Decomposition Method Research Articles

Analytical solution of the 1-D population balance equation using Laplace transformation and Adomian Decomposition Method

The population balance equation (PBE) is a fundamental tool in chemical engineering for modeling particulate processes where particle size distribution significantly impacts product quality and process performance. It finds extensive applications in crystallization, polymerization, granulation, L-L extraction and aerosol dynamics. In this study, we present an analytical technique for solving the one-dimensional population balance equation (PBE). This technique combines Laplace transformation with the Adomian Decomposition Method (LADM), where the Laplace transformation is applied with respect to time, and the Adomian Decomposition Method (ADM) is used to address the resulting equation along the spatial coordinate. We examine specific cases involving pure convection, pure growth, pure breakage, and the combined processes of growth and breakage. This methodology provides analytical solutions involving the transport and particle-particle interaction phenomena of the dispersed phase.

An evaluation approach to PM2.5 policy effectiveness over South Korea based on a newly proposed scalable spatial decomposition method

Abstract Air quality management policies often exhibit spatial inconsistencies in effectiveness due to the diverse spatial scales of air pollution variability, which result from source characteristics as well as geographical and meteorological factors. To address this, the present study proposes a scalable spatial decomposition method to separate spatiotemporal air pollution data into background (nationwide), intercity-scale (tens of kilometers), and neighborhood-scale (several kilometers) components. This decomposition was achieved by introducing spatially varying effective ranges for intercity-scale variability at each station, based on the correlation coefficient distance of the background-removed component. Applying this approach to hourly fine particulate matter (PM2.5) concentrations from 535 monitoring stations across South Korea for 2021–2022, we evaluated the effectiveness of PM2.5 management policies. During the polluted cold season (December to March), the intercity-scale component contributed an average of approximately 18% of the total PM2.5 concentration in the Seoul Metropolitan Area (SMA) and Central Area (CA), which are densely populated and industrialized regions. In contrast, this component helped reduce PM2.5 levels in southeastern coastal areas, where high winds facilitate dispersion. The neighborhood-scale component contributed positively to PM2.5 levels near industrial complexes and ports but negatively in residential and commercial areas. The results demonstrate the effectiveness of central government-led intercity-scale regulations on total emissions allowances in the SMA and CA and highlight the need for additional local management targeting individual point sources near industrial complexes and ports. This study provides intuitive spatial decomposition tools for understanding PM2.5 pollution across spatial scales and offers policymakers a foundation for developing multi-scale mitigation strategies.

Enhanced PM2.5 prediction in Delhi using a novel optimized STL-CNN-BILSTM-AM hybrid model

Accurate air pollution predictions in urban areas facilitate the implementation of efficient actions to control air pollution and the formulation of strategies to mitigate contamination. This includes establishing an early warning system to notify the public. Creating precise estimates for PM2.5 air pollutants in large cities is a challenging task because of the numerous relevant factors and quick fluctuations. This study introduces a novel hybrid model named STL-CNN-BILSTM-AM. It combines the seasonal-trend decomposition method with LOESS (STL) to simplify learning tasks and increase prediction accuracy for complex, nonlinear time-series data. Convolutional neural networks (CNNs) extract features from decomposed components of PM2.5 and other feature variables, such as pollutants and meteorological variables. Bidirectional long-short-term memory (BILSTM) uses these features to extract temporal relationships, enabling the forecasting of daily PM2.5 levels at four locations in Delhi. This hybrid model uses attention mechanisms to extract the most significant information, as well as Bayesian optimization to tune the hyperparameters. The suggested model greatly improved performance in all four regions used in this study, as evidenced by the findings. We compared it with the CNN-BILSTM, BILSTM, LSTM, and CNN models, and the suggested model outperformed the state-of-the-art models by utilizing STL decomposition components and other features. The overall results show that the STL-CNN-BILSTM-AM is better at predicting air quality, especially the concentration of PM2.5 in cities when the data has a high seasonal trend and is complex.Graphical

Comparative analysis of two decomposition methods for urban domestic water usage patterns

Comparative analysis of two decomposition methods for urban domestic water usage patterns

Indirect effects of the COVID-19 pandemic: A cause-of-death analysis of life expectancy changes in 24 countries, 2015 to 2022.

Worldwide, mortality was strongly affected by the COVID-19 pandemic, both directly through COVID-19 deaths and indirectly through changes in other causes of death. Here, we examine the impact of the pandemic on COVID-19 and non-COVID-19 mortality in 24 countries: Australia, Austria, Brazil, Bulgaria, Canada, Chile, Croatia, Czechia, Denmark, England and Wales, Hungary, Japan, Latvia, Lithuania, The Netherlands, Northern Ireland, Poland, Russia, Scotland, South Korea, Spain, Sweden, Switzerland, and the United States. Using demographic decomposition methods, we compare age- and cause-specific contributions to changes in female and male life expectancy at birth in 2019-2020, 2020-2021, and 2021-2022 with those before the COVID-19 pandemic (2015-2019). We observe large life expectancy losses due to COVID-19 in most countries, usually followed by partial recoveries. Life expectancy losses due to cardiovascular disease (CVD) mortality were widespread during the pandemic, including in countries with substantial (Russia, Central and Eastern Europe, and the Baltic countries) and more modest (United States) improvements in CVD mortality before the pandemic. Many Anglo-Saxon countries, including Canada, Scotland, and the United States, continued their prepandemic trajectories of rising drug-related mortality. Most countries saw small changes in suicide mortality during the pandemic, while alcohol mortality increased and cancer mortality continued to decline. Patterns for other causes were more variable. By 2022, life expectancy had still not returned to prepandemic levels in several countries. Our results suggest important indirect effects of the pandemic on non-COVID-19 mortality through the consequences of COVID-19 infection, nonpharmaceutical interventions, and underreporting of COVID-19-related deaths.

Spall: accurate and robust unveiling cellular landscapes from spatially resolved transcriptomics data using a decomposition network

Recent developments in spatially resolved transcriptomics (SRT) enable the characterization of spatial structures for different tissues. Many decomposition methods have been proposed to depict the cellular distribution within tissues. However, existing computational methods struggle to balance spatial continuity in cell distribution with the preservation of cell-specific characteristics. To address this, we propose Spall, a novel decomposition network that integrates scRNA-seq data with SRT data to accurately infer cell type proportions. Spall introduced the GATv2 module, featuring a flexible dynamic attention mechanism to capture relationships between spots. This improves the identification of cellular distribution patterns in spatial analysis. Additionally, Spall incorporates skip connections to address the loss of cell-specific information, thereby enhancing the prediction capability for rare cell types. Experimental results show that Spall outperforms the state-of-the-art methods in reconstructing cell distribution patterns on multiple datasets. Notably, Spall reveals tumor heterogeneity in human pancreatic ductal adenocarcinoma samples and delineates complex tissue structures, such as the laminar organization of the mouse cerebral cortex and the mouse cerebellum. These findings highlight the ability of Spall to provide reliable low-dimensional embeddings for downstream analyses, offering new opportunities for deciphering tissue structures.

Step-Wise Parameter Adaptive FMD Incorporating Clustering Algorithm in Rolling Bearing Compound Fault Diagnosis

Ideally, the vibration signal of a rolling bearing should be symmetrical. However, in practical operation, the vibration signals in both time and frequency domains often exhibit asymmetry due to factors such as load, speed, and wear. The relatively weak composite fault characteristics are easily masked. Although the Feature Modal Decomposition (FMD) method is outstanding in diagnosing composite faults in bearings, its effectiveness is easily constrained by parameter selection. To address this, this paper proposes a stepwise parameter adaptive FMD method combined with a clustering algorithm, specifically designed for diagnosing composite faults in rolling bearings. Firstly, this study employs the Density Peak Clustering algorithm to determine the number of modes n in the composite fault vibration signal. Subsequently, considering the signal spectral energy and modal characteristics, a new composite fault index is formulated, namely, the adaptive weighted frequency domain kurtosis-to-information entropy ratio, as the fitness function. The Whale Optimization Algorithm determines the filter length L and the number of segments K, thereby achieving step-wise signal decomposition. Through in-depth analysis of signal symmetry and asymmetry, simulation and experimental verification confirm the effectiveness of this method. Compared with four other index-optimized FMD methods and traditional techniques, this method significantly reduces the influence of parameters on FMD, is capable of separating the characteristic frequencies related to composite faults, and performs excellently in the diagnosis of composite faults in rolling bearings.

Synthesis and Magnetic Characterization of Dispersed Fe$$_x$$Ni$$_{100-x}$$ (x = 10, 20, 30, 40, and 50) Nanoalloys Using the Thermal Decomposition Method

Synthesis and Magnetic Characterization of Dispersed Fe$$_x$$Ni$$_{100-x}$$ (x = 10, 20, 30, 40, and 50) Nanoalloys Using the Thermal Decomposition Method

Four-way decomposition of the effects of nutrient supplement and physical exercise on depression among older Chinese: a nationwide cross-sectional analysis

BackgroundStudies on the associations between nutrient supplement, physical exercise, and depression among persons 65 years and older in China are still lacking. We aimed to investigate the association between nutrient supplement and depression and to explore the role of physical exercise in this association.MethodsA total of 8,427 older Chinese adults from the Chinese Longitudinal Healthy Longevity Survey were included in this study. The Center for Epidemiologic Studies Depression Scale was used to assess participants’ depression, and nutrient supplement and physical exercise were evaluated using self-reports. Linear regression and logistic regression were performed to explore the association between nutrient supplement and depression, and a four-way decomposition method was used to explore the effects of nutrient supplement and physical exercise on depression.ResultsA total of 26.2% of participants suffered from depression. Prior to decomposition, multivariable linear regression and logistic regression models showed that older adults who received nutrient supplement had lower depression score (β: -0.704; 95% confidence interval [CI]: -1.004, -0.404) and a lower risk of depression (odds ratio: 0.710; 95% CI: 0.564, 0.894), especially for calcium and multivitamins. Four-way decomposition analysis suggested that physical exercise mediated the associations between nutrient (protein, calcium, iron, zinc, multivitamins, vitamin A/D, docosahexaenoic acid, and others) supplement and depression (all P < 0.05).ConclusionsCalcium or multivitamin supplements were associated with inverse depression, and the reason why this association existed could be partly explained by the mediating effect of physical exercise.

Re-examining Wage Disparities Across Segments of the Indian Labor Market

This article examines income disparities by considering both employer and employee perspectives of informality to scrutinize labor market segmentation in India. Additionally, the research investigates the impacts of varying degrees of urbanization, migration patterns, and industrial structures on formal and informal employment in the labor force. Utilizing data from the National Sample Survey Employment and Unemployment Survey rounds, specifically the 2004–2005 (61st) and 2011–2012 (68th) rounds, along with the Periodic Labour Force Survey 2018–2019 round, quantile regression models and the Recentred Influence Function decomposition method were employed to analyze wage inequality. A selection-corrected wage equation and its estimate were also presented by applying Bourguignon, Fournier, and Gurgand’s model-based selection correction. The study’s findings indicate that by 2019, the labor market had divided into two groups: organized formal workers and others. Further, the study reports wage convergence at lower quantiles and a widening gap at higher quantiles between organized formal and unorganized informal workers. Organized formal workers witness rising earnings, indicating positive wage growth, yet their share in overall employment remains small, which is significant given low job creation and high educated unemployment. At higher wage quantiles, there is a premium for being an informal worker in the organized sector compared to the unorganized sector, indicating a queue for formal employment opportunities in the organized sector. Despite the service sector’s significant role in Indian growth, it lags in creating formal job opportunities, unlike the manufacturing and construction sectors, which emphasize their substantial contribution to formal job generation. This study underlines that categorizing a firm as merely organized or a worker as formally employed is insufficient. Upgrades in these classifications should be accompanied by premiums, with wages being a key consideration. JEL Classification J31, J42, J62, J71

Research on Unmanned Aerial Vehicle Emergency Support System and Optimization Method Based on Gaussian Global Seagull Algorithm

In emergency rescue scenarios, drones can be equipped with different payloads as needed to aid in tasks such as disaster reconnaissance, situational awareness, communication support, and material assistance. However, rescue missions typically face challenges such as limited reconnaissance boundaries, heterogeneous communication networks, complex data fusion, high task latency, and limited equipment endurance. To address these issues, an unmanned emergency support system tailored for emergency rescue scenarios is designed. This system leverages 5G edge computing technology to provide high-speed and flexible network access along with elastic computing power support, reducing the complexity of data fusion across heterogeneous networks. It supports the control and data transmission of drones through the separation of the control plane and the data plane. Furthermore, by applying the Tammer decomposition method to break down the system optimization problem, the Global Learning Seagull Algorithm for Gaussian Mapping (GLSOAG) is proposed to jointly optimize the system’s energy consumption and latency. Through simulation experiments, the GLSOAG demonstrates significant advantages over the Seagull Optimization Algorithm (SOA), Particle Swarm Optimization (PSO), and Beetle Antennae Search Algorithm (BAS) in terms of convergence speed, optimization accuracy, and stability. The system optimization approach effectively reduces the system’s energy consumption and latency costs. Overall, our work alleviates the pain points faced in rescue scenarios to some extent.

Synthesis of barium titanate with narrow particle size distribution by the oxalate thermal decomposition method

Synthesis of barium titanate with narrow particle size distribution by the oxalate thermal decomposition method

Model Decomposition-Based Approach to Optimizing the Efficiency of Wireless Power Transfer Inside a Metal Enclosure

This paper describes a numerically efficient method for optimizing the high power transfer efficiency (PTE) of a resonant cavity-based Wireless Power Transfer (WPT) system for the wireless charging of smart clothing. The WPT system under study unitizes a carbon steel closet intended to store smart clothing overnight as a resonant cavity. The WPT system is designed to operate at 865.5 MHz; however, the operating frequency can be adjusted over a wide range. The main reason behind choosing a resonant cavity-based WPT system is that it has several advantages over the competitive WPT methods. Specifically, in contrast to its Far-field Power Transfer (FPT) and Inductive Power Transfer (IPT) counterparts, resonant cavity-based WPTs do not exhibit path loss and significant PTE sensitivity to the distance between the Tx and Rx coils and misalignment, respectively. The non-uniformity of the fields within the closet is addressed by using an optimized Yagi-like transmitting antenna with an additional element affecting the waveguide mode phases. The changes in the mode phases increase the volume inside the cavity, where the PTE values are higher than 50% (the high PTE region). In the present study, the model decomposition method is adapted to substantially accelerate the process of finding the optimal WPT system parameters. Additionally, the decomposition method explains the mechanism responsible for extending the high PTE region. The generalized scattering matrices are computed using the full-wave simulator Ansys HFSS for three sub-models. Then, the calculated S matrices are combined to evaluate the system’s PTE. The decomposition method is validated against full-wave simulations of the original WPT system’s model for several different parameter value combinations. The simulated results obtained for a sub-optimal model are experimentally verified by measuring the PTE of a real-life closet-based WPT system. The measured and calculated results are found to be in close agreement with the maximum measured PTE, as high as 60%.

Fertility Decline in Malawi: A Decomposition Analysis

Fertility in Malawi has been declining since the late 1980s. Total Fertility Rate is reported to have declined by 1.1 children per woman from 5.7 in 2010 to 4.6 in 2015. This reduction indicates a continuing rapid decline in fertility in the country. In view of the foregoing, this study aims to examine the influence of the age structure of the population, nuptiality, and marital fertility on fertility in Malawi. This study used the Malawi Demographic and Health Survey data from 1992, 2000, 2004, 2010, and 2015–2016. Standardization and decomposition methods were used to re-examine fertility trends in Malawi. The results confirms that fertility is declining in Malawi and the fall is clustered among women younger than 30 years of age. The contribution of marital fertility to the decline of Total Fertility Rate was 65.0% during the period 1992–2000, 89.5% during 2000–2004, 2.6% during 2004–2010, and 4.3% during 2010–2015, respectively. Over the same period, the respective contribution of the proportion married was 29.4%, 10.8%, 77.9%, and 92.6%. These percentages suggest that marital fertility followed by proportion of married were important factors before 2005. After 2005, fertility levels and patterns in Malawi are largely influenced by nuptiality. However, there is need for further studies to explain the marriage and fertility nexus in the Malawian context.

Familial co-aggregation and shared familiality among neurodevelopmental problems and with aggressive behavior, depression, anxiety, and substance use.

To refine the knowledge on familial transmission, we examined the (shared) familial components among neurodevelopmental problems (i.e. two attention-deficit/hyperactivity-impulsivity disorder [ADHD] and six autism spectrum disorder [ASD] subdomains) and with aggressive behavior, depression, anxiety, and substance use. Data were obtained from a cross-sectional study encompassing 37 688 participants across three generations from the general population. ADHD subdomains, ASD subdomains, aggressive behavior, depression, anxiety, and substance use were assessed. To evaluate familial (co-)aggregation, recurrence risk ratios (λR) were estimated using Cox proportional hazards models. The (shared) familiality (f2), which is closely related to (shared) heritability, was assessed using residual maximum likelihood-based variance decomposition methods. All analyses were adjusted for sex, age, and age2. The familial aggregation and familiality of neurodevelopmental problems were moderate (λR = 2.40-4.04; f2 = 0.22-0.39). The familial co-aggregation and shared familiality among neurodevelopmental problems (λR = 1.39-2.56; rF = 0.52-0.94), and with aggressive behavior (λR = 1.79-2.56; rF = 0.60-0.78), depression (λR = 1.45-2.29; rF = 0.43-0.76), and anxiety (λR = 1.44-2.31; rF = 0.62-0.84) were substantial. The familial co-aggregation and shared familiality between all neurodevelopmental problems and all types of substance use were weak (λR = 0.53-1.57; rF = -0.06-0.35). Neurodevelopmental problems belonging to the same disorder were more akin than cross-disorder problems. That said, there is a clear (shared) familial component to neurodevelopmental problems, in part shared with other psychiatric problems (except for substance use). This suggests that neurodevelopmental disorders, disruptive behavior disorders, and internalizing disorders share genetic and environmental risk factors.

Gender Wage Gap Analysis in Riau Province Using the Blinder-Oaxaca Decomposition Method

This study investigates the gender wage gap in Riau Province using the Blinder-Oaxaca decomposition method to examine its underlying factors. The analysis reveals a significant wage disparity, where women earn, on average, 29.56% less than men, despite higher educational attainment among women. The decomposition results highlight that only 2.44% of the gap is explained by observable factors such as education and employment type, while 76.76% remains unexplained, indicating the prevalence of discrimination and unmeasured structural barriers. This study identifies unique regional dynamics, including the paradox of women in urban areas earning less than their rural counterparts, contrary to global trends. Additionally, the study underscores the role of formal employment in reducing wage disparities, with women in formal jobs earning significantly more than those in informal sectors. These findings suggest that while improving education and transitioning women into formal employment can partially address wage disparities, structural reforms targeting workplace discrimination and cultural norms are essential for achieving gender wage equity. The study contributes to the literature by providing localized insights into gender wage gaps in Riau Province, emphasizing the need for targeted policy interventions to enhance equity in labor market outcomes.

Adaptive Ramanujan package decomposition method: a novel precise health indicator of rolling bearings

ABSTRACT In this paper, an adaptive Ramanujan packet decomposition (ARPD) method based on precise envelope segmentation is proposed to improve the accuracy of weak fault feature extraction and realise early non-destructive testing and condition evaluation of rolling bearings. Firstly, the power spectral density of the original signal is envelope-processed by accurate envelope segmentation method, so as to reduce the extreme points produced by interference frequency, and then realise the optimal frequency band division and reduce the influence of noise components. Secondly, the Ramanujan spectrum signal-to-noise ratio (RSSNR) index is introduced to quantify the fault characteristic information of the corresponding component in each frequency band. The largest component of the index is selected as the optimal mode, and the current number of layers is defined as the optimal number of modes. Finally, through the idea of iterative decomposition and RSSNR index, the problem that the optimal mode number is difficult to determine accurately is eliminated, and the optimal mode number is determined adaptively. The results of simulation and experimental signal analysis show that ARPD method can accurately divide the frequency bands and has excellent weak fault feature extraction ability, so it is an effective early non-destructive testing and condition evaluation method for rolling bearings.

Data-Driven Voltage Control Method of Active Distribution Networks Based on Koopman Operator Theory

The advent of large-scale distributed generation (DG) has introduced several challenges to the voltage control of active distribution networks (ADNs). These challenges include the heterogeneity of control devices, the complexity of models, and their inherent fluctuations. To maintain ADN voltage stability more economically and quickly, a data-driven ADN voltage control scheme is proposed in this paper. Firstly, based on the multi-run state sensitivity matrix, buses with similar voltage responses are clustered, and critical buses are selected to downsize the scale of the model. Secondly, a linear voltage-to-power dynamics model in high-dimensional state space is trained based on the offline data of critical bus voltages, DGs, and energy storage system (ESS) outputs, utilizing the Koopman theory and the Extended Dynamic Mode Decomposition (EDMD) method. A linear model predictive voltage controller, which takes ADN stability and control cost into account, is also proposed. Finally, the effectiveness and applicability of the method are verified by applying it to an improved 33-bus ADN system. The proposed control method can respond more quickly and accurately to the voltage fluctuation problems caused by source-load disturbances and short-circuit faults.

SOLUTION OF THE SPECTRUM ALLOCATION PROBLEM FOR A LINEAR CONTROL SYSTEM WITH CLOSED FEEDBACK

The method for constructing a feedback matrix to solve the problem spectrum allocation (spectrum control, pole assignment) for linear dynamic system is given. A new proof of the well-known theorem about the connection between the complete controllability of a dynamic system with existence of the feedback matrix is formed in the process of construction by the cascade decomposition method. The entire set of arbitrary elements that influence the non-uniqueness of the matrix is identified. Examples of constructing a feedback matrix in the case of a real spectrum and in the presence of complex conjugate eigenvalues, as well as for the case of multiple eigenvalues, are given. The stability of the specified spectrum under small perturbations of the system parameters with a fixed feedback matrix is studied.

Perturbational Decomposition Analysis for Quantum Ising Model with Weak Transverse Fields.

This work presents a perturbational decomposition method for simulating quantum evolution under the one-dimensional Ising model with both longitudinal and transverse fields. By treating the transverse field terms as perturbations in the expansion, our approach is particularly effective in systems with moderate longitudinal fields and weak to moderate transverse fields relative to the coupling strength. Through systematic numerical exploration, we characterize parameter regimes and evolution time windows where the decomposition achieves measurable improvements over conventional Trotter decomposition methods. The developed perturbational approach and its characterized parameter space may provide practical guidance for choosing appropriate simulation strategies in different parameter regimes of the one-dimensional Ising model.