Search Results (899)

The development of More Electric Aircraft (MEA) necessitates that Electro-Hydrostatic Actuator (EHA) controllers achieve exceptional power density within rigorously constrained volumes. However, the compact layout design of these controllers constitutes a challenging NP-hard problem, characterized by strong multi-physics coupling—such as electromagnetic, thermal, and structural fields—and complex nonlinear constraints. Traditional meta-heuristic algorithms frequently suffer from premature convergence and struggle to balance global exploration with local exploitation. To address these challenges, the core contribution of this paper is the proposal of a novel Fractional-Order Anteater Foraging Optimization Algorithm (AFO), which is successfully applied to an established EHA controller layout optimization model. At the algorithmic level, by incorporating the Grünwald–Letnikov fractional derivative, the algorithm exploits the inherent memory property of fractional calculus to dynamically adjust the search step size and direction based on historical evolutionary information, thereby preventing stagnation in local optima. At the engineering application level, a high-fidelity mathematical model of the EHA controller is established, comprising 11 design variables and 10 critical physical constraints, including parasitic inductance minimization, thermal radiation efficiency, and electromagnetic interference (EMI) isolation. Extensive validation against the CEC2005 and CEC2022 benchmark functions demonstrates the superior convergence accuracy and stability of the AFO algorithm. In a specific EHA case study, the proposed method reduced the controller volume by 33.9% while strictly satisfying all multi-physics constraints, compared to traditional methods. Furthermore, a physical prototype was fabricated based on the optimized layout, and experimental tests confirmed its stable operation and excellent thermal performance. The results validate the efficacy of incorporating fractional calculus into bio-inspired algorithms to solve complex, high-dimensional engineering optimization problems. Full article

This paper presents a unified theoretical and numerical investigation of Hilfer-type fuzzy fractional control systems with infinite continuous delay. By employing contraction mapping principles and compact semigroup theory, we establish rigorous solvability conditions together with Ulam–Hyers–Rassias stability results expressed in terms of Mittag–Leffler functions. To complement the analytical framework, we design and implement numerical schemes based on Euler and IMEX approaches, which confirm the theoretical predictions through simulations. The computational experiments demonstrate the robustness of the proposed framework under delayed feedback and fractional memory effects, highlighting its relevance to practical domains such as biological regulation, porous media transport, and intelligent traffic systems. The contribution of this study lies in the bridge between mathematical rigor and computational implementation, thus advancing the theory of fractional differential inclusions and providing a versatile tool for the stability analysis and control of complex systems with uncertainty and hereditary dynamics. Full article

Pore structure and multifractal characteristics are two critical indicators for evaluating the heterogeneity of tight sandstone reservoirs. An integrated analysis comprising physical property tests, X-ray diffraction, casting thin sections, scanning electron microscopy, high-pressure mercury intrusion (HPMI), and constant-rate mercury intrusion (CRMI) is conducted on five samples from the Jurassic Sangonghe Formation in the northern Turpan-Hami Basin to investigate the full-scale pore size distribution (FPSD) and its multifractal characteristics. The results indicate that the pores in tight sandstone are mainly residual intergranular pores, dissolution pores, intercrystalline pores, and microfractures. The FPSD exhibits a bimodal or trimodal pattern, with dominant pore sizes ranging from 0.00516 μm to 1.15 $\mathsf{\mu }\mathrm{m}$. Two key multifractal parameters, the multifractal dimension range ($D_{min}-D_{max}$) and the relative dispersion ($R_d$), were utilized to effectively characterize pore structure heterogeneity and asymmetry. Higher $D_{min}-D_{max}$ values correspond to stronger heterogeneity, whereas lower $R_d$ values indicate a dominance of nanoscale pores. Furthermore, $D_{min}-D_{max}$ and $R_d$ exhibit negative correlations with permeability and clay mineral content, and positive correlations with feldspar content. This study demonstrates the utility of FPSD in characterizing pore structure and highlights the applicability of multifractal theory in assessing the heterogeneity of tight sandstone reservoirs. Full article

Understanding the evolution of coal pore–fracture structures under coupled stress paths and creep deformation is critical for enhancing coalbed methane extraction and preventing coal and gas outbursts. In this study, coal samples from the Ningtiaota Mine were investigated using online Nuclear Magnetic Resonance (NMR) technology combined with triaxial loading–creep coupled experiments. The dynamic evolution of pore–fracture structures (PFSs) under different deviatoric stress levels was characterized and visualized in real time and across multiple scales. The results reveal a pronounced stress-dependent pore evolution during creep. Under low-stress conditions, seepage pores were compressed and gradually transformed into adsorption pores, whereas under high-stress conditions, seepage pores expanded and interconnected, dominating deformation and failure. Fractal theory was employed to quantify pore structure complexity, and repeated experiments demonstrated a significant positive correlation between the fractal dimension and the fractional order. Based on these findings, a fractal-dimension-based fractional creep model was developed by introducing a Riemann–Liouville fractional dashpot. The proposed model accurately captures the nonlinear creep behavior of coal and provides a microstructural interpretation of the fractional order. This study provides theoretical and experimental support for long-term stability assessment of deep coal–rock masses and prediction of coalbed methane migration. Full article

Pneumatic transmission lines play a critical role in the dynamic performance of soft robotic actuation systems, yet their behaviour is difficult to capture using conventional integer-order (IO) models. In long, slender pipelines, compressibility, viscothermal losses, and wave propagation give rise to distributed damping and non-exponential relaxation dynamics that are not well represented by finite-dimensional models. This paper presents a control-oriented, experimentally validated fractional-order (FO) modelling framework for pneumatic pipeline dynamics under closed-end boundary conditions. Models are calibrated using measured step-response data from a 13.2 m pipeline, with all parameters—including the fractional order—identified through a unified optimisation procedure. In addition to global fitting accuracy, model performance is evaluated using control-relevant metrics, including effective delay, initial slope and early transient behaviour, and early-time error. The results show that FO models provide a more compact and structurally consistent representation of long-memory dynamics while improving the accuracy of control-relevant features compared to their IO counterparts. These findings demonstrate that fractional dynamics offer a physically meaningful and practically useful framework for modelling pneumatic transmission lines, with direct implications for high-performance control design in soft robotic systems. Full article

This article focuses on the fixed-time synchronization problem for fractional-order fuzzy cellular neural networks (FOFCNNs) with information interactions and time-varying delays. To capture the complex dynamics of practical networks, nonlinear activation functions along with fuzzy AND and OR operators are incorporated into the master–slave systems. To achieve fixed-time synchronization despite these complexities, a novel adaptive multi-module controller is proposed. This controller integrates three functionally distinct components to accelerate the convergence rate, eliminate the effects of delays, and introduce negative feedback during communication, respectively. By employing fractional calculus tools, inequality techniques, and the proposed control law, sufficient criteria for the synchronization of the considered systems are rigorously established. Compared with existing synchronization works, this paper has significant advantages in model generality and controller design. Additionally, an explicit settling-time estimate is derived, which depends solely on control parameters and is independent of the initial conditions. Full article

Coalbed methane is vital for the transition toward low-carbon energy systems, yet its recovery efficiency is critically limited by inaccurate classification of movable water during drainage and depressurization due to the complex pore–fracture system. To understand the influence of the pore–fracture structure on water flow law in coal reservoirs, this study constructed the relationship based on the memory effect of multiscale complex pore–fracture structures on seepage. Nuclear magnetic resonance (NMR) measurements were performed on water-saturated coal samples both before and after centrifugation, enabling the experimental identification of absolute irreducible water, partial movable water, and absolute movable water and yielding dual cutoffs. The complexity of the pore–fracture structure of the samples was quantified by multifractal analysis of the NMR test results. A fractional derivative model was developed to determine dual cutoffs, T_2c1 and T_2c2, based on the memory effect and validated against experimental data. Compared to empirical models, the proposed fractional derivative model improves R² fitting accuracy by 4.2% for T_2c1 and 9.7% for T_2c2, demonstrating its superior capability in translating structural complexity into physically meaningful cutoff determination. This work provides a mechanism-based approach for water typing, presenting a reliable foundation for drainage and depressurization in coalbed methane reservoir. Full article

Moderate thermal exposure can significantly influence the mechanical behavior of volcanic rocks by inducing microcrack development and altering crack network characteristics. However, quantifying such damage processes remains challenging when relying solely on conventional mechanical parameters. In this study, the evolution of crack network complexity in andesite and andesitic–basaltic rocks subjected to moderate thermal exposure (200 °C) is investigated using fractal analysis integrated with mechanical and mineralogical observations. Six core specimens were tested under uniaxial compression, including three natural specimens and three specimens thermally treated at 200 °C prior to loading. After failure, crack surfaces were digitized and fractal dimensions (D) were calculated using the box-counting method. Petrographic observations and X-ray powder diffraction (XRPD) analyses were conducted to characterize the mineralogical composition and microstructural features controlling crack development. The results indicate that thermal exposure primarily reduces rock stiffness rather than peak strength. While the uniaxial compressive strength (UCS) of two specimens remains nearly unchanged after heating, the elastic modulus (E) decreases in all thermally treated specimens. Mineralogical observations reveal a heterogeneous volcanic fabric dominated by plagioclase and pyroxene within a fine-grained groundmass, with secondary calcite phases occurring in veins and pocket fillings. Fractal analysis shows generally lower D values in thermally treated specimens, suggesting crack redistribution and coalescence rather than increased network complexity, consistent with the observed reduction in stiffness and a tendency toward more ductile deformation behavior. Full article

This paper investigates the finite time stability (FTS) of multi-delayed systems with Riemann-Liouville fractional order (RLFO). Firstly, a lemma on the FTS criterion is established for RLFO multi-delay systems, which lays the theoretical groundwork for the subsequent analysis of network synchronization and identification. Secondly, for hybrid coupled complex networks (CNs) with RLFO, multiple delays, and a non-Lipschitz vector field, we explore finite-time synchronization and topology identification (TI) without imposing the linear independence condition (LIC). This is achieved by constructing: (1) a regulated control network with topology observers, and (2) an auxiliary network with isolated nodes. Based on the proposed FTS criterion, along with the designed control protocol and adaptive topology observer, sufficient conditions for the finite time synchronization and TI of multi-delayed CNs are derived as linear matrix inequalities (LMIs). Finally, a numerical simulation on the Lorenz system is carried out to validate the derived results and evaluate the efficacy of the proposed method. Full article

The dominant pores governing methane adsorption in coal are micropores (pore size < 2 nm). Their spatial heterogeneity can be quantitatively characterized using multifractal theory; however, the evolution patterns and mechanisms of microporous structures across different coalification degrees remain unclear. This research selected a series of coal samples from different ranks and identified the coalification degree using the maximum vitrinite reflectance (Rₒ_,max). By comprehensively employing low-temperature CO₂ adsorption experiments and multifractal analysis, the evolution patterns of the microporous structures and their multifractal spectral parameters were systematically revealed, and the underlying control mechanisms were explored. Results indicate that micropore volume (PV) and specific surface area (SSA) first exhibit a decrease and then increase as Rₒ_,max increases, with the trough occurring during the second coalification jump at Rₒ_,max = 1.2–1.4%. The pore sizes exhibit bimodal distributions, with the primary peak occurring in the range of 0.45–0.65 nm and the secondary peak occurring in the range of 0.8–0.9 nm. All microporous structures possess pronounced multifractal characteristics. The generalized dimension spectrum width (ΔD) and singularity spectrum width (Δα) exhibit an increasing–decreasing–increasing trend with Rₒ_,max, whereas the Hurst exponent (H) follows an inverted parabolic curve, first increases then decreases. This contrasts with the trends in PV and SSA, indicating that the evolution of pore-space heterogeneity and connectivity is independent of and lags the changes in micropore quantity. These patterns are governed by a structural phase transition within the coal macromolecular network. Marked by the second coalification jump, the microporous system shifts from a flexible degradation–polycondensation paradigm to a rigid ordering–construction paradigm. This transition drives the asynchronous, synergistic evolutions of pore quantity, spatial heterogeneity (ΔD and Δα), and topological connectivity (H). This research provides a theoretical basis for quantitatively evaluating pore heterogeneity in coal reservoirs. Full article

The motivation for this paper is that most of the works on secondary frequency control are focused on conventional synchronous communication approaches. To extend this research, this paper investigates the sampled-data-based $H_{\infty }$ load frequency control (LFC) problem for fractional-order islanded microgrids under a multi-region communication scheme. In contrast to conventional synchronous communication approaches, the proposed scheme allows each regional sensor to operate asynchronously based on its own sampling interval. To model this multi-region communication mechanism, a unified sampling sequence is constructed by collecting all sampling instants from regional sensors. Accordingly, a closed-loop system model is established through the introduction of virtual state variables. Furthermore, a novel class of looped functionals is developed to fully exploit the sampling interval characteristics of each regional sensor. By employing inequality techniques and stability analysis, sufficient conditions are derived to achieve multi-region sampled-data-based $H_{\infty }$ LFC for fractional-order islanded microgrids. In addition, a co-design method is proposed to simultaneously determine the control gain and the maximum allowable sampling period. The simulations are conducted in MATLAB/Simulink (R2024a) and the LMI conditions are solved by using the LMI Toolbox and YALMIP. Finally, comprehensive simulations in MATLAB/Simulink validate the proposed scheme. For the two-region system, the method achieves a maximum sampling period of ${\zeta }_{\max }=0.106$ s with an $H_{\infty }$ performance ratio of $2.87$ (below $\gamma =5$) and settling times of $8.5$ s and $9.2$ s. Compared to synchronous sampling, it reduces the communication bandwidth by 50% for slower regions while maintaining comparable performance. For the single-region multi-rate case ($0.104$ s and $0.140$ s sampling periods), the $H_{\infty }$ ratio is $3.12$, also satisfying $\gamma =5$. The relationship between $\gamma$ and ${\zeta }_{\max }$ is quantified: ${\zeta }_{\max }$ increases from $0.050$ s to $0.106$ s as $\gamma$ increases from 3 to 5, confirming that relaxed disturbance attenuation allows larger sampling intervals. Full article

Understanding how pore-system geometry governs mechanical performance remains essential for designing slag-blended cementitious materials. This study investigates the time-dependent coupling between porosity P and fractal dimension D and its implications for strength development and brittleness evolution in cementitious materials with slag dosage variation (0–40%). Compressive strength (f_c), flexural strength (f_f), the compressive-to-flexural strength ratio (f_c/f_f, used as a practical brittleness proxy), porosity (%), fractal dimension, and low-field nuclear magnetic resonance (LF-NMR) permeability (k, mD) were evaluated at 3, 7, and 28 days. Results reveal a pronounced age dependence in microstructure–property relationships. At 28 days, increasing slag dosage led to monotonic pore refinement and geometric reorganization, evidenced by reduced porosity (4.84% → 3.88%), increased fractal dimension (2.754 → 2.820), and decreased permeability (0.00025 → 0.00011 mD), accompanied by enhanced mechanical performance (47.73 → 49.33 MPa in f_c; 6.34 → 7.11 MPa in f_f) and reduced brittleness (f_c/f_f: 7.53 → 6.94). In contrast, a critical 7-day decoupling was observed: slag mixtures exhibited substantially lower porosity (≈5.42–5.69% vs. 7.07% for the reference) yet lower compressive strength (≈34.81–35.29 MPa vs. 38.65 MPa), indicating that porosity alone is insufficient to interpret early-age compressive capacity. Across ages, permeability and fractal trends highlight the role of pore-network connectivity and geometric complexity in governing transport resistance and fracture-related behavior. Overall, the findings demonstrate that a time-dependent porosity–fractal coupling framework provides a coherent pathway “from pore geometry to strength,” particularly for brittleness-relevant indices where geometric effects are amplified. Full article

In this paper, we investigate the (1 + 1)-dimensional nonlinear truncated M-fractional FitzHugh–Nagumo model. The main objective is to analyze the dynamical behavior and obtain exact solutions for the model. First, a fractional transformation is applied to convert the governing partial differential equation into an ordinary differential equation. Subsequently, a Galilean transformation is employed to reduce the resulting equation to a dynamical system. The bifurcation structure and chaotic dynamics of the model are then examined. The presence of chaos is further confirmed through the phase portrait, basin of attraction, return map, Lyapunov exponent, permutation entropy, Poincaré map, power spectrum, attractor, fractal dimension, multistability, time analysis, and recurrence plot. In addition, the sensitivity of the system to the initial conditions is analyzed. Finally, exact solutions for the model are constructed using the unified Riccati equation expansion method. The obtained results are illustrated using two-dimensional, three-dimensional, and contour plots. Full article

Wetting–air-drying cycling significantly alters the internal damage evolution and failure behavior of sandstone, and identifying reliable acoustic-emission (AE) precursors during loading is important for understanding the rupture mechanism of water-affected rock. In this study, uniaxial compression tests with AE monitoring were conducted on green sandstone subjected to different numbers of wetting–air-drying cycles. Ringing counts, RA–AF parameters, b-value evolution, AE spatial localization, and the correlation dimension D₂ were jointly used to characterize mechanical deterioration, failure-mode transition, and fractal dynamic evolution. The results show that increasing cycling causes a progressive decrease in peak stress and elastic modulus, while AE activity evolves from a relatively dispersed state to stronger pre-peak concentration. The RA–AF distributions indicate that the dominant AE population gradually shifts from tensile-feature dominance toward mixed/shear-involved behavior, suggesting increasing shear participation during failure. The b-value captures stage-dependent damage evolution but exhibits relatively strong fluctuations under increasingly nonstationary event distributions. In contrast, D₂ shows a clearer pre-peak turning feature, and the corresponding stress level remains relatively consistent among different cycling groups. These results indicate that wetting–air-drying cycling not only accelerates the mechanical degradation of green sandstone, but also substantially modifies its rupture dynamics. The D₂ feature may therefore serve as a potential precursor parameter for characterizing pre-peak complexity transition in water-affected sandstone. Full article

This paper investigates the fractal dynamical behavior of a discrete Caputo fractional-order hepatitis C virus model. First, we analyze the stability of the system by using spectral radius and design the fractional-order controller based on coordinate transformation. Then, a nonlinear coupling controller is constructed to achieve synchronization between two fractional-order models with different parameters and different fractional orders, and the synchronization is supported by rigorous mathematical proof. Numerical simulations are used to verify the effectiveness of control and synchronization. Full article