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26 pages, 1111 KB  
Article
Heat Waves and Photovoltaic Performance: Modelling, Sensitivity, and Economic Impacts in Portugal
by Rui Castro and Isabela Teixeira
Sustainability 2026, 18(1), 289; https://doi.org/10.3390/su18010289 (registering DOI) - 27 Dec 2025
Abstract
The increasing frequency and intensity of heat waves across Southern Europe pose growing challenges to the performance and profitability of photovoltaic (PV) systems. This study quantifies the impact of elevated ambient temperatures on three large-scale PV power plants located in distinct Portuguese climatic [...] Read more.
The increasing frequency and intensity of heat waves across Southern Europe pose growing challenges to the performance and profitability of photovoltaic (PV) systems. This study quantifies the impact of elevated ambient temperatures on three large-scale PV power plants located in distinct Portuguese climatic zones: Amareleja, Alcoutim, and Tábua. Using 15 years of hourly meteorological data from PVGIS (2009–2023), five temperature models—NOCT, Faiman, PVSyst, NOCT (SAM), and Sandia—were implemented to estimate cell temperature and corresponding PV output under reference and elevated temperature conditions (+2 °C and +5 °C). A three-fold sensitivity analysis assessed (i) the influence of module parameters (temperature coefficient and NOCT), (ii) the effect of stochastic, non-uniform temperature perturbations mimicking realistic heat waves, and (iii) the impact of the selected PV performance model by comparing the simplified linear temperature-corrected approach with the one-diode and three-parameter (1D + 3P) model. Results show that a uniform +2 °C rise reduces annual energy yield by 0.74% and a +5 °C rise by 1.85%, while stochastic perturbations slightly amplify these losses to 0.80% and 2.01%. The 1D + 3P model predicts stronger nonlinear effects, with reductions of −2.42% and −6.06%. Although modest at plant scale, such impacts could translate into annual national revenue losses exceeding 10 million EUR, considering Portugal’s 6.32 GW installed PV capacity. The findings highlight the importance of accounting for realistic temperature dynamics and model uncertainty when assessing PV performance under a warming climate. Full article
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12 pages, 593 KB  
Article
Estimation of Information Flow-Based Causality with Coarsely Sampled Time Series
by X. San Liang
Entropy 2026, 28(1), 34; https://doi.org/10.3390/e28010034 (registering DOI) - 26 Dec 2025
Abstract
The past decade has seen a growing applications of the information flow-based causality analysis, particularly with the concise formula of its maximum likelihood estimator. At present, the algorithm for its estimation is based on differential dynamical systems, which, however, may raise an issue [...] Read more.
The past decade has seen a growing applications of the information flow-based causality analysis, particularly with the concise formula of its maximum likelihood estimator. At present, the algorithm for its estimation is based on differential dynamical systems, which, however, may raise an issue for coarsely sampled time series. Here, we show that, for linear systems, this is suitable at least qualitatively, but, for highly nonlinear systems, the bias increases significantly as the sampling frequency is reduced. This study provides a partial solution to this problem, showing how causality analysis can be made faithful with coarsely sampled series, provided that the statistics are sufficient. The key point here is that, instead of working with a Lie algebra, we turn to work with its corresponding Lie group. An explicit and concise formula is obtained, with only sample covariances involved. It is successfully applied to a system comprising a pair of coupled Rössler oscillators. Particularly remarkable is the success when the two oscillators are nearly synchronized. As more often than not observations may be scarce, this solution, albeit partial, is very timely. Full article
18 pages, 3256 KB  
Article
Performance Analysis and Coefficient Generation Method of Parallel Hammerstein Model Under Underdetermined Condition
by Nanzhou Hu, Youyang Xiang, Mingyang Li, Xianglu Li and Jie Tian
Sensors 2026, 26(1), 183; https://doi.org/10.3390/s26010183 (registering DOI) - 26 Dec 2025
Abstract
Nonlinear signal models are widely used in power amplifier predistortion, full-duplex self-interference cancellation, and other scenarios. The parallel Hammerstein (PH) model is a typical nonlinear signal model, but its serial and parallel hybrid architecture brings difficulties in performance analysis and coefficient estimation. This [...] Read more.
Nonlinear signal models are widely used in power amplifier predistortion, full-duplex self-interference cancellation, and other scenarios. The parallel Hammerstein (PH) model is a typical nonlinear signal model, but its serial and parallel hybrid architecture brings difficulties in performance analysis and coefficient estimation. This paper focuses on the performance analysis and coefficient estimation of the PH model for nonlinear systems with memory effects, such as power amplifiers. By comparing the PH model with the memory polynomial (MP) model under identical basis functions, we analyze its performance across varying numbers of parallel branches, nonlinear orders, and memory depths. Using singular value decomposition (SVD), we derive a closed-form expression for the PH model’s performance under underdetermined conditions, establishing its relationship to the non-zero singular values of the MP model’s coefficient matrix. Based on this, we propose a coefficient generation method combining SVD and least squares (LS), which directly computes coefficients and assesses performance during execution. Simulations confirm the method’s effectiveness, showing that selecting branches associated with larger singular values achieves near-optimal performance with reduced complexity. Full article
30 pages, 812 KB  
Article
State and Fault Estimation for Uncertain Complex Networks Using Binary Encoding Schemes Under Switching Couplings and Deception Attacks
by Nan Hou, Mengdi Chang, Hongyu Gao, Zhongrui Hu and Xianye Bu
Sensors 2026, 26(1), 182; https://doi.org/10.3390/s26010182 (registering DOI) - 26 Dec 2025
Abstract
A state and fault estimator is designed in this paper for nonlinear complex networks using binary encoding schemes subject to parameter uncertainties, randomly switching couplings, randomly occurring deception attacks and bounded stochastic noises. A Markov chain is employed to reflect the randomly switching [...] Read more.
A state and fault estimator is designed in this paper for nonlinear complex networks using binary encoding schemes subject to parameter uncertainties, randomly switching couplings, randomly occurring deception attacks and bounded stochastic noises. A Markov chain is employed to reflect the randomly switching phenomena of topological structures (or outer coupling strengths) and internal coupling strengths in complex networks. Binary encoding scheme is utilized to adjust the measurement signal transmission, where the signal is quantized and encoded into a binary bit string which is transmitted via a binary symmetric channel. Random bit flipping resulted from channel noises and randomly occurring deception attacks launched by hacker may take place inevitably during the network transmission process, whose occurrences are represented by two sequences of Bernoulli distributed random variables. The influence of random bit flipping is viewed as an equivalent stochastic noise, which facilitates the estimator design afterwards. The malicious signal is characterized by a nonlinear function satisfying an inequality constraint condition. The received binary bit string is decoded and used for estimating the system state and the fault. This paper aims to design a state and fault estimator such that the estimation error dynamic system is exponentially ultimately bounded in mean square, and the ultimate upper bound is minimized. A sufficient condition is put forth that ensures the existence of the expected state and fault estimator via adopting statistical property analysis, Lyapunov stability theory and matrix inequality technique. An exponentially ultimately bounded state and fault estimator in mean square is designed for such a kind of complex networks using the matrix inequality method. The estimator gain parameter is readily obtained by tackling an optimization issue subject to matrix inequalities constraints using Matlab software. Finally, two simulation examples are carried on which validate the effectiveness of the proposed state and fault estimation approach. The work in this paper plays a role in enriching the research system of estimation for complex network, and providing theoretical guidance for engineering applications. Full article
29 pages, 14822 KB  
Article
Estimation of Cotton Aboveground Biomass Based on UAV Multispectral Images: Multi-Feature Fusion and CNN Model
by Shuhan Huang, Xinjun Wang, Hanyu Cui, Qingfu Liang, Songrui Ning, Haoran Yang, Panfeng Wang and Jiandong Sheng
Agronomy 2026, 16(1), 74; https://doi.org/10.3390/agronomy16010074 (registering DOI) - 26 Dec 2025
Abstract
Precise estimation of cotton aboveground biomass (AGB) plays a crucial role in effectively analyzing growth variations and development of cotton, as well as guiding agricultural management practices. Multispectral (MS) sensors mounted on UAVs offer a practical and accurate approach for estimating the AGB [...] Read more.
Precise estimation of cotton aboveground biomass (AGB) plays a crucial role in effectively analyzing growth variations and development of cotton, as well as guiding agricultural management practices. Multispectral (MS) sensors mounted on UAVs offer a practical and accurate approach for estimating the AGB of cotton. Many previous studies have mainly emphasized the combination of spectral and texture features, as well as canopy height (CH). However, current research overlooks the potential of integrating spectral, textural features, and CH to estimate AGB. In addition, the accumulation of AGB often exhibits synergistic effects rather than a simple additive relationship. Conventional algorithms, including Bayesian Ridge Regression (BRR) and Random Forest Regression (RFR), often fail to accurately capture the nonlinear and intricate correlations between biomass and its relevant variables. Therefore, this research develops a method to estimate cotton AGB by integrating multiple feature information with a deep learning model. Spectral and texture features were derived from MS images. Cotton CH extracted from UAV point cloud data. Variables of multiple features were selected using Spearman’s Correlation (SC) coefficients and the variance inflation factor (VIF). Convolutional neural network (CNN) was chosen to build a model for estimating cotton AGB and contrasted with traditional machine learning models (RFR and BRR). The results indicated that (1) combining spectral, textural features, and CH yielded the highest precision in cotton AGB estimation; (2) compared to traditional ML models (RFR and BRR), the accuracy of applying CNN for estimating cotton AGB is better. CNN has more advanced power to learn complex nonlinear relationships among cotton AGB and multiple features; (3) the most effective strategy in this study involves combining spectral, texture features, and CH, selecting variables using the SC and VIF methods, and employing CNN for estimating AGB of cotton. The R2 of this model is 0.80, with an RMSE of 0.17 kg·m−2 and an MAE of 0.11 kg·m−2. This study develops a framework for evaluating cotton AGB by multiple features fusion with a deep learning model. It provides technical support for monitoring crop growth and improving field management. Full article
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18 pages, 3217 KB  
Article
Multilayer Perceptron, Radial Basis Function, and Generalized Regression Networks Applied to the Estimation of Total Power Losses in Electrical Systems
by Giovana Gonçalves da Silva, Ronald Felipe Marca Roque, Moisés Arreguín Sámano, Neylan Leal Dias, Ana Claudia de Jesus Golzio and Alfredo Bonini Neto
Mach. Learn. Knowl. Extr. 2026, 8(1), 4; https://doi.org/10.3390/make8010004 (registering DOI) - 26 Dec 2025
Abstract
This paper presents an Artificial Neural Network (ANN) approach for estimating total real and reactive power losses in electrical power systems. Three network architectures were explored: the Multilayer Perceptron (MLP), the Radial Basis Function (RBF) network, and the Generalized Regression Neural Network (GRNN). [...] Read more.
This paper presents an Artificial Neural Network (ANN) approach for estimating total real and reactive power losses in electrical power systems. Three network architectures were explored: the Multilayer Perceptron (MLP), the Radial Basis Function (RBF) network, and the Generalized Regression Neural Network (GRNN). The main advantage of the proposed methodology lies in its ability to rapidly compute power loss values throughout the system. ANN models are especially effective due to their capacity to capture the nonlinear characteristics of power systems, thus eliminating the need for iterative procedures. The applicability and effectiveness of the approach were evaluated using the IEEE 14-bus test system and compared with the continuation power flow method, which estimates losses using conventional numerical techniques. The results indicate that the ANN-based models performed well, achieving mean squared error (MSE) values below the predefined threshold during both training and validation (0.001). Notably, the networks accurately estimated the total power losses within the expected range, with residuals on the order of 10−4. Among the models tested, the RBF network showed slightly superior performance in terms of error metrics, requiring fewer centers to meet the established criteria compared to the MLP and GRNN models (11 centers). However, the GRNN achieved the shortest processing time; even so, all three networks produced satisfactory and consistent results, particularly in identifying the critical points of electrical power systems, which is of fundamental importance for ensuring system stability and operational reliability. Full article
(This article belongs to the Section Learning)
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25 pages, 103370 KB  
Article
NeRF-Enhanced Visual–Inertial SLAM for Low-Light Underwater Sensing
by Zhe Wang, Qinyue Zhang, Yuqi Hu and Bing Zheng
J. Mar. Sci. Eng. 2026, 14(1), 46; https://doi.org/10.3390/jmse14010046 (registering DOI) - 26 Dec 2025
Abstract
Marine robots operating in low illumination and turbid waters require reliable measurement and control for surveying, inspection, and monitoring. This paper present a sensor-centric visual–inertial simultaneous localization and mapping (SLAM) pipeline that combines low-light enhancement, learned feature matching, and NeRF-based dense reconstruction to [...] Read more.
Marine robots operating in low illumination and turbid waters require reliable measurement and control for surveying, inspection, and monitoring. This paper present a sensor-centric visual–inertial simultaneous localization and mapping (SLAM) pipeline that combines low-light enhancement, learned feature matching, and NeRF-based dense reconstruction to provide stable navigation states. A lightweight encoder–decoder with global attention improves signal-to-noise ratio and contrast while preserving feature geometry. SuperPoint and LightGlue deliver robust correspondences under severe visual degradation. Visual and inertial data are tightly fused through IMU pre-integration and nonlinear optimization, producing steady pose estimates that sustain downstream guidance and trajectory planning. An accelerated NeRF converts monocular sequences into dense, photorealistic reconstructions that complement sparse SLAM maps and support survey-grade measurement products. Experiments on AQUALOC sequences demonstrate improved localization stability and higher-fidelity reconstructions at competitive runtime, showing robustness to low illumination and turbidity. The results indicate an effective engineering pathway that integrates underwater image enhancement, multi-sensor fusion, and neural scene representations to improve navigation reliability and mission effectiveness in realistic marine environments. Full article
(This article belongs to the Special Issue Intelligent Measurement and Control System of Marine Robots)
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13 pages, 301 KB  
Article
A Self-Similar Analysis of the Solutions to the Cross-Diffusion System
by Abdinabi Mukhamadiyev, Jasur Urunbaev, Makhmud Bobokandov, Zafar Rakhmonov and Toshtemir Khujakulov
Mathematics 2026, 14(1), 83; https://doi.org/10.3390/math14010083 - 25 Dec 2025
Abstract
We study the qualitative behaviour of weak solutions to a doubly nonlinear cross-diffusion system in an inhomogeneous medium with nonlinear boundary flux. The main novelty of the paper lies in the analysis of a cross-diffusive p-Laplacian system weighted by a spatially varying [...] Read more.
We study the qualitative behaviour of weak solutions to a doubly nonlinear cross-diffusion system in an inhomogeneous medium with nonlinear boundary flux. The main novelty of the paper lies in the analysis of a cross-diffusive p-Laplacian system weighted by a spatially varying density in the form ρ(x)=(1+|x|)n, combined with nonlinear boundary interactions. By constructing self-similar weak solutions of Barenblatt type and employing a nonlinear separation of variables, the system is reduced to a coupled family of ordinary differential equations that characterise admissible similarity profiles. This approach allows us to identify Fujita-type critical conditions separating global solutions from finite-time blow-up and to derive explicit estimates for the solution profiles. Consequently, we establish critical thresholds driven by the interaction between cross-diffusion, degeneracy, boundary nonlinearity, and medium inhomogeneity. Full article
27 pages, 4168 KB  
Article
Optimizing Mortar Mix Design for Concrete Roofing Tiles Using Machine Learning and Particle Packing Theory: A Case Study
by Jorge Fernando Sosa Gallardo, Vivian Felix López Batista, Aldo Fernando Sosa Gallardo, María N. Moreno-García and Maria Dolores Muñoz Vicente
Appl. Sci. 2026, 16(1), 236; https://doi.org/10.3390/app16010236 - 25 Dec 2025
Abstract
The increasing demand for sustainable construction materials has motivated the optimization of mortar mix designs to reduce cement consumption and its environmental impact while maintaining adequate mechanical performance. This study develops a machine learning (ML) model for optimizing mortar mixtures used in concrete [...] Read more.
The increasing demand for sustainable construction materials has motivated the optimization of mortar mix designs to reduce cement consumption and its environmental impact while maintaining adequate mechanical performance. This study develops a machine learning (ML) model for optimizing mortar mixtures used in concrete roofing tiles by integrating aggregate particle packing techniques with non-linear regression algorithms, using an industry-grade dataset generated in the Central Laboratory of Wienerberger Ltd. Unlike most previous studies, which mainly focus on compressive strength, this research targets the transverse strength of industrial roof tile mortar. The proposed approach combines Tarantula Curve gradation limits, experimentally derived packing density (η), and ML regression within a unified and application-oriented workflow, representing a research direction rarely explored in the literature for optimizing concrete mix transverse strength. Fine concrete aggregates were characterized through a sand sieve analysis and subsequently adjusted according to the Tarantula Curve method to optimize packing density and minimize void content. Physical properties of cements and fine aggregates were assessed, and granulometric mixtures were evaluated using computational methods to calculate fineness modulus summation (FMS) and packing density. Mortar samples were tested for transverse strength at 1, 7, and 28 days using a three-point bending test, generating a robust dataset for modeling training. Three ML models—Random Forest Regressor (RFR), XG-Boost Regressor (XGBR), and Support Vector Regressor (SVR)—were evaluated, confirming their ability to capture nonlinear relationships between mix parameters and transverse strength. The analysis of input variables,which consistently ranked as the highest contributors according to impurity-based and permutation-based importance metrics, revealed that the duration of curing, density, and the summation of the fineness modulus significantly influenced the estimated transverse strength derived from the models. The integration of particle size distribution optimization and ML demonstrates a viable pathway for reducing cement content, lowering costs, and achieving sustainable mortar mix designs in the tile manufacturing industry. Full article
(This article belongs to the Topic Software Engineering and Applications)
11 pages, 2379 KB  
Article
Fractional Long-Range Dependence Model for Remaining Useful Life Estimation of Roller Bearings
by Shoukun Chen, Piercarlo Cattani, Hongqing Zheng, Qinglan Zheng and Wanqing Song
Fractal Fract. 2026, 10(1), 12; https://doi.org/10.3390/fractalfract10010012 - 25 Dec 2025
Abstract
Estimation of remaining useful life (RUL) of roller bearings is a prevalent problem for predictive maintenance in manufacturing. However, roller bearings are subject to a variety of factors during their operation. As a result, we deal with a slow nonlinear degradation process, which [...] Read more.
Estimation of remaining useful life (RUL) of roller bearings is a prevalent problem for predictive maintenance in manufacturing. However, roller bearings are subject to a variety of factors during their operation. As a result, we deal with a slow nonlinear degradation process, which is long-range dependent, self-similar and has non-Gaussian characteristics. Proper data pre-processing enables us to use Pareto’s probability density function (PDF), Generalized Pareto motion (GPm) and its fractional-order extension (fGPm) as the degradation predictive model. Estimation of the Hurst exponent shows that this model has a long-range correlation and self-similarity. Through the analysis of the uncertainty of the end point of the bearing’s RUL and the prediction process, not only did it verify the high adaptability of fGPm in simulating complex degradation processes but also the criteria for judging self-similarity, and LRD characteristics were established. The case study mainly proves the validity of the theory, providing an effective analytical tool for a deeper understanding of the degradation mechanism. Full article
(This article belongs to the Special Issue Fractional Order Modeling and Fault Detection in Complex Systems)
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31 pages, 1182 KB  
Article
From Reliability Modelling to Cognitive Orchestration: A Paradigm Shift in Aircraft Predictive Maintenance
by Igor Kabashkin and Timur Tyncherov
Mathematics 2026, 14(1), 76; https://doi.org/10.3390/math14010076 - 25 Dec 2025
Abstract
This study formulates predictive maintenance of complex technical systems as a constrained multi-layer probabilistic optimization problem that unifies four interdependent analytical paradigms. The mathematical framework integrates: (i) Weibull reliability modelling with parametric lifetime estimation; (ii) Bayesian posterior updating for dynamic adaptation under uncertainty; [...] Read more.
This study formulates predictive maintenance of complex technical systems as a constrained multi-layer probabilistic optimization problem that unifies four interdependent analytical paradigms. The mathematical framework integrates: (i) Weibull reliability modelling with parametric lifetime estimation; (ii) Bayesian posterior updating for dynamic adaptation under uncertainty; (iii) nonlinear machine-learning inference for data-driven pattern recognition; and (iv) ontology-based semantic reasoning governed by logical axioms and domain-specific constraints. The four layers are synthesized through a formal orchestration operator, defined as a sequential composition, where each sub-operator is governed by explicit mathematical constraints: Weibull cumulative distribution functions, Bayesian likelihood-posterior relationships, gradient-based loss minimization, and description logic entailment. The system operates within a cognitive digital twin architecture, with orchestration convergence formalized through iterative parameter refinement until consistency between numerical predictions and semantic validation is achieved. The framework is validated through a case study on aircraft wheel-hub crack prediction. The mathematical formulation establishes a rigorous analytical foundation for cognitive predictive maintenance systems applicable to safety-critical technical systems including aerospace, energy infrastructure, transportation networks, and industrial machinery. Full article
31 pages, 14784 KB  
Article
Neighborhood-Level Green Infrastructure and Heat-Related Health Risks in Tabriz, Iran: A Spatial Epidemiological Analysis
by Maryam Rezaei Ghaleh and Robert Balling
Atmosphere 2026, 17(1), 25; https://doi.org/10.3390/atmos17010025 - 25 Dec 2025
Abstract
Urban heat waves are intensifying under climate change, posing growing public health risks, particularly in rapidly urbanizing cities. Green infrastructure is widely promoted as a nature-based solution for heat mitigation, yet its health benefits may vary across urban contexts. This study examines how [...] Read more.
Urban heat waves are intensifying under climate change, posing growing public health risks, particularly in rapidly urbanizing cities. Green infrastructure is widely promoted as a nature-based solution for heat mitigation, yet its health benefits may vary across urban contexts. This study examines how neighborhood-level green infrastructure modifies heat-related health risks in Tabriz, Iran—a historically cold city experiencing increasing heat stress. The Normalized Difference Vegetation Index (NDVI) was derived from Landsat 8 imagery for 190 neighborhoods and classified into quartiles. Heat waves were defined as two or more consecutive days with mean temperatures at or above the 95th percentile. Emergency department visits for cardiovascular, respiratory, and all-cause conditions (2018–2020) were analyzed using Distributed Lag Non-linear Models with quasi-Poisson regression. Neighborhoods with low-to-moderate greenness (second and third NDVI quartiles) consistently exhibited lower relative risks of heat-related cardiovascular and all-cause visits, while both the lowest and highest NDVI quartiles showed elevated risk estimates. Risk patterns varied by lag period and demographic subgroup, with higher vulnerability observed among males and younger adults in highly vegetated areas, though estimates were imprecise. These findings suggest a non-linear relationship between urban greenness and heat-related health risks. Moderate green infrastructure appears most protective, underscoring the importance of context-sensitive and equitable greening strategies for climate adaptation in heat-vulnerable cities. Full article
(This article belongs to the Section Biometeorology and Bioclimatology)
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16 pages, 790 KB  
Article
Delayed Sampling-Based Power Grid Parameter Modeling and Estimation Method for Wind Power System with DC Component
by Youfeng Zhou, Guangqi Li, Zhiyong Dai, Xiaofei Liu, Yuyan Liu, Yihua Zhu and Chao Luo
Electronics 2026, 15(1), 91; https://doi.org/10.3390/electronics15010091 - 24 Dec 2025
Abstract
Wind power systems often introduce interfering DC components that distort power measurements and threaten grid stability. To address these issues, this paper proposes a novel delayed sampling-based grid parameter estimation method that explicitly accounts for DC disturbances. By transforming the estimation problem into [...] Read more.
Wind power systems often introduce interfering DC components that distort power measurements and threaten grid stability. To address these issues, this paper proposes a novel delayed sampling-based grid parameter estimation method that explicitly accounts for DC disturbances. By transforming the estimation problem into a linear regression form via nonlinear algebraic transformation, an adaptive recursive identification algorithm is developed to estimate grid frequency, amplitude, phase, and DC component simultaneously. Rigorous stability analysis is provided to guarantee convergence and robustness of the estimator in the presence of DC components. Experimental results demonstrate fast transient response and zero steady-state error, validating the effectiveness of the proposed method for real-time grid parameter estimation. Full article
34 pages, 1320 KB  
Article
Comparative Battery State of Charge (SoC) Estimation Using Shallow and Deep Machine Learning Models
by Mohammed Almubarak, Md Ismail Hossain and Md Shafiullah
Sustainability 2026, 18(1), 209; https://doi.org/10.3390/su18010209 - 24 Dec 2025
Abstract
This paper evaluates neural-network approaches for lithium-ion battery state-of-charge (SoC) estimation under a unified pipeline, fixed data partitions, and identical preprocessing. We study FNNs trained with Levenberg–Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG) across three hidden sizes (10, 20, 30) [...] Read more.
This paper evaluates neural-network approaches for lithium-ion battery state-of-charge (SoC) estimation under a unified pipeline, fixed data partitions, and identical preprocessing. We study FNNs trained with Levenberg–Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG) across three hidden sizes (10, 20, 30) and three topologies: Fitting, Nonlinear Input–Output (Nonlinear I/O), and time-series NAR/NARX. Models are assessed using test MSE and RMSE, correlation (R), generalization gap, convergence indicators (final gradient, damping factor), wall time per epoch, and a relative compute-cost index. On the Fitting task, BR-Fitting-FNN with 20 neurons provides the best accuracy-efficiency balance, while LM-Fitting-FNN with 30 neurons reaches slightly lower error at a higher cost. For Nonlinear I/O, BR-Nonlinear I/O-FNN with 30 neurons achieves the lowest test MSE with clear evidence of effective weight shrinkage; LM-Nonlinear I/O-FNN with 20 neurons is a close alternative. In time-series settings, LM-NAR-FNN with 10 neurons attains the lowest test error and fastest epochs but shows a very negative gap that suggests test-split favorability; BR-NAR-FNN with 30 neurons is more costly yet consistently strong. For NARX, LM-NARX-FNN with 20 neurons yields the best test accuracy and robust convergence. Overall, BR delivers the most reliable accuracy–robustness trade-off as networks widen, LM often achieves the best raw accuracy with careful split validation, and SCG offers the lowest training cost when resources are limited. These results provide practical guidance for selecting SoC estimators to match accuracy targets, computing budgets, and deployment constraints in battery management systems. Full article
42 pages, 1317 KB  
Article
Adaptive Parallel Methods for Polynomial Equations with Unknown Multiplicity
by Mudassir Shams and Bruno Carpentieri
Algorithms 2026, 19(1), 21; https://doi.org/10.3390/a19010021 - 24 Dec 2025
Abstract
New two-step simultaneous iterative techniques are proposed for solving polynomial equations with multiple roots of unknown multiplicity. The developed schemes achieve a local convergence order of ten and address key limitations of existing solvers, namely their dependence on prior multiplicity information and their [...] Read more.
New two-step simultaneous iterative techniques are proposed for solving polynomial equations with multiple roots of unknown multiplicity. The developed schemes achieve a local convergence order of ten and address key limitations of existing solvers, namely their dependence on prior multiplicity information and their reduced efficiency when dealing with clustered or repeated roots. Root multiplicities are adaptively estimated within the iterative process, avoiding additional function evaluations beyond those required for parallel updates. The robustness and stability of the proposed methods are assessed using both random and distant initial guesses and validated on benchmark polynomials as well as nonlinear models from biomedical engineering. The numerical results show notable improvements in residual error, iteration count, CPU time, memory usage, and overall convergence rate compared with established classical techniques. These findings demonstrate that the proposed schemes provide reliable, high-order, and computationally efficient tools for solving challenging nonlinear problems in science and engineering. Full article
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