulation study. Second, based on the cutting relationship of the fault to the coal seam, we divided the reflection structure of the fault structure into plane scattering and dihedral angle scattering. We realized the mingled echoes’ decomposition using the improved Yamaguchi decomposition technique. To analyse the applicability of the modified Yamaguchi and Freeman decomposition methods in the identification of fault inclination, we use the upright fault simulation data for the discussion, and we find that the improved Yamaguchi decomposition method is more advantageous in the identification of fault inclination in the mine. The decomposition results based on the simulation data of fault models with different dip angles found that when the dip angle of the fault is less than 90°, the scattering of the fault structure is dominated by planar scattering and dihedral angle scattering; when the dip angle of the fault is greater than or equal to 90°, the scattering of the fault structure is dominated by planar scattering, and the scattering power of the dihedral angle model is zero. By analysing the effect of fault strike on the decomposition results, it is found that the fault strike angle has little effect on the identification of fault tendency. Finally, the application potential of this paper's method is tested by constructing complex numerical models and probing experiments. Therefore, the method proposed in this paper can solve the fault tendency identification under a thick coal seam.

A hybrid wind power prediction model based on seasonal feature decomposition and enhanced feature extraction

Efficient and accurate wind power prediction is crucial for enhancing the reliability and safety of power system. The data-driven forecasting methods are regarded as an effective solution. However, the inherent randomness and nonlinearity of wind power systems, along with the abundance of redundant information in measurement data, present challenges to forecasting methods. The integration of precise and efficient techniques for data feature decomposition and extraction is essential in conjunction with advanced data-driven forecasting models. Focus on the seasonal variation characteristics of wind energy, a hybrid wind power prediction model based on seasonal feature decomposition and enhanced feature extraction is proposed. The effectiveness and superiority of the proposed method in predictive accuracy are demonstrated through comprehensive multi-model experiment comparisons.

A framework to Prediction occupant injuries in rotated seating arrangements

This paper describes an innovative computational framework that can address the passive safety of occupants and the prediction of injuries for a wide range of rotated seat arrangements in future autonomous vehicles. An Active Human Model (AHM) wearing a 3-point seat belt with kinematics previously validated using test data was positioned in the rotated seats and simulations were performed for a pre-crash braking phase followed by a frontal collision. The pre-crash braking pulse was parameterised for intensity and shape, both of which affect the collision speed. Computer routines were created to adjust the restraint system response to the impact speed, as well as the crash pulse pattern, based on a Honda Accord MY2011 Finite Element (FE) model. A Design of Experiments (DoE) study was created to explore 400 possible scenarios, and 12 standard injury responses were extracted and converted into AIS2 + and AIS3 + risk values. A Reduced Order Model (ROM), based on the Proper Orthogonal Decomposition (POD) technique, was trained using the 400 scenarios and used to find the seating positions that resulted in AIS2 + and AIS3 + values higher than the base values obtained with the Honda Accord MY2011 FE model. The paper concludes that this new framework is capable of carry out fast computations of dangerous seating positions and the occupant’s kinematics in seconds. The novel framework provides vehicle designers and vehicle safety teams with the capability to identify potentially dangerous positions for the rotated seating arrangements that are envisaged to feature in the cabins of future autonomous vehicles.

Experimental decomposition of nonlinear hydrodynamic loads and hydroelastic responses in wave–structure interactions of monopile wind turbines

This study explores the nonlinear effects of hydrodynamic loads and hydroelastic responses in monopile-supported offshore wind turbines, with a focus on their harmonic structures. High-quality experimental data were collected in a shallow water basin across various irregular waves. Their harmonic components up to the fourth order were successfully isolated using a novel four-phase decomposition technique, which effectively extracts harmonics from random time series. The results highlight significant contributions of higher-order harmonics across various sea states. Specifically, two physical models were employed: a flexible monopile to capture structural hydroelastic deformations during large wave events and a rigid monopile to accurately estimate hydrodynamic loads without hydroelastic effects. Additionally, numerical results from fully nonlinear potential-flow calculations were compared, revealing that while the potential-flow solver underestimates total wave loading, especially for higher harmonics. In terms of the free-surface elevations and hydrodynamic forces, this study confirms that their higher-order harmonics align well with the scaling of their corresponding linear components in both amplitude and phase. This enables the prediction of higher-order profiles based solely on their linear components. However, this efficient model is inadequate for accurately estimating the higher-order harmonics of monopile's hydroelastic responses during these extreme wave events, highlighting the need for further refinement.

Direct hydroacoustics analyses of pipe orifice using lattice Boltzmann method

Acoustic waves in water pipes pose a structural threat but also offer a valuable tool for non-invasive inspection. Complex pipe geometries such as bends and surface liners create complex fluid boundaries, triggering interactions between fluid flow and acoustics. The lattice Boltzmann method (LBM) excels at capturing these interactions near complex boundaries, in contrast to the finite volume method, which can result in errors. However, the application of LBM in water pipes has been limited by stability problems. This study proposes a two-step (DM-TS) collision operator based on a direct method (LBM-HA) for stable LBM simulations in water pipes. LBM-HA enables direct hydroacoustic predictions for both acoustic and dynamic flow fields in a pipe orifice. A novel acoustic-dynamic complex boundary condition was formulated from the linearized Euler's equation to account for the physical effects of the bounded domain of the LBM-HA analysis. To distinguish between dynamic and acoustic components, wavenumber and frequency decomposition techniques were applied to the pressure data obtained within the pipe. In addition, mode decomposition of the acoustic pressure was conducted to identify the dominant acoustic modes. By comparing the LBM-HA results with experimental data, we highlighted the method's potential for direct hydroacoustic analysis considering the acoustic characteristics of the water pipe.

H∞ adaptive ETF control for degenerate jump systems under actuator faults and impulsive deception attacks with application to DCMIP device

This article considers the issue of H∞ adaptive event-triggered feedback control for degenerate jump systems under actuator faults and impulsive deception attacks. Based on periodic sampling strategy, a mode-dependent adaptive event-triggered scheme is developed, which can save communication resources, avoid the Zeno phenomenon and take full advantage of Markovian mode information. By constructing the neoteric Lyapunov-Krasovskii (L-K) functional containing piecewise linear impulsive auxiliary functions and applying singular value decomposition (SVD) technique, the fresh stochastic admissibility conditions for degenerate Markovian jump systems under actuator faults and impulsive deception attacks are obtained under the framework of linear matrix inequalities (LMIs), and then the adaptive event-triggered scheme with weighted matrices and feedback controller are designed simultaneously. By applying freedom weight matrix method and the property that the network-induced delay derivative is one, the non-strict LMI conditions are transformed into strict ones, such that the stochastic admissibility of the degenerate jump systems and state feedback controller gains are realized adequately. Finally, a direct current motor-controlled inverted pendulum (DCMIP) device is used to confirm the feasibility of the presented approach.

A Gray Scale Image Compression Using Hierarchical DWT Decomposition and Mixing Quantization Techniques

This paper describes a hybrid grayscale compression system based on the discrete wavelet transform (DWT) and a polynomial coding technique for mixing quantization schemes to increase the compression ratio while maintaining quality. The proposed compression system consists of three main steps: first, decomposing an image using a three-level DWT; second, applying the 2-D linear polynomial coding technique to the approximation sub-band; and third, dividing the detailed sub-bands of each level into the Most Significant Value (MSV) and Least Significant Value (LSV), where the former is compressed using iterative scalar uniform quantization and the latter by soft quantization thresholding. For testing the performance of the suggested compression system, five standard images of size 256×256 pixels were adopted. The suggested technique showed superior performance in terms of reconstructed (decoded) image quality and compression ratio (gain), where the compression ratio is between 21–27 with a PSNR value between 36–38 dB and the compression ratio of JPEG is between 7–20 with a PSNR value between 33–37 dB.

Forecasting of Solar Irradiation Based on the Deep Learning Model Using Complete Ensemble Empirical Mode Decomposition Technique

Since solar energy plants have been developing so quickly in recent years, accurate solar power forecasting plays a significant role in contemporary intelligent grid systems and setup a bilateral contract negotiation between suppliers and customers. This paper introduces a novel three-step method for predicting two-channel solar irradiance that combines cutting-edge techniques like Bidirectional Long Short-Term Memory, Wasserstein Generative adversarial Networks and Complete Ensemble Empirical Mode Decomposition with adaptive noise. This methodology that is being suggested involves a framework of decomposition integration which allows for the effective isolation of the solar output signal into sub-sequences that are simple and can be differentiated based on their unique frequency disparities. This is achieved after the subsequences have been separated, and then they are subjected to individual prediction models. The high subsequences are predicted using the WGAN model, while the low subsequences are forecasted using the Bi-LSTM model. This approach ensures the specific characteristics of each subsequence are captured in the prediction process. The experimental result shows that the proposed model surpasses the performance of the suboptimal model in terms of evaluation metrics: RMSE, MAPE and R2. Compared to the suboptimal model, the RMSE, MAPE of all seasons

Financial Time Series Forecasting Based on Long-Short Term Memory, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Batch Normalization

Long-short term memory (LSTM) is a state-of-art and widely used model to forecast financial time series. However, primitive LSTM networks do not perform well due to over-fitting problems of the deep learning model and nonlinear and non-stationary characteristics of financial time series data. In addition, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is an outstanding data frequency decomposition technique that can decompose original time series into several intrinsic mode functions and a residue. Thus, this paper proposed a novel hybrid network CEEMDAN-LSTM-BN based on LSTM. Specifically, to avoid over-fitting, the modified LSTM-BN network consists of two LSTM layers, two Batch Normalization (BN) layers following each LSTM layer, and a dropout layer. Each of the intrinsic mode functions and the residue would be processed by CEEMDAN-LSTM-BN and the final prediction results are obtained by reconstructing each predictive series. The advantages of the proposed CEEMDANLSTM-BN networks are verified by comparing them to primitive LSTM, other hybrid models, and some famous machine learning models. Moreover, the robustness of the networks is assessed by numerical experiments on different stock indices datasets.

Advanced Diagnosis of Air Gap Eccentricity in Three-Phase Induction Motor Using DWT Decomposition and AI Techniques

Advanced Diagnosis of Air Gap Eccentricity in Three-Phase Induction Motor Using DWT Decomposition and AI Techniques