Search Results (222)

The Bagley–Torvik equation (BTE) is an important model in mathematical physics and mechanics, but obtaining its analytical solution remains challenging. For its numerical treatment, the presence of composite functions in the generalized BTE poses additional difficulties, and efficient approaches for handling nonlinear terms are still lacking in the literature. This study proposes an improved numerical method for the fractional BTE with integral boundary conditions. By employing an integration technique, the original problem is transformed into a weakly singular Fredholm–Hammerstein (F–H) integral equation of the second kind. To address the nonlinear terms, an enhanced piecewise Taylor expansion scheme is developed to construct the discrete form, while the uniqueness of the solution is proven using the contraction mapping theorem in Banach spaces. The convergence and error analyses are rigorously carried out, and numerical experiments confirm the accuracy and efficiency of the proposed approach. Full article

The primary objective of this study is to provide a more precise and beneficial mathematical model for assessing corruption dynamics by utilizing non-local derivatives. This research aims to provide solutions that accurately capture the complexities and practical behaviors of corruption. To illustrate how corruption levels within a community change over time, a non-linear deterministic mathematical model has been developed. The authors present a non-integer order model that divides the population into five subgroups: susceptible, exposed, corrupted, recovered, and honest individuals. To study these corruption dynamics, we employ a new method for solving a time-fractional corruption model, which we term the q-homotopy analysis transform approach. This approach produces an effective approximation solution for the investigated equations, and data is shown as 3D plots and graphs, which give a clear physical representation. The stability and existence of the equilibrium points in the considered model are mathematically proven, and we examine the stability of the model and the equilibrium points, clarifying the conditions required for a stable solution. The resulting solutions, given in series form, show rapid convergence and accurately describe the model’s behaviour with minimal error. Furthermore, the solution’s uniqueness and convergence have been demonstrated using fixed-point theory. The proposed technique is better than a numerical approach, as it does not require much computational work, with minimal time consumed, and it removes the requirement for linearization, perturbations, and discretization. In comparison to previous approaches, the proposed technique is a competent tool for examining an analytical outcomes from the projected model, and the methodology used herein for the considered model is proved to be both efficient and reliable, indicating substantial progress in the field. Full article

Forecasting day-ahead electricity prices is a crucial research area. Both wholesale and retail sectors highly value improved forecast accuracy. Renewable energy sources have grown more influential and effective in the US power market. However, current forecasting models have shortcomings, including inadequate consideration of renewable energy impacts and insufficient feature selection. Many studies lack reproducibility, clear presentation of input features, and proper integration of renewable resources. This study addresses these gaps by incorporating a comprehensive set of input features, while these features are engineered to capture complex market dynamics. The model’s unique aspect is its inclusion of renewable-related inputs, such as temperature data for solar energy effects and wind speed for wind energy impacts on US electricity prices. The research also employs data preprocessing techniques like windowing, cleaning, normalization, and feature engineering to enhance input data quality and relevance. We developed four advanced hybrid deep learning models to improve electricity price prediction accuracy and reliability. Our approach combines variational mode decomposition (VMD) with four deep learning (DL) architectures: dense neural networks (DNNs), convolutional neural networks (CNNs), long short-term memory (LSTM) networks, and bidirectional LSTM (BiLSTM) networks. This integration aims to capture complex patterns and time-dependent relationships in electricity price data. Among these, the VMD-BiLSTM model consistently outperformed the others across all window implementations. Using 24 input features, this model achieved a remarkably low mean absolute error of 0.2733 when forecasting prices in the MISO market. Our research advances electricity price forecasting, particularly for the US energy market. These hybrid deep neural network models provide valuable tools and insights for market participants, energy traders, and policymakers. Full article

This study proposes an integrated framework for the optimal sizing of off-grid hybrid energy systems, combining photovoltaic panels, wind turbines, battery storage, a diesel generator, and an inverter. The methodology uniquely integrates long-term meteorological forecasting through a hybrid approach based on the Discrete Wavelet Transform and Long Short-Term Memory networks, together with metaheuristic optimization techniques (Particle Swarm Optimization and Genetic Algorithm), to minimize the system’s total annual cost. A case study was conducted in Guanambi, Brazil, using ten years (2012–2021) of hourly data on wind speed, solar irradiance, and ambient temperature. Forecasting results show that the hybrid Discrete Wavelet Transform–Long Short-Term Memory model outperforms the conventional Long Short-Term Memory approach, reducing error metrics and improving predictive accuracy. In the optimization stage, Particle Swarm Optimization consistently achieved lower costs and more stable convergence compared to the Genetic Algorithm. The optimal configuration comprised 450 photovoltaic panels, 10 wind turbines, 66 lithium iron phosphate battery, and 1 diesel generator, yielding a total annual cost of $105,381.17, a cost of energy of $0.1243/kWh, and minimal diesel dependence ($8825.89 annually). The proposed framework demonstrates robustness, economic viability, and applicability for providing sustainable and reliable electricity in isolated regions with high renewable energy potential. Full article

Ensuring grid stability in the transition to renewable energy sources requires accurate power demand forecasting. This study addresses the need for precise forecasting by differentiating among industrial, commercial, and residential consumers through customer clusterisation, tailoring the forecasting models to capture the unique consumption patterns of each group. Feature selection incorporated temporal, socio-economic, and weather-related data obtained from the Copernicus Earth Observation (EO) program. A variety of AI and machine learning algorithms for short-term load forecasting (STLF) and very-short-term load forecasting (VSTLF) are explored and compared, determining the most effective approaches. With all that, the main contribution of this work are the new forecasting approaches proposed, which have demonstrated superior performance compared to simpler models, both for STLF and VSTLF, highlighting the importance of customized forecasting strategies for different consumer groups and demonstrating the impact of incorporating detailed weather data on forecasting accuracy. These advancements contribute to more reliable power demand predictions, with our novel forecasting approaches reducing the Mean Absolute Percentage Error (MAPE) by up to 1–3% for industrial and 1–10% for commercial consumers compared to baseline models, thereby supporting grid stability. Full article

The direct current resistivity method holds advantages such as rapid, efficient, and automatic data acquisition. It is an important geophysical exploration technology for monitoring dynamic changes in subsurface geology. However, this method has such issues as volume effect and non-uniqueness in inversion. To meet the demand for high-resolution direct current resistivity inversion of dynamic geological models characterized by discontinuous changes, this study proposed a cross-gradient constrained time-lapse inversion method, thereby enhancing inversion imaging accuracy. A cross-gradient constraint term between models was incorporated into the objective function of time-lapse inversion to constrain the structural consistency and highlight local resistivity changes. This method avoided excessively smooth imaging as often caused by over-reliance on a reference model in time-lapse inversion, thereby significantly improving both the spatial resolution and quantitative accuracy of direct current resistivity monitoring inversion images. Numerical examples confirmed that the proposed method delivers higher inversion imaging accuracy in identifying dynamic resistivity changes, evidenced by a substantially lower normalized mean-square error (MSE). Furthermore, physical model experiments and a case study confirmed the stability of this method under actual monitoring conditions. The proposed method provides a more precise and effective inversion imaging technique for refined monitoring of dynamic changes in subsurface geologic bodies. Full article

In this paper, we propose a new class of self-mappings, referred to as polynomial Kannan contractions, which extend the classical Kannan contractions by incorporating higher-order polynomial distance terms with variable coefficient functions. Unlike polynomial contractions, polynomial Kannan contractions are not necessarily continuous. We establish fixed point results for such mappings under suitable conditions on the coefficient functions, in addition to presenting the error estimates for the associated Picard iteration. Furthermore, we provide some supported numerical examples to show that our extensions are proper and significant. As an application, we show that our results ensure the existence and uniqueness of solutions for a certain class of fractional differential equations. Full article

This study provides the first empirical evidence on the impact of innovation and firm growth on performance across G7 economies, using a unique panel dataset of 252 firms from 2020 to 2024. This study examines two core dimensions of firm performance—labor productivity and asset turnover—and employs multiple innovation proxies, including R&D Intensity, R&D-to-Assets, and R&D Growth Rate. To address potential endogeneity arising from reverse causality and omitted variable bias, the author implements the heteroskedasticity-based instrumental variable estimator, which constructs internal instruments from the model’s error structure. The study’s results reveal a consistent and significant positive causal effect of innovation on labor productivity, confirming its role as a driver of firm-level efficiency. However, innovation exhibits a negative and significant association with asset turnover, highlighting short-term trade-offs in operational efficiency, particularly in firms with aggressive R&D strategies. This study further finds that these effects are moderated by firm profitability and industry conditions, suggesting the importance of strategic and contextual alignment in innovation outcomes. Taken together, the findings offer new insights into the dual nature of innovation, enhancing productivity while imposing transitional efficiency costs and carrying significant implications for corporate innovation strategy and public policy in advanced economies. Full article

The preprocessing of infrared spectra can significantly improve predictive accuracy for protein, carbohydrate, lipid, or other nutrition components, yet optimal preprocessing selection is typically empirical, tedious, and dataset specific. This study introduces a Bayesian optimization-based framework designed for the automated selection of optimal spectral preprocessing pipelines within a chemometric modeling context. The framework was applied to mid-infrared spectra of milk to predict compositional parameters for fat, protein, lactose, and total solids. A total of 385 averaged spectra corresponding to 198 unique samples was split into a 70/30 ratio (training/test) using a group-aware Kennard-Stone algorithm, resulting in 269 averaged spectra (135 unique samples) for training and 116 spectra (58 unique samples) for testing. Six regression models: Elastic Net, Gradient Boosting Machines (GBM), Partial Least Squares (PLS), RidgeCV Regression, LassoLarsCV, and Support Vector Regression (SVR) were evaluated across three preprocessing conditions: (1) no preprocessing, (2) literature-derived custom preprocessing (e.g., MSC, SNV, and first and second derivatives), and (3) optimized preprocessing via the proposed Bayesian framework. Optimized preprocessing consistently outperformed other methods, with RidgeCV achieving the best performance for all components except lactose, where PLS slightly outperformed it. Improvements in predictive accuracy, particularly in terms of RMSEP were observed across all milk components. The best RMSEP results were achieved for protein (RMSEP = 0.054, $R^2=0.981$) and lactose (RMSEP = 0.026, $R^2=0.917$), followed by fat (RMSEP = 0.139, $R^2=0.926$) and total solids (RMSEP = 0.154, $R^2=0.960$). Literature-based pipelines demonstrated inconsistent effectiveness, highlighting the limitations of transferring preprocessing methods between datasets. The Bayesian optimization approach identified relatively simple yet highly effective preprocessing pipelines, typically involving few steps. By eliminating manual trial and error, this data-driven strategy offers a robust and generalizable solution that streamlines spectral modeling in dairy analysis and can be readily applied to other types of spectroscopic data across various domains. Full article

In this study, we propose a novel metaheuristic algorithm named Kangaroo Escape optimization Technique (KET), inspired by the survival-driven escape strategies of kangaroos in unpredictable environments. The algorithm integrates a chaotic logistic energy adaptation strategy to balance a two-phase exploration process—zigzag motion and long-jump escape—and an adaptive exploitation phase with local search guided by either nearby elite solutions or random peers. A unique decoy drop mechanism is introduced to prevent premature convergence and ensure dynamic diversity. KET is applied to optimize the parameters of a fractional-order Proportional Integral Derivative (PID) controller for Load Frequency Control (LFC) in interconnected power systems. The designed fractional-order PID controller-based KET optimization extends the conventional PID by introducing fractional calculus into the integral and derivative terms, allowing for more flexible and precise control dynamics. This added flexibility enables enhanced robustness and tuning capability, particularly useful in complex and uncertain systems such as modern power systems. Comparative results with existing state-of-the-art algorithms demonstrate the superior robustness, convergence speed, and control accuracy of the proposed approach under dynamic scenarios. The proposed KET-fractional order PID controller offers 29.6% greater robustness under worst-case conditions and 36% higher consistency across multiple runs compared to existing techniques. It achieves optimal performance faster than the Neural Network Algorithm (NNA), achieving its best Integral of Time Absolute Error (ITAE) value within the first 20 iterations, demonstrating its superior learning rate and early-stage search efficiency. In addition to LFC, the robustness and generality of the proposed KET were validated on a standard speed reducer design problem, demonstrating superior optimization performance and consistent convergence when compared to several recent metaheuristics. Full article

The growing demand for efficient energy management has become essential for achieving sustainable development across social, economic, and environmental sectors. Accurate energy demand forecasting plays a pivotal role in energy management. However, energy demand data present unique challenges due to their complex characteristics, such as multi-seasonality, hidden structures, long-range dependency, irregularities, volatilities, and nonlinear patterns, making energy demand forecasting challenging. We propose a hybrid dimension reduction deep learning algorithm, Temporal Variational Residual Network (TVRN), to address these challenges and enhance forecasting performance. This model integrates variational autoencoders (VAEs), Residual Neural Networks (ResNets), and Bidirectional Long Short-Term Memory (BiLSTM) networks. TVRN employs VAEs for dimensionality reduction and noise filtering, ResNets to capture local, mid-level, and global features while tackling gradient vanishing issues in deeper networks, and BiLSTM to leverage past and future contexts for dynamic and accurate predictions. The performance of the proposed model is evaluated using energy consumption data, showing a significant improvement over traditional deep learning and hybrid models. For hourly forecasting, TVRN reduces root mean square error and mean absolute error, ranging from 19% to 86% compared to other models. Similarly, for daily energy consumption forecasting, this method outperforms existing models with an improvement in root mean square error and mean absolute error ranging from 30% to 95%. The proposed model significantly enhances the accuracy of energy demand forecasting by effectively addressing the complexities of multi-seasonality, hidden structures, and nonlinearity. Full article

Proton therapy has emerged as a highly precise and tissue-sparing radiotherapy technique, capitalizing on the unique energy deposition pattern of protons characterized by the Bragg peak. Ensuring treatment accuracy relies on calibration phantoms, often composed of tissue-equivalent polymeric materials. This study investigates the dosimetric behavior of four commonly used polymers—Parylene, Epoxy, Lexan, and Mylar—by analyzing their linear energy transfer (LET) values and Bragg curve characteristics across various proton energies. Experimental LET data were collected and used to train and evaluate the predictive power for Bragg peak of multiple artificial intelligence models, including kNN, SVR, MLP, RF, LWRF, XGBoost, 1D-CNN, LSTM, and BiLSTM. These algorithms were optimized using 10-fold cross-validation and assessed through statistical error and performance metrics including MAE, RAE, RMSE, RRSE, CC, and R². Results demonstrate that certain AI models, particularly RF and LWRF, accurately (in terms of all evaluation metrics) predict Bragg peaks in Epoxy polymers, reducing the reliance on costly and time-consuming simulations. In terms of CC and R² metrics, the LWRF model demonstrated superior performance, achieving scores of 0.9969 and 0.9938, respectively. However, when evaluated against MAE, RMSE, RAE, and RRSE metrics, the RF model emerged as the top performer, yielding values of 12.3161, 15.8223, 10.3536, and 11.4389, in the same order. Additionally, the SVR model achieved the highest number of statistically significant differences when compared pairwise with the other eight models, showing significance against six of them. The findings support the use of AI as a robust tool for designing reliable calibration phantoms and optimizing proton therapy planning. This integrative approach enhances the synergy between materials science, medical physics, and data-driven modeling in advanced radiotherapy systems. Full article

Gallium nitride high-electron-mobility transistors (GaN HEMTs) are critical for high-power applications like AI power supplies and robotics but face reliability challenges due to increased dynamic ON-resistance (R_{DS_ON}) from electrical and thermomechanical stresses. This paper presents a novel self-calibrating temperature-sensitive electrical parameter (TSEP) model that uses gate leakage current (I_G) to estimate junction temperature with high accuracy, uniquely addressing aging effects overlooked in prior studies. By integrating I_G, aging-induced degradation, and failure-in-time (FIT) models, the approach achieves a junction temperature estimation error of less than 1%. Long-term hard-switching tests confirm its effectiveness, with calibrated R_{DS_ON} measurements enabling precise remaining useful life (RUL) predictions. This methodology significantly improves GaN HEMT reliability assessment, enhancing their performance in resilient power electronics systems. Full article

Soil moisture (SM) is a key variable in agricultural ecosystems and is crucial for drought prevention and control management. However, SM is influenced by underlying surface and meteorological conditions, and it changes rapidly in time and space. To capture the changes in SM and improve the accuracy of short-term and medium-to-long-term predictions on a daily scale, an LSTMseq2seq model driven by both observational data and mechanism models was constructed. This framework combines historical meteorological elements and SM, as well as the SM change characteristics output by the VIC model, to predict SM over a 90-day period. The model was validated using SMAP SM. The proposed model can accurately predict the spatiotemporal variations in SM in Jiangxi Province. Compared with classical machine learning (ML) models, traditional LSTM models, and advanced transformer models, the LSTMseq2seq model achieved R² values of 0.949, 0.9322, 0.8839, 0.8042, and 0.7451 for the prediction of surface SM over 3 days, 7 days, 30 days, 60 days, and 90 days, respectively. The mean absolute error (MAE) ranged from 0.0118 m³/m³ to 0.0285 m³/m³. This study also analyzed the contributions of meteorological features and simulated future SM state changes to SM prediction from two perspectives: time importance and feature importance. The results indicated that meteorological and SM changes within a certain time range prior to the prediction have an impact on SM prediction. The dual-driven LSTMseq2seq model has unique advantages in predicting SM and is conducive to the integration of physical mechanism models with data-driven models for handling input features of different lengths, providing support for daily-scale SM time series prediction and drought dynamics prediction. Full article

This paper introduces a novel and flexible class of continuous probability distributions, termed the Alpha Power Survival Ratio-X (APSR-X) family. Unlike many existing transformation-based families, the APSR-X class integrates an alpha power transformation with a survival ratio structure, offering a new mechanism for enhancing shape flexibility while maintaining mathematical tractability. This construction enables fine control over both the tail behavior and the symmetry properties, distinguishing it from traditional alpha power or survival-based extensions. We focus on a key member of this family, the two-parameter Alpha Power Survival Ratio Exponential (APSR-Exp) distribution, deriving essential mathematical properties including moments, quantile functions and hazard rate structures. We estimate the model parameters using eight frequentist methods: the maximum likelihood (MLE), maximum product of spacings (MPSE), least squares (LSE), weighted least squares (WLSE), Anderson–Darling (ADE), right-tailed Anderson–Darling (RADE), Cramér–von Mises (CVME) and percentile (PCE) estimation. Through comprehensive Monte Carlo simulations, we evaluate the estimator performance using bias, mean squared error and mean relative error metrics. The proposed APSR-X framework uniquely enables preservation or controlled modification of the symmetry in probability density and hazard rate functions via its shape parameter. This capability is particularly valuable in reliability and survival analyses, where symmetric patterns represent balanced risk profiles while asymmetric shapes capture skewed failure behaviors. We demonstrate the practical utility of the APSR-Exp model through three real-world applications: economic (tax revenue durations), engineering (mechanical repair times) and medical (infection durations) datasets. In all cases, the proposed model achieves a superior fit over that of the conventional alternatives, supported by goodness-of-fit statistics and visual diagnostics. These findings establish the APSR-X family as a unique, symmetry-aware modeling framework for complex lifetime data. Full article