Decomposition Method Research Articles

Balance Sparse Decomposition Method with Nonconvex Regularization for Gearbox Fault Diagnosis

As an important part of rotating machinery, gearboxes often fail due to their complex working conditions and harsh working environment. Therefore, it is very necessary to effectively extract the fault features of the gearboxes. Gearbox fault signals usually contain multiple characteristic components and are accompanied by strong noise interference. Traditional sparse modeling methods are based on synthesis models, and there are few studies on analysis and balance models. In this paper, a balance nonconvex regularized sparse decomposition method is proposed, which based on a balance model and an arctangent nonconvex penalty function. The sparse dictionary is constructed by using Tunable Q-Factor Wavelet Transform (TQWT) that satisfies the tight frame condition, which can achieve efficient and fast solution. It is optimized and solved by alternating direction method of multipliers (ADMM) algorithm, and the non-convex regularized sparse decomposition algorithm of synthetic and analytical models are given. Through simulation experiments, the determination methods of regularization parameters and balance parameters are given, and compared with the L1 norm regularization sparse decomposition method under the three models. Simulation analysis and engineering experimental signal analysis verify the effectiveness and superiority of the proposed method.

Simulation and Experimental Research of V-Crack Testing of Rail Surfaces Based on Laser Ultrasound

Rail surface cracks are widespread damage that can lead to uneven surfaces of railheads and affect traveling safety. Non-destructive testing is needed to inspect rails regularly to ensure the normal operation of railroads. This paper proposes a laser ultrasonic testing method combining variational mode decomposition and diffractive Rayleigh wave time-of-flight to detect tiny cracks on the rail surface quantitatively. The finite element method was combined with experiments to simulate and experimentally investigate cracks of different sizes numerically. In the numerical simulation, the location of the crack was determined by B-scan. Afterward, the interaction between various types of ultrasound and cracks was comparatively analyzed, and the crack size was quantitatively characterized using useful information from the ultrasound signals. The results show that the time-of-flight method can detect arbitrary cracks with low error. Therefore, the experimentally acquired ultrasound signals used the time difference between the diffracted Rayleigh wave and other ultrasound waves to detect the crack information quantitatively. The variational mode decomposition method was used to separate the ultrasonic signals and extract the best surface wave modes to improve the signal-to-noise ratio. The results show that the combination of variational mode decomposition and time-of-flight method can effectively detect the size of cracks.

Entropy analysis of Williamson fluid flow in a vertical porous channel with asymmetric cooling: Adomian decomposition method

AbstractThe paper presents the execution of the Adomian Decomposition Method to treat thermo‐fluidics of Williamson fluid flow in a vertical parallel plates channel filled with Williamson fluid–saturated porous medium. The channel walls experience asymmetric cooling. The fully developed flow setup constitutes a non‐linear boundary value problem tackled by the Adomain Decomposition Method (ADM) with the help of MAPLE. The computational procedure yields velocity, temperature distributions, skin friction, and Nusselt number. The results thus obtained are compared with those obtained by the RK‐Fehlberg numerical method to ascertain the accuracy of ADM. The results for quantities of interest viz. Skin friction. Nusselt number, entropy, and global entropy are shown in tabular/pictorial forms. These quantities exhibit qualitative and quantitative responses to embedded parameters discussed in detail in results and discussions section.

A displacement prediction model Based on IQGA-LSSVM for Mogu toppling rock slope in Lianghekou reservoir, China

Predicting landslide displacement is essential for developing early warning systems, assessing disaster risks, and understanding spatiotemporal evolution patterns. To address the limitations of insufficient accuracy in traditional landslide displacement prediction models, this study proposes a landslide displacement prediction model that combines an improved quantum genetic algorithm (IQGA) with a least squares support vector machine (LSSVM). The Mogu toppling rock slope is employed as a case study to demonstrate the application of the empirical mode decomposition (EMD) method for the decomposition of landslide displacement into trend and periodic components. Subsequently, these components are accurately predicted using Fourier series fitting and the IQGA-LSSVM model, respectively. The prediction results are subsequently evaluated and analyzed. The findings indicate that this model outperforms traditional QGA-LSSVM models, BP neural networks, and Support Vector Machine models in terms of prediction accuracy. Furthermore, the study illustrates how high-accuracy landslide displacement prediction models can effectively prevent and control disasters in critical areas such as hydraulic and hydropower engineering, urban planning, and geological disaster management.

Multi-Objective Combinatorial Optimization Algorithm Based on Asynchronous Advantage Actor–Critic and Graph Transformer Networks

Multi-objective combinatorial optimization problems (MOCOPs) are designed to identify solution sets that optimally balance multiple competing objectives. Addressing the challenges inherent in applying deep reinforcement learning (DRL) to solve MOCOPs, such as model non-convergence, lengthy training periods, and insufficient diversity of solutions, this study introduces a novel multi-objective combinatorial optimization algorithm based on DRL. The proposed algorithm employs a uniform weight decomposition method to simplify complex multi-objective scenarios into single-objective problems and uses asynchronous advantage actor–critic (A3C) instead of conventional REINFORCE methods for model training. This approach effectively reduces variance and prevents the entrapment in local optima. Furthermore, the algorithm incorporates an architecture based on graph transformer networks (GTNs), which extends to edge feature representations, thus accurately capturing the topological features of graph structures and the latent inter-node relationships. By integrating a weight vector layer at the encoding stage, the algorithm can flexibly manage issues involving arbitrary weights. Experimental evaluations on the bi-objective traveling salesman problem demonstrate that this algorithm significantly outperforms recent similar efforts in terms of training efficiency and solution diversity.

Pixel-Level Decision Fusion for Land Cover Classification Using PolSAR Data and Local Pattern Differences

Combining various viewpoints to produce coherent and cohesive results requires decision fusion. These methodologies are essential for synthesizing data from multiple sensors in remote sensing classification in order to make conclusive decisions. Using fully polarimetric Synthetic Aperture Radar (PolSAR) imagery, our study combines the benefits of both approaches for detection by extracting Pauli’s and Krogager’s decomposition components. The Local Pattern Differences (LPD) method was employed on every decomposition component for pixel-level texture feature extraction. These extracted features were utilized to train three independent classifiers. Ultimately, these findings were handled as independent decisions for each land cover type and were fused together using a decision fusion rule to produce complete and enhanced classification results. As part of our approach, after a thorough examination, the most appropriate classifiers and decision rules were exploited, as well as the mathematical foundations required for effective decision fusion. Incorporating qualitative and quantitative information into the decision fusion process ensures robust and reliable classification results. The innovation of our approach lies in the dual use of decomposition methods and the application of a simple but effective decision fusion strategy.

Theoretical and Numerical Studies of Fractional Volterra-Fredholm Integro-Differential Equations in Banach Space

This paper examines the theoretical, analytical, and approximate solutions of the Caputo fractional Volterra-Fredholm integro-differential equations (FVFIDEs). Utilizing Schaefer's fixed-point theorem, the Banach contraction theorem and the Arzel\`{a}-Ascoli theorem, we establish some conditions that guarantee the existence and uniqueness of the solution. Furthermore, the stability of the solution is proved using the Hyers-Ulam stability and Gronwall-Bellman's inequality. Additionally, the Laplace Adomian decomposition method (LADM) is employed to obtain the approximate solutions for both linear and non-linear FVFIDEs. The method's efficiency is demonstrated through some numerical examples.

On the analysis and deeper properties of the fractional complex physical models pertaining to nonsingular kernels.

This study solves the coupled fractional differential equations defining the massive Thirring model and the Kundu Eckhaus equation using the Natural transform decomposition method. The massive Thirring model is a dynamic component of quantum field theory, consisting of a coupled nonlinear complex differential equations. Initially, we study the suggested equations under the fractional derivative of Caputo-Fabrizio. The Atangana-Baleanu derivative is then used to evaluate the comparable equations. The results are significant and necessary for exploring a range of physical processes. This paper uses modern approach and the fractional operators in this situation to develop satisfactory approximations to the offered problems. The proposed approach combines the natural transform technique with the efficient Adomian decomposition scheme. Obtaining numerical findings in the form of a fast-converge series significantly improves the scheme's accuracy. Some graphical plot distributions are presented to show that the present approach is very simple and straightforward. We performed a fractional order analysis of assumed phenomena to demonstrate and validate the effectiveness of the future technique. The behaviour of the approximate series solution for several fractional orders is shown visually. Additionally, the nature of the derived outcome has been observed for various fractional orders. The derived results demonstrate how simple and efficient the proposed method is to apply for analysing the behaviour of fractionally-order complex nonlinear differential equations that arise in related fields of engineering and science.

Passive control of thermoacoustic instability in a high-efficiency domestic gas stove with fine-tuning burner

Thermoacoustic oscillation is a significant challenge in the development of advanced thermal power and propulsion systems. The present work focuses on the whistling phenomenon in the practical burners of a developing high-efficiency domestic gas stove. The acoustic analysis is conducted by a Helmholtz acoustic solver, identifying the 1/2 wave longitudinal mode in the outer ring or center nozzle and its upstream pipe and estimating the modal eigenfrequencies fa=599Hz and fb=647Hz which are close to the main frequency of the whistling measured in experiments. The sequential flame images captured by a high-speed camera are processed by a dynamic mode decomposition method to illustrate flame structure oscillations at the peak frequency mode. The results verify that thermoacoustic oscillations are the generation mechanism of the whistling and display the periodic fluctuation characteristics of the flame and the spatial distribution of heat release. Moreover, both structural fine-tuning designs help to achieve better suppression for thermoacoustic oscillations and avoid the whistling phenomenon. These structural fine-tuning strategies have been researched for several decades but rarely reported to be applied to industrial burners in previous work. Motivated by this, it will provide a new insight into the investigation of burner structures on thermoacoustic behaviors and the application of these passive control strategies.

Accounting for socio-economic inequalities in health to inform SDG decision making: A proof-of-concept study

Most SDG-inequality indices rely on a unidimensional design which cannot reflect how a given health outcome is distributed along the socio-economic spectrum. The concentration index can overcome this limitation. With an application to adult excess weight data, the concentration index was illustrated along with a decomposition method which allowed for key predictors to be identified. An Erreyger's concentration index and Shapley decomposition-based approach provide a relatively simple analytical tool to the monitoring of socio-economic inequalities in health. Such analytical approach should be considered as a monitoring tool by public managers to inform SDG policy and budgetary decisions.

Prediction of Turbulent Boundary Layer Flow Dynamics with Transformers

Time-marching of turbulent flow fields is computationally expensive using traditional Computational Fluid Dynamics (CFD) solvers. Machine Learning (ML) techniques can be used as an acceleration strategy to offload a few time-marching steps of a CFD solver. In this study, the Transformer (TR) architecture, which has been widely used in the Natural Language Processing (NLP) community for prediction and generative tasks, is utilized to predict future velocity flow fields in an actuated Turbulent Boundary Layer (TBL) flow. A unique data pre-processing step is proposed to reduce the dimensionality of the velocity fields, allowing the processing of full velocity fields of the actuated TBL flow while taking advantage of distributed training in a High Performance Computing (HPC) environment. The trained model is tested at various prediction times using the Dynamic Mode Decomposition (DMD) method. It is found that under five future prediction time steps with the TR, the model is able to achieve a relative Frobenius norm error of less than 5%, compared to fields predicted with a Large Eddy Simulation (LES). Finally, a computational study shows that the TR achieves a significant speed-up, offering computational savings approximately 53 times greater than those of the baseline LES solver. This study demonstrates one of the first applications of TRs on actuated TBL flow intended towards reducing the computational effort of time-marching. The application of this model is envisioned in a coupled manner with the LES solver to provide few time-marching steps, which will accelerate the overall computational process.

Analytical Solution of Some Non – Linear Delay Differential Equations Using Adomian Decomposition Method

Analytical Solution of Some Non – Linear Delay Differential Equations Using Adomian Decomposition Method

Fusion-driven fault diagnosis based on adaptive tuning feature mode decomposition and synergy graph enhanced transformer for bearings under noisy conditions

Bearing fault diagnosis is critical for maintaining the reliability of health monitoring in electromechanical systems. However, traditional feature extraction methods often struggle to accurately capture fault information in complex environments. This paper proposes an adaptive tuning feature mode decomposition (ATFMD) method, based on the intrinsic signal characteristics, to effectively extract robust features. ATFMD dynamically adjusts to complex fault signals, providing more representative feature inputs and pruning redundant features induced by noise. Additionally, given the limitations of single-dimensional feature domains in fully revealing fault information, this study constructs feature topology graphs by mapping spatial phase and time–frequency characteristics, offering a comprehensive representation of fault information. To achieve complementary fusion of fault information within the feature topological graph, this paper proposes the synergy graph enhanced transformer (SGET). SGET optimizes the fusion process by reinforcing feature interactions through its synergy graph representation module. Additionally, a hierarchical cross-attention mechanism is employed to modulate attention distribution across feature dimensions, enhancing the sensitivity to critical features during fusion. Experimental validation was conducted on two distinct rotating machinery transmission systems. The results demonstrate that the proposed method maintains exceptional robustness and generalization, even in the presence of severe noise and complex fault conditions. Compared to the leading methods, including MS-DGCNs, CapsFormer, TFT, and ConvFormer, the proposed method achieves notable accuracy improvements of 8.13 %, 8.71 %, 11.94 %, and 6.25 %, respectively, under challenging conditions.

Toroidal mode trapping in a magnetic meta-molecule

Abstract In this paper, we establish the relationship between the eigenmodes and the scattering characteristics of a meta-molecule made of magnetic disks from the point of view of the manifestation of its toroidal response. In particular, we examine the electric and magnetic dipole contributions to the scattering cross-sections obtained in the framework of the multipole decomposition method while accounting for the polarizability and magnetization induced in the structure by the field of incoming radiation. We find out that with increasing permeability, the toroidal mode is trapped in the meta-molecule due to the presence of its magnetization part, which may have a practical perspective in gyrotropy, permittivity, and permeability sensing.

Reachable set control of singular semi-Markov jump multi-agent systems with input delay via state decomposition method

This paper addresses the challenge of reachable set estimation in singular multi-agent systems with time-delay and semi-Markov switching topologies. The primary goal is to construct an ellipsoid that encompasses all states originating from the origin. Furthermore, criteria for reachable sets with reduced conservatism are developed. The singular multi-agent systems are reduced by the Laplace matrix, then the Lyapunov–Krasovskii functional is constructed by using decomposed state vector. In addition, the sufficient conditions for the reachable set of singular multi-agent systems bounded by ellipsoids are given by matrix theory and linear matrix inequality. Numerical examples show that our results is effective.

Coordinated control algorithm of hydrogen production-battery based hybrid energy storage system for suppressing fluctuation of PV power

Photovoltaic (PV) power generation has issues of volatility and intermittency. Currently, PV plants are generally equipped with 10% rated capacity lithium-ion (Li) battery energy storage systems in China, who often fail to suppress fluctuation in the output power of PV plants effectively and meet the grid-connected standard. The hybrid energy storage system (HESS) combining with hydrogen production and Li battery system can produce hydrogen by water electrolysis during the peak period of PV power generation, effectively improving PV utilization efficiency, while smoothing PV power fluctuation and improving grid connection electricity quality. Firstly, models of the solid oxide electrolysis cell (SOEC) and alkaline electrolysis cell (AEC) systems for hydrogen production, and Li battery energy storage system are established, and the transient response characteristics of each system are analyzed. Secondly, an adaptive wavelet packet decomposition (AWPD) method for PV power signal decomposition is proposed based on the wavelet packet decomposition (WPD) method. Thirdly, a capacity configuration method for HESS are proposed based on the APWD method. Fourthly, a coordinated control strategy for HESS is proposed with the transient response characteristics of different energy storage systems and the state of charge for Li battery system. Finally, the proposed method is validated through simulation experiments based on the actual power data of the PV plant. The results show that the developed methods can effectively utilize partial PV power generation to produce hydrogen, improve PV utilization, and the combined output power of PV plant and HESS can fulfill the grid-connected standard.

Domain decomposition for physics-data combined neural network based parametric reduced order modelling

This paper proposes a novel domain decomposition (DD) method for the parametric reduced-order model based on the Physics-Data Combined Neural Network (DD-PDCNN). The computational domain is partitioned into a number of subdomains, and a Physics-Data Combined Neural Network (PDCNN) is constructed for each subdomain, which not only represents the dynamics within its region but also considers interactions with neighbouring subdomains. The interface conditions between subdomains are considered by averaging solutions at the neighbourhoods, incorporating averaged solutions, predicted solutions at current and next time levels into reduced governing equations. The implicit coupling among the subdomains ensures global continuity and establishes boundary conditions for each subdomain.The performance of this new DD-PDCNN is compared with that of PDCNN without domain decomposition, data-driven model and traditional Reduced Basis(RB) model. The capability of this model is tested using a number of parametric nonlinear problems, such as the Korteweg-de Vries (KdV) equation, the two-dimensional Kovasznay flow and the two-dimensional incompressible Navier–Stokes equation. The results indicate that the proposed method offers an effective way to construct an accurate reduced order model for parameterised PDEs through machine learning. In particular, in specific parameter ranges where distinct physical phenomenon regions are prominent, the method outperforms the model without domain decomposition, demonstrating excellent performance on several challenging problems.

Method for assessing the durability of structures under stationary and non-stationary random loading using variational mode decomposition (VMD)

In the era of digital transformation, most devices are equipped with a variety of sensors, which provide information to be used in developing intelligent models for predicting the fatigue life. The development of digital models of real objects for fatigue life estimation faces the lack of algorithms for performing such an estimation. The problem arises in the adaptive and automatic analysis of signals from real sensors installed on the object and their subsequent processing to estimate the fatigue life of the object. We propose a new method for assessing the fatigue life of structures based on application of the adaptive method of variational mode decomposition to signals gained from sensors, including non-stationary ones. Variational mode decomposition involves decomposition of an initial complex random process into simpler random processes (modes) that are stationary and narrowband. An original method of summarizing damage resulted from the action of the modes obtained as a result of the decomposition is used. The developed method can be used as an algorithmic support for the generation of digital doubles of the residual lifetimes of natural products. The proposed method is compared with the «rainflow» method in the time domain. Different realizations of random stationary and non-stationary signals with different bandwidths are compared numerically. In addition, the traditional frequency methods of Dirlik and Benasciutti have been compared with the «rainflow» method. The analysis showed good results for the proposed method, i.e., the error was smaller compared to traditional frequency methods, especially for non-stationary processes.

Ultra-Short-Term Photovoltaic Power Prediction by NRGA-BiLSTM Considering Seasonality and Periodicity of Data

Photovoltaic (PV) power generation is highly stochastic and intermittent, which poses a challenge to the planning and operation of existing power systems. To enhance the accuracy of PV power prediction and ensure the safe operation of the power system, a novel approach based on seasonal division and a periodic attention mechanism (PAM) for PV power prediction is proposed. First, the dataset is divided into three components of trend, period, and residual under fuzzy c-means clustering (FCM) and the seasonal decomposition (SD) method according to four seasons. Three independent bidirectional long short-term memory (BiLTSM) networks are constructed for these subsequences. Then, the network is optimized using the improved Newton–Raphson genetic algorithm (NRGA), and the innovative PAM is added to focus on the periodic characteristics of the data. Finally, the results of each component are summarized to obtain the final prediction results. A case study of the Australian DKASC Alice Spring PV power plant dataset demonstrates the performance of the proposed approach. Compared with other paper models, the MAE, RMSE, and MAPE performance evaluation indexes show that the proposed approach has excellent performance in predicting output power accuracy and stability.

Exploring the pyrolytic degradation of seventeen phthalate esters using the non-targeted regions of interest-multivariate curve resolution (ROIMCR) chemometric method

The global use of phthalate esters (PAEs) in plastic production entails a need for developing effective remediation strategies to minimize exposure and health risks. In this study, pyrolysis degradation processes are evaluated for 17 different PAEs that were analyzed by high-resolution gas chromatography-mass spectrometry (Pyr-GC-Orbitrap-MS) at different temperatures (300 °C, 400 °C, 500 °C, 600 °C, 700 °C, 800 °C) both in electron ionization (EI) and positive chemical ionization (PCI) mode. All the analytical data generated have been processed with the Regions of Interest Multivariate Curve Resolution (ROIMCR) chemometrics method. A preliminary selection of the Mass Spectrometry Regions of Interest (ROIs) coupled to a bilinear factor decomposition method (MCR-ALS) allowed the identification of 4 principal components, which were used to define the thermal degradation process. ROIMCR method is a powerful tool for non-targeted analysis which allows the resolution of the elution and spectral profiles of the different constituents present in the analyzed samples, which were confirmed using PCI. Moreover, ROIMCR was used to resolve and identify the different products generated during the studied degradation processes. As a result, 10 new thermal degradation products were identified in the analysis of the different sample sets. Finally, the degradation efficiencies higher than 99.8 % were obtained for all the PAEs at 800 °C, except for benzoic acid-benzyl ester, whose removal efficiency decreased to 94.8 %. As phthalates are widespread and toxic compounds for the environment and for humans, there is a need for new remediation technologies. This study provides new knowledge to understand their elimination through thermal processes. We combine mass spectrometric data with powerful chemometric processing to determine the removal efficiency, to understand the degradation process and to identify the degradation compounds formed through thermal decomposition.