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Search Results (316)

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Keywords = proportional fractional derivative

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14 pages, 1906 KiB  
Article
Integrating CT-Based Lung Fibrosis and MRI-Derived Right Ventricular Function for the Detection of Pulmonary Hypertension in Interstitial Lung Disease
by Kenichi Ito, Shingo Kato, Naofumi Yasuda, Shungo Sawamura, Kazuki Fukui, Tae Iwasawa, Takashi Ogura and Daisuke Utsunomiya
J. Clin. Med. 2025, 14(15), 5329; https://doi.org/10.3390/jcm14155329 - 28 Jul 2025
Viewed by 388
Abstract
Background/Objectives: Interstitial lung disease (ILD) is frequently complicated by pulmonary hypertension (PH), which is associated with reduced exercise capacity and poor prognosis. Early and accurate non-invasive detection of PH remains a clinical challenge. This study evaluated whether combining quantitative CT analysis of [...] Read more.
Background/Objectives: Interstitial lung disease (ILD) is frequently complicated by pulmonary hypertension (PH), which is associated with reduced exercise capacity and poor prognosis. Early and accurate non-invasive detection of PH remains a clinical challenge. This study evaluated whether combining quantitative CT analysis of lung fibrosis with cardiac MRI-derived measures of right ventricular (RV) function improves the diagnostic accuracy of PH in patients with ILD. Methods: We retrospectively analyzed 72 ILD patients who underwent chest CT, cardiac MRI, and right heart catheterization (RHC). Lung fibrosis was quantified using a Gaussian Histogram Normalized Correlation (GHNC) software that computed the proportions of diseased lung, ground-glass opacity (GGO), honeycombing, reticulation, consolidation, and emphysema. MRI was used to assess RV end-systolic volume (RVESV), ejection fraction, and RV longitudinal strain. PH was defined as a mean pulmonary arterial pressure (mPAP) ≥ 20 mmHg and pulmonary vascular resistance ≥ 3 Wood units on RHC. Results: Compared to patients without PH, those with PH (n = 21) showed significantly reduced RV strain (−13.4 ± 5.1% vs. −16.4 ± 5.2%, p = 0.026) and elevated RVESV (74.2 ± 18.3 mL vs. 59.5 ± 14.2 mL, p = 0.003). CT-derived indices also differed significantly: diseased lung area (56.4 ± 17.2% vs. 38.4 ± 12.5%, p < 0.001), GGO (11.8 ± 3.6% vs. 8.65 ± 4.3%, p = 0.005), and honeycombing (17.7 ± 4.9% vs. 12.8 ± 6.4%, p = 0.0027) were all more prominent in the PH group. In receiver operating characteristic curve analysis, diseased lung area demonstrated an area under the curve of 0.778 for detecting PH. This increased to 0.847 with the addition of RVESV, and further to 0.854 when RV strain was included. Combined models showed significant improvement in risk reclassification: net reclassification improvement was 0.700 (p = 0.002) with RVESV and 0.684 (p = 0.004) with RV strain; corresponding IDI values were 0.0887 (p = 0.03) and 0.1222 (p = 0.01), respectively. Conclusions: Combining CT-based fibrosis quantification with cardiac MRI-derived RV functional assessment enhances the non-invasive diagnosis of PH in ILD patients. This integrated imaging approach significantly improves diagnostic precision and may facilitate earlier, more targeted interventions in the management of ILD-associated PH. Full article
(This article belongs to the Section Nuclear Medicine & Radiology)
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24 pages, 1197 KiB  
Article
Fractional Gradient-Based Model Reference Adaptive Control Applied on an Inverted Pendulum-Cart System
by Maibeth Sánchez-Rivero, Manuel A. Duarte-Mermoud, Lisbel Bárzaga-Martell, Marcos E. Orchard and Gustavo Ceballos-Benavides
Fractal Fract. 2025, 9(8), 485; https://doi.org/10.3390/fractalfract9080485 - 24 Jul 2025
Viewed by 298
Abstract
This study introduces a novel model reference adaptive control (MRAC) framework that incorporates fractional-order gradients (FGs) to regulate the displacement of an inverted pendulum-cart system. Fractional-order gradients have been shown to significantly improve convergence rates in domains such as machine learning and neural [...] Read more.
This study introduces a novel model reference adaptive control (MRAC) framework that incorporates fractional-order gradients (FGs) to regulate the displacement of an inverted pendulum-cart system. Fractional-order gradients have been shown to significantly improve convergence rates in domains such as machine learning and neural network optimization. Nevertheless, their integration with fractional-order error models within adaptive control paradigms remains unexplored and represents a promising avenue for research. The proposed control scheme extends the classical MRAC architecture by embedding Caputo fractional derivatives into the adaptive law governing parameter updates, thereby improving both convergence dynamics and control flexibility. To ensure optimal performance across multiple criteria, the controller parameters are systematically tuned using a multi-objective Particle Swarm Optimization (PSO) algorithm. Two fractional-order error models (FOEMs) incorporating fractional gradients (FOEM2-FG, FOEM3-FG) are investigated, with their stability formally analyzed via Lyapunov-based methods under conditions of sufficient excitation. Validation is conducted through both simulation and real-time experimentation on a physical pendulum-cart setup. The results demonstrate that the proposed fractional-order MRAC (FOMRAC) outperforms conventional MRAC, proportional-integral-derivative (PID), and fractional-order PID (FOPID) controllers. Specifically, FOMRAC-FG achieved superior tracking performance, attaining the lowest Integral of Squared Error (ISE) of 2.32×105 and the lowest Integral of Squared Input (ISI) of 6.40 in simulation studies. In real-time experiments, FOMRAC-FG maintained the lowest ISE (5.11×106). Under real-time experiments with disturbances, it still achieved the lowest ISE (1.06×105), highlighting its practical effectiveness. Full article
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40 pages, 4643 KiB  
Article
An Innovative LFC System Using a Fuzzy FOPID-Enhanced via PI Controller Tuned by the Catch Fish Optimization Algorithm Under Nonlinear Conditions
by Saleh Almutairi, Fatih Anayi, Michael Packianather and Mokhtar Shouran
Sustainability 2025, 17(13), 5966; https://doi.org/10.3390/su17135966 - 28 Jun 2025
Viewed by 443
Abstract
Load frequency control (LFC) remains a critical challenge in ensuring the stability of modern power grids. The integration of nonlinear dynamics into LFC design is paramount to achieving robust performance, which directly underpins grid reliability. This study introduces a novel hybrid control strategy—a [...] Read more.
Load frequency control (LFC) remains a critical challenge in ensuring the stability of modern power grids. The integration of nonlinear dynamics into LFC design is paramount to achieving robust performance, which directly underpins grid reliability. This study introduces a novel hybrid control strategy—a fuzzy fractional-order proportional–integral–derivative (Fuzzy FOPID) controller augmented with a proportional–integral (PI) compensator—for LFC applications in two distinct dual-area interconnected power systems. To optimize the controller’s parameters, the recently developed Catch Fish Optimization Algorithm (CFOA) is employed, leveraging the Integral Time Absolute Error (ITAE) as the primary cost function for precision tuning. A comprehensive comparative analysis is conducted to benchmark the proposed controller against the existing methodologies documented in the literature. Nonlinear elements’ impact on the system stability is also investigated. The investigation evaluates the impact of critical nonlinearities, including governor dead band (GDB) and generation rate constraints (GRCs), on system performance. The simulation results demonstrate that the CFOA-tuned Fuzzy FOPID + PI controller exhibits superior robustness and dynamic response compared to conventional approaches, effectively mitigating frequency deviations and maintaining grid stability under nonlinear operating conditions. Furthermore, the CFOA demonstrates marginally superior convergence and tuning accuracy relative to the widely adopted Particle Swarm Optimization (PSO) algorithm. These findings underscore the proposed controller’s potential as a high-performance solution for real-world LFC systems, particularly in scenarios characterized by nonlinearities and interconnected grid complexities. This study advances the field by bridging the gap between fractional-order fuzzy control theory and practical power system applications, offering a validated strategy for enhancing grid resilience in dynamic environments. Full article
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10 pages, 2978 KiB  
Article
Acute Effects of Fusion Pacing Versus Standard CRT on Myocardial Function in Heart Failure Patients with LBBB
by Michał Kucio, Andrzej Kułach, Tomasz Skowerski, Mariusz Bałys, Mariusz Skowerski and Grzegorz Smolka
J. Clin. Med. 2025, 14(13), 4433; https://doi.org/10.3390/jcm14134433 - 22 Jun 2025
Viewed by 385
Abstract
Background/Objectives: Although cardiac resynchronization therapy (CRT) plays an established role in the management of heart failure, a significant proportion of patients do not respond despite appropriate candidate selection. The optimization of CRT pacing is one strategy to enhance response. Fusion pacing algorithms aim [...] Read more.
Background/Objectives: Although cardiac resynchronization therapy (CRT) plays an established role in the management of heart failure, a significant proportion of patients do not respond despite appropriate candidate selection. The optimization of CRT pacing is one strategy to enhance response. Fusion pacing algorithms aim to synchronize intrinsic right ventricular (RV) conduction with paced left ventricular (LV) activation, resulting in a more physiological ventricular depolarization pattern. This approach may improve electrical synchrony and enhance left ventricular contraction compared to conventional simultaneous biventricular pacing. The aim of this study was to compare the acute, beat-to-beat effects of standard biventricular pacing versus fusion pacing on myocardial function, using both conventional and speckle-tracking echocardiography in heart failure patients with left bundle branch block (LBBB). Methods: In total, 27 heart failure patients (21 men and 6 women) with reduced ejection fraction (EF < 35%), left bundle branch block (QRS > 150 ms), and newly implanted CRT-D systems (Abbott) underwent echocardiographic assessment immediately after device implantation. Echocardiographic parameters—including left atrial strain, left ventricular strain, TAPSE, mitral and tricuspid valve function, and cardiac output—were measured at 5 min intervals under three different pacing conditions: pacing off, simultaneous biventricular pacing, and fusion pacing using Abbott’s SyncAV® algorithm. Results: In our study, CRT led to a significant shortening of the QRS duration from 169 ± 19 ms at baseline to 131 ± 17 ms with standard biventricular pacing, and further to 118 ± 16 ms with fusion pacing (p < 0.05). Despite the electrical improvement, no significant changes were observed in global longitudinal strain (GLS: −9.15 vs. −9.39 vs. −9.13; p = NS), left ventricular stroke volume (67.5 mL vs. 68.4 mL vs. 68.5 mL; p = NS), or left atrial parameters including strain, area, and ejection fraction. However, fusion pacing was associated with more homogeneous segmental strain patterns, improved aortic valve closure time, and enhanced right ventricular function as reflected by tissue Doppler-derived S’. Conclusions: Immediate QRS narrowing observed in CRT patients—particularly with fusion pacing optimization—is associated with a more homogeneous pattern of left ventricular contractility and improvements in selected measures of mechanical synchrony. However, these acute electrical changes do not translate into immediate improvements in stroke volume, global LV strain, or left atrial function. Longer-term follow-up is needed to determine whether the electrical benefits of CRT, especially with fusion pacing, lead to meaningful hemodynamic improvements. Full article
(This article belongs to the Special Issue Advances in Atrial Fibrillation Treatment)
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36 pages, 6279 KiB  
Article
Eel and Grouper Optimization-Based Fuzzy FOPI-TIDμ-PIDA Controller for Frequency Management of Smart Microgrids Under the Impact of Communication Delays and Cyberattacks
by Kareem M. AboRas, Mohammed Hamdan Alshehri and Ashraf Ibrahim Megahed
Mathematics 2025, 13(13), 2040; https://doi.org/10.3390/math13132040 - 20 Jun 2025
Cited by 1 | Viewed by 497
Abstract
In a smart microgrid (SMG) system that deals with unpredictable loads and incorporates fluctuating solar and wind energy, it is crucial to have an efficient method for controlling frequency in order to balance the power between generation and load. In the last decade, [...] Read more.
In a smart microgrid (SMG) system that deals with unpredictable loads and incorporates fluctuating solar and wind energy, it is crucial to have an efficient method for controlling frequency in order to balance the power between generation and load. In the last decade, cyberattacks have become a growing menace, and SMG systems are commonly targeted by such attacks. This study proposes a framework for the frequency management of an SMG system using an innovative combination of a smart controller (i.e., the Fuzzy Logic Controller (FLC)) with three conventional cascaded controllers, including Fractional-Order PI (FOPI), Tilt Integral Fractional Derivative (TIDμ), and Proportional Integral Derivative Acceleration (PIDA). The recently released Eel and Grouper Optimization (EGO) algorithm is used to fine-tune the parameters of the proposed controller. This algorithm was inspired by how eels and groupers work together and find food in marine ecosystems. The Integral Time Squared Error (ITSE) of the frequency fluctuation (ΔF) around the nominal value is used as an objective function for the optimization process. A diesel engine generator (DEG), renewable sources such as wind turbine generators (WTGs), solar photovoltaics (PVs), and storage components such as flywheel energy storage systems (FESSs) and battery energy storage systems (BESSs) are all included in the SMG system. Additionally, electric vehicles (EVs) are also installed. In the beginning, the supremacy of the adopted EGO over the Gradient-Based Optimizer (GBO) and the Smell Agent Optimizer (SAO) can be witnessed by taking into consideration the optimization process of the recommended regulator’s parameters, in addition to the optimum design of the membership functions of the fuzzy logic controller by each of these distinct algorithms. The subsequent phase showcases the superiority of the proposed EGO-based FFOPI-TIDμ-PIDA structure compared to EGO-based conventional structures like PID and EGO-based intelligent structures such as Fuzzy PID (FPID) and Fuzzy PD-(1 + PI) (FPD-(1 + PI)); this is across diverse symmetry operating conditions and in the presence of various cyberattacks that result in a denial of service (DoS) and signal transmission delays. Based on the simulation results from the MATLAB/Simulink R2024b environment, the presented control methodology improves the dynamics of the SMG system by about 99.6% when compared to the other three control methodologies. The fitness function dropped to 0.00069 for the FFOPI-TIDμ-PIDA controller, which is about 200 times lower than the other controllers that were compared. Full article
(This article belongs to the Special Issue Mathematical Methods Applied in Power Systems, 2nd Edition)
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13 pages, 1542 KiB  
Article
Reducing the Primary Resonance Vibrations of a Cantilever Beam Using a Proportional Fractional-Order Derivative Controller
by M.N. Abd El-Salam and Rageh K. Hussein
Mathematics 2025, 13(11), 1886; https://doi.org/10.3390/math13111886 - 4 Jun 2025
Viewed by 316
Abstract
Many studies aim to suppress vibrations in vibrating dynamic systems, such as bridges, highways, and aircraft. In this study, we scrutinize the primary resonance of a cantilever beam excited by an external force via a proportional fractional-order derivative controller (PFD). The average method [...] Read more.
Many studies aim to suppress vibrations in vibrating dynamic systems, such as bridges, highways, and aircraft. In this study, we scrutinize the primary resonance of a cantilever beam excited by an external force via a proportional fractional-order derivative controller (PFD). The average method is used to obtain the approximate solution of the vibrating system. The stability of the control system is illustrated using the Routh–Hurwitz criterion. We investigate the performance of some chosen parameters of the studied system to generate response curves. The performance of the linear fractional feedback control is studied at different values of the fractional order. Full article
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28 pages, 531 KiB  
Article
Representation Formulas and Stability Analysis for Hilfer–Hadamard Proportional Fractional Differential Equations
by Safoura Rezaei Aderyani, Reza Saadati and Donal O’Regan
Fractal Fract. 2025, 9(6), 359; https://doi.org/10.3390/fractalfract9060359 - 29 May 2025
Viewed by 422
Abstract
This paper introduces a novel version of the Gronwall inequality specifically related to the Hilfer–Hadamard proportional fractional derivative. By utilizing Picard’s method of successive approximations along with the definition of Mittag–Leffler functions, we derive a representation formula for the solution of the Hilfer–Hadamard [...] Read more.
This paper introduces a novel version of the Gronwall inequality specifically related to the Hilfer–Hadamard proportional fractional derivative. By utilizing Picard’s method of successive approximations along with the definition of Mittag–Leffler functions, we derive a representation formula for the solution of the Hilfer–Hadamard proportional fractional differential equation featuring constant coefficients, expressed in the form of the Mittag–Leffler kernel. We establish the uniqueness of the solution through the application of Banach’s fixed-point theorem, leveraging several properties of the Mittag–Leffler kernel. The current study outlines optimal stability, a new Ulam-type concept based on classical special functions. It aims to improve approximation accuracy by optimizing perturbation stability, offering flexible solutions to various fractional systems. While existing Ulam stability concepts have gained interest, extending and optimizing them for control and stability analysis in science and engineering remains a new challenge. The proposed approach not only encompasses previous ideas but also emphasizes the enhancement and optimization of model stability. The numerical results, presented in tables and charts, are provided in the application section to facilitate a better understanding. Full article
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35 pages, 24700 KiB  
Article
Optimizing Load Frequency Control of Multi-Area Power Renewable and Thermal Systems Using Advanced Proportional–Integral–Derivative Controllers and Catch Fish Algorithm
by Saleh A. Alnefaie, Abdulaziz Alkuhayli and Abdullah M. Al-Shaalan
Fractal Fract. 2025, 9(6), 355; https://doi.org/10.3390/fractalfract9060355 - 29 May 2025
Viewed by 685
Abstract
Renewable energy sources (RESs) are increasingly combined into the power system due to market liberalization and environmental and economic benefits, but their weather-dependent variability causes power production and demand mismatches, leading to issues like frequency and regional power transmission fluctuations. To maintain synchronization [...] Read more.
Renewable energy sources (RESs) are increasingly combined into the power system due to market liberalization and environmental and economic benefits, but their weather-dependent variability causes power production and demand mismatches, leading to issues like frequency and regional power transmission fluctuations. To maintain synchronization in power systems, frequency must remain constant; disruptions in the proper balance of production and load might produce frequency variations, risking serious issues. Therefore, a mechanism known as load frequency control (LFC) or automated generation control (AGC) is needed to keep the frequency and tie-line power within predefined stable limits. In this study, advanced proportional–integral–derivative PID controllers such as fractional-order PID (FOPID), cascaded PI(PDN), and PI(1+DD) for LFC in a two-area power system integrated with RES are optimized using the catch fish optimization algorithm (CFA). The controllers’ optimal gains are attained through using the integral absolute error (IAE) and ITAE objective functions. The performance of LFC with CFA-tuned PID, PI, cascaded PI(PDN), and FOPID, PI(1+DD) controllers is compared to other optimization techniques, including sine cosine algorithm (SCA), particle swarm optimization (PSO), brown bear algorithm (BBA), and grey wolf optimization (GWO), in a two-area power system combined with RESs under various conditions. Additionally, by contrasting the performance of the PID, PI, cascaded PI(PDN), and FOPID, PI(1+DD) controllers, the efficiency of the CFA is confirmed. Additionally, a sensitivity analysis that considers simultaneous modifications of the frequency bias coefficient (B) and speed regulation (R) within a range of ±25% validates the efficacy and dependability of the suggested CFA-tuned PI(1+DD). In the complex dynamics of a two-area interconnected power system, the results show how robust the suggested CFA-tuned PI(1+DD) control strategy is and how well it can stabilize variations in load frequency and tie-line power with a noticeably shorter settling time. Finally, the results of the simulation show that CFA performs better than the GWO, BBA, SCA, and PSO strategies. Full article
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25 pages, 1198 KiB  
Article
State Estimation Based State Augmentation and Fractional Order Proportional Integral Unknown Input Observers
by Abdelghani Djeddi, Abdelaziz Aouiche, Chaima Aouiche and Yazeed Alkhrijah
Mathematics 2025, 13(11), 1786; https://doi.org/10.3390/math13111786 - 27 May 2025
Viewed by 349
Abstract
This paper presents a new method for the simultaneous estimation of system states and unknown inputs in fractional-order Takagi–Sugeno (FO-TS) systems with unmeasurable premise variables (UPVs), by introducing a fractional-order proportional-integral unknown input observer (FO-PIUIO) based on partial state augmentation. This approach permits [...] Read more.
This paper presents a new method for the simultaneous estimation of system states and unknown inputs in fractional-order Takagi–Sugeno (FO-TS) systems with unmeasurable premise variables (UPVs), by introducing a fractional-order proportional-integral unknown input observer (FO-PIUIO) based on partial state augmentation. This approach permits the estimation of both states and unknown inputs, which are essential for system monitoring and control. Partial state augmentation allows the integration of unknown inputs into a partially augmented model, ensuring accurate estimates of both states and unknown inputs. The state estimation error is formulated as a perturbed system. The convergence conditions for the state estimation errors between the system and the observer are derived using the second Lyapunov method and the L2 approach. Compared to traditional integer-order unknown input observers or fuzzy observers with measurable premise variables, in our method, fractional-order dynamics are combined with partial state augmentation uniquely for the persistent estimation of states along with unknown inputs in unmeasurable premise variable systems. Such a combination allows for robust estimation even under uncertainties in systems and long memory phenomena and is a significant step forward from traditional methods. Finally, a numerical example is provided to illustrate the performance of the proposed observer. Full article
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17 pages, 3425 KiB  
Article
Research on Fractional-Order Control of Anchor Drilling Machine Optimized by Intelligent Algorithms
by Jingkai Li, Jun Zhang, Jiaquan Xie, Wei Shi and Jianzhong Zhao
Appl. Sci. 2025, 15(10), 5656; https://doi.org/10.3390/app15105656 - 19 May 2025
Viewed by 454
Abstract
Anchor–bolt support operations are lengthy and conducted under harsh conditions, restricting the efficiency and safety of roadway excavation. To address these challenges, we developed an integrated solution combining mechanical structure optimization with control algorithms. Specifically, we designed a novel automated drilling system equipped [...] Read more.
Anchor–bolt support operations are lengthy and conducted under harsh conditions, restricting the efficiency and safety of roadway excavation. To address these challenges, we developed an integrated solution combining mechanical structure optimization with control algorithms. Specifically, we designed a novel automated drilling system equipped with a robotic manipulator and an anchor–bolt magazine to handle modular hollow self-drilling anchor bolts, enabling automated support operations. To achieve precise docking in unmanned conditions, we employed an inner-loop fractional-order proportional–integral–derivative (FOPID) controller optimized by an improved particle swarm optimization (ILPSO) algorithm. Additionally, robust control based on H∞ control theory was introduced to ensure reliable system performance under disturbances and model uncertainties. Simulation results indicate that the ILPSO-tuned FOPID controller significantly outperforms conventional controllers in dynamic response accuracy; frequency–domain analysis further confirms that the H∞ control approach enhances system stability. Collectively, these results provide a theoretical basis for advancing automated mining technologies. Full article
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54 pages, 10398 KiB  
Article
Reduced-Order Modeling (ROM) of a Segmented Plug-Flow Reactor (PFR) for Hydrogen Separation in Integrated Gasification Combined Cycles (IGCC)
by Osama A. Marzouk
Processes 2025, 13(5), 1455; https://doi.org/10.3390/pr13051455 - 9 May 2025
Cited by 2 | Viewed by 1058
Abstract
In an integrated gasification combined cycle (IGCC), a gasification process produces a gas stream from a solid fuel, such as coal or biomass. This gas (syngas or synthesis gas) resulting from the gasification process contains carbon monoxide, molecular hydrogen, and carbon dioxide (other [...] Read more.
In an integrated gasification combined cycle (IGCC), a gasification process produces a gas stream from a solid fuel, such as coal or biomass. This gas (syngas or synthesis gas) resulting from the gasification process contains carbon monoxide, molecular hydrogen, and carbon dioxide (other gaseous components may also be present depending on the gasified solid fuel and the gasifying agent). Separating hydrogen from this syngas stream has advantages. One of the methods to separate hydrogen from syngas is selective permeation through a palladium-based metal membrane. This separation process is complicated as it depends nonlinearly on various variables. Thus, it is desirable to develop a simplified reduced-order model (ROM) that can rapidly estimate the separation performance under various operational conditions, as a preliminary stage of computer-aided engineering (CAE) in chemical processes and sustainable industrial operations. To fill this gap, we present here a proposed reduced-order model (ROM) procedure for a one-dimensional steady plug-flow reactor (PFR) and use it to investigate the performance of a membrane reactor (MR), for hydrogen separation from syngas that may be produced in an integrated gasification combined cycle (IGCC). In the proposed model, syngas (a feed stream) enters the membrane reactor from one side into a retentate zone, while nitrogen (a sweep stream) enters the membrane reactor from the opposite side into a neighbor permeate zone. The two zones are separated by permeable palladium membrane surfaces that are selectively permeable to hydrogen. After analyzing the hydrogen permeation profile in a base case (300 °C uniform temperature, 40 atm absolute retentate pressure, and 20 atm absolute permeate pressure), the temperature of the module, the retentate-side pressure, and the permeate-side pressure are varied individually and their influence on the permeation performance is investigated. In all the simulation cases, fixed targets of 95% hydrogen recovery and 40% mole-fraction of hydrogen at the permeate exit are demanded. The module length is allowed to change in order to satisfy these targets. Other dependent permeation-performance variables that are investigated include the logarithmic mean pressure-square-root difference, the hydrogen apparent permeance, and the efficiency factor of the hydrogen permeation. The contributions of our study are linked to the fields of membrane applications, hydrogen production, gasification, analytical modeling, and numerical analysis. In addition to the proposed reduced-order model for hydrogen separation, we present various linear and nonlinear regression models derived from the obtained results. This work gives general insights into hydrogen permeation via palladium membranes in a hydrogen membrane reactor (MR). For example, the temperature is the most effective factor to improve the permeation performance. Increasing the absolute retentate pressure from the base value of 40 atm to 120 atm results in a proportional gain in the permeated hydrogen mass flux, with about 0.05 kg/m2.h gained per 1 atm increase in the retentate pressure, while decreasing the absolute permeate pressure from the base value of 20 bar to 0.2 bar causes the hydrogen mass flux to increase exponentially from 1.15 kg/m2.h. to 5.11 kg/m2.h. This study is linked with the United Nations Sustainable Development Goal (SDG) numbers 7, 9, 11, and 13. Full article
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32 pages, 6743 KiB  
Article
Analytical Properties and Hermite–Hadamard Type Inequalities Derived from Multiplicative Generalized Proportional σ-Riemann–Liouville Fractional Integrals
by Fuxiang Liu and Jielan Li
Symmetry 2025, 17(5), 702; https://doi.org/10.3390/sym17050702 - 4 May 2025
Cited by 1 | Viewed by 444
Abstract
This paper investigates the analytical properties of multiplicative generalized proportional σ-Riemann–Liouville fractional integrals and the corresponding Hermite–Hadamard-type inequalities. Central to our study are two key notions: multiplicative σ-convex functions and multiplicative generalized proportional σ-Riemann–Liouville fractional integrals, both of which serve [...] Read more.
This paper investigates the analytical properties of multiplicative generalized proportional σ-Riemann–Liouville fractional integrals and the corresponding Hermite–Hadamard-type inequalities. Central to our study are two key notions: multiplicative σ-convex functions and multiplicative generalized proportional σ-Riemann–Liouville fractional integrals, both of which serve as the foundational framework for our analysis. We first introduce and examine several fundamental properties of the newly defined fractional integral operator, including continuity, commutativity, semigroup behavior, and boundedness. Building on these results, we derive a novel identity involving this operator, which forms the basis for establishing new Hermite–Hadamard-type inequalities within the multiplicative setting. To validate the theoretical results, we provide multiple illustrative examples and perform graphical visualizations. These examples not only demonstrate the correctness of the derived inequalities but also highlight the practical relevance and potential applications of the proposed framework. Full article
(This article belongs to the Section Mathematics)
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19 pages, 2109 KiB  
Article
Robust Frequency Regulation Management System in a Renewable Hybrid Energy Network with Integrated Storage Solutions
by Subhranshu Sekhar Pati, Umamani Subudhi and Sivkumar Mishra
Electricity 2025, 6(2), 22; https://doi.org/10.3390/electricity6020022 - 1 May 2025
Viewed by 968
Abstract
The rapid proliferation of renewable energy sources (RESs) has significantly reduced system inertia, thereby intensifying stability challenges in modern power grids. To address these issues, this study proposes a comprehensive approach to improve the grid stability concerning RESs and load disturbances. The methodology [...] Read more.
The rapid proliferation of renewable energy sources (RESs) has significantly reduced system inertia, thereby intensifying stability challenges in modern power grids. To address these issues, this study proposes a comprehensive approach to improve the grid stability concerning RESs and load disturbances. The methodology integrates controlled energy storage systems, including ultra-capacitors (UC), superconducting magnetic energy storage (SMES), and battery storage, alongside a robust frequency regulation management system (FRMS). Central to this strategy is the implementation of a novel controller which combines a constant with proportional–integral–derivative (PID) and modified fractional-order (MFO) control, forming 1+MFOPID controller. The controller parameters are optimized using a novel formulation of an improved objective function that incorporates both frequency and time domain characteristics to achieve superior performance. The efficacy of the proposed controller is validated by comparing its performance with conventional PID and fractional-order PID controllers. System stability is further analyzed using eigenvector analysis. Additionally, this study evaluates the performance of various energy storage systems and their individual contributions to frequency regulation, with a particular emphasis on the synergistic benefits of battery storage in conjunction with other storages. Finally, sensitivity analysis is conducted to assess the impact of parameter uncertainties in the system design, reinforcing the robustness of the proposed approach. Full article
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15 pages, 2033 KiB  
Article
Skin Anti-Aging Properties of the Glycopeptide- and Glycoprotein-Enriched Fraction from a Cosmetic Variation of the Longevity Medicine, Gongjin-Dan
by Gwang Jin Lee, Jiwon Park, Hyeon Jun Jeon, Tae Heon Kim, Hyejin Lee, Seongsu Kang, Seung Jin Hwang, Nam Seo Son and Nae-Gyu Kang
Cosmetics 2025, 12(3), 91; https://doi.org/10.3390/cosmetics12030091 - 1 May 2025
Viewed by 963
Abstract
This study deals with the extraction of active compounds for a formula (Angelica gigas, Cornus officinalis, Ganoderma lucidum, Thymus vulgaris, and Asparagus cochinchinensis) and the evaluation of its skin anti-aging properties. This formulation was inspired by the [...] Read more.
This study deals with the extraction of active compounds for a formula (Angelica gigas, Cornus officinalis, Ganoderma lucidum, Thymus vulgaris, and Asparagus cochinchinensis) and the evaluation of its skin anti-aging properties. This formulation was inspired by the oriental medicine Gongjin-dan (Angelica gigas, Cornus officinalis, deer antler, and musk), which has been used as a restorative drug for longevity. Enzyme-based extraction and chemical purification were used to obtain a mixed fraction (GEF) enriched in glycopeptides and glycoproteins from the five herbal materials. The chemical characteristics of GEF, including the carbohydrate groups attached to the peptides and proteins, the total carbohydrate and protein contents, and the composition of monosaccharides and amino acids were determined. The chemical characteristics that were significantly different from those of the extract, generally prepared in the same ratio, were the abundance of glycopeptides and glycoproteins and the high proportions of conditionally essential amino acids (51.0%) and acidic/basic amino acids (67.7%). These are necessary components for strengthening the skin layers against aging. The in vitro skin anti-aging properties of GEF on human fibroblasts (HS68), keratinocytes (HaCaT), and adipose-derived mesenchymal stem cells (ADMSCs) were evaluated. It was found that MMP-1 gene expression was inhibited (18–28%) and fibrillin-1 protein (23–37%) was restored contrary to the effect of UV irradiation. COL1A1 and COL4A1 gene expression (25–35%), HAS2 gene expression (22–213%), and adipogenesis (15%) were facilitated. These results demonstrate the potential of GEF as a raw material for skin anti-aging and reinforce the scientific evidence supporting a traditional medicine with a long history. Full article
(This article belongs to the Section Cosmetic Dermatology)
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19 pages, 999 KiB  
Article
Development of a Predictive Model for the Biological Activity of Food and Microbial Metabolites Toward Estrogen Receptor Alpha (ERα) Using Machine Learning
by Maksim Kuznetsov, Olga Chernyavskaya, Mikhail Kutuzov, Daria Vilkova, Olga Novichenko, Alla Stolyarova, Dmitry Mashin and Igor Nikitin
Big Data Cogn. Comput. 2025, 9(4), 86; https://doi.org/10.3390/bdcc9040086 - 1 Apr 2025
Viewed by 654
Abstract
The interaction of estrogen receptor alpha (ERα) with various metabolites—both endogenous and exogenous, such as those present in food products, as well as gut microbiota-derived metabolites—plays a critical role in modulating the hormonal balance in the human body. In this study, we evaluated [...] Read more.
The interaction of estrogen receptor alpha (ERα) with various metabolites—both endogenous and exogenous, such as those present in food products, as well as gut microbiota-derived metabolites—plays a critical role in modulating the hormonal balance in the human body. In this study, we evaluated a suite of 27 machine learning models and, following systematic optimization and rigorous performance comparison, identified linear discriminant analysis (LDA) as the most effective predictive approach. A meticulously curated dataset comprising 75 molecular descriptors derived from compounds with known ERα activity was assembled, enabling the model to achieve an accuracy of 89.4% and an F1 score of 0.93, thereby demonstrating high predictive efficacy. Feature importance analysis revealed that both topological and physicochemical descriptors—most notably FractionCSP3 and AromaticProportion—play pivotal roles in the potential binding to ERα. Subsequently, the model was applied to chemicals commonly encountered in food products, such as indole and various phenolic compounds, indicating that approximately 70% of these substances exhibit activity toward ERα. Moreover, our findings suggest that food processing conditions, including fermentation, thermal treatment, and storage parameters, can significantly influence the formation of these active metabolites. These results underscore the promising potential of integrating predictive modeling into food technology and highlight the need for further experimental validation and model refinement to support innovative strategies for developing healthier and more sustainable food products. Full article
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