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Keywords = asymmetric length distribution

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27 pages, 8829 KB  
Article
A Study on the Effect of Transverse Flow Intensity on the Cavitation Characteristics of a Vehicle Launched Underwater
by Yao Shi, Jinyi Ren, Shan Gao, Guiyong Zhang and Guang Pan
Appl. Sci. 2026, 16(3), 1152; https://doi.org/10.3390/app16031152 - 23 Jan 2026
Viewed by 81
Abstract
The high-speed motion of a vehicle underwater induces cavitation, and the resulting cavity alters the surface pressure distribution and flow field characteristics. This study employs a numerical approach combining the kω SST (Shear Stress Transport) turbulence model, the VOF (Volume of [...] Read more.
The high-speed motion of a vehicle underwater induces cavitation, and the resulting cavity alters the surface pressure distribution and flow field characteristics. This study employs a numerical approach combining the kω SST (Shear Stress Transport) turbulence model, the VOF (Volume of Fluid) multiphase flow model, the Schnerr–Sauer cavitation model, and the overlapping mesh technique. The numerical method is validated through the good agreement between simulation results and experimental data for both cavity shape and vehicle trajectory, with a maximum relative error of 6.1% in vertical displacement. The results indicate that during the launch-tube exit phase, with σ=0.235 and Fr=47.9, the vehicle acceleration causes the pressure at its shoulder to drop below the saturated vapor pressure, initiating cavitation. Under transverse flow (intensity U = 0.016–0.05), the cavity becomes asymmetric. Specifically, the axial length and radial thickness on the back side are significantly larger than those on the face side, and this asymmetry intensifies with increasing transverse flow intensity. Furthermore, after exiting the launcher, the vehicle’s trajectory and attitude deflect towards the back side and the deflection amplitude increases, with horizontal displacement and attitude angle variation positively correlated with transverse flow intensity. Full article
(This article belongs to the Special Issue Research on the Movement Dynamics of Ships and Underwater Vehicles)
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19 pages, 6579 KB  
Article
Study on Torque and Contact Characteristics of Thrust Bearing with Skewed Rollers in No-Back Brake
by Tianming Ren, Shuanglu Li, Ziyu Cheng and Ming Feng
Machines 2026, 14(1), 132; https://doi.org/10.3390/machines14010132 - 22 Jan 2026
Viewed by 59
Abstract
To investigate the performance of skewed roller thrust bearings (SRTBs) in the no-back brake of horizontal stabilizer trim actuators (HSTAs), this study conducts systematic theoretical modelling, experimental validation, and numerical simulation focusing on torque and contact characteristic optimization. First, a theoretical model for [...] Read more.
To investigate the performance of skewed roller thrust bearings (SRTBs) in the no-back brake of horizontal stabilizer trim actuators (HSTAs), this study conducts systematic theoretical modelling, experimental validation, and numerical simulation focusing on torque and contact characteristic optimization. First, a theoretical model for resistance torque of the SRTB was established based on the kinematics and load behaviours, followed by a systematic investigation into the effects of roller centre position and skew angle on the bearing’s resistance torque. An experimental platform was built, and tests were carried out on the bearings to verify the results of the theoretical analysis. Subsequently, a tangent arc profile was applied to the rollers to mitigate stress concentration at their ends, and the influences of crown drop and straight segment length on roller contact stress were explored by finite element method. Finally, considering the actual operating conditions of no-back brake components, the effect of roller centre position on brake deformation and roller contact stress was studied. The results show that the resistance torque increases with both roller skew angle and centre position, but is insensitive to rotational speed. Roller contact stress first decreases rapidly and then increases gradually with crown drop, indicating the existence of an optimal crown drop value. This optimal value first decreases and then increases with increasing straight segment length, with the optimal parameters determined as 9 μm (crown drop) and 4 mm (straight segment length). In practical applications, asymmetric loading on the two sides of the ratchet disc causes uneven roller contact distribution and stress concentration. Adjusting the roller centre position to balance the deformation of the ratchet disc and rod shoulder can effectively reduce contact stress, with the optimal position being approximately 48 mm (slightly offset from the load centre of 49 mm). This study provides valuable insights for the optimal design of SRTBs and no-back brakes. Full article
(This article belongs to the Section Friction and Tribology)
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19 pages, 1087 KB  
Article
Neuromuscular and Kinetic Adaptations to Symmetric and Asymmetric Load Carriage During Walking in Individuals with Chronic Low Back Pain
by Raheleh Tajik, Wissem Dhahbi, Raghad Mimar, Mehdi Khaleghi Tazji, Halil İbrahim Ceylan, Serdar Bayrakdaroğlu, Valentina Stefanica and Nadhir Hammami
Bioengineering 2026, 13(1), 82; https://doi.org/10.3390/bioengineering13010082 - 12 Jan 2026
Viewed by 318
Abstract
Aim: This study examined how load size and symmetry affect trunk muscle activation patterns, vertical ground reaction forces, and estimated lumbar spine compression during overground walking in individuals with chronic low back pain (CLBP) and those without symptoms. Methods: Thirty male participants (15 [...] Read more.
Aim: This study examined how load size and symmetry affect trunk muscle activation patterns, vertical ground reaction forces, and estimated lumbar spine compression during overground walking in individuals with chronic low back pain (CLBP) and those without symptoms. Methods: Thirty male participants (15 with CLBP, 15 controls; ages 23–28 years) performed walking tests under four load conditions: symmetric and asymmetric carriage at 10% and 20% of body weight. Bilateral surface electromyography measured activation from seven trunk muscles (rectus abdominis, external oblique, internal oblique, latissimus dorsi, lumbar erector spinae, multifidus) and the thoracolumbar fascia region, normalized to maximum voluntary isometric contractions (%MVIC). Force plates recorded vertical ground reaction forces synchronized with heel-strike events. A repeated-measures ANOVA with Bonferroni corrections was used to analyze the effects of load configuration and magnitude. Results: Asymmetric loading at 20% body weight caused significantly higher peak vertical ground reaction forces compared to symmetric loading (mean difference = 47.3 N, p < 0.001), with a significant interaction between load magnitude and configuration (p = 0.004, ηp2 = 0.26). Participants with CLBP showed consistently higher trunk muscle activation throughout the gait cycle (peak: 37% MVIC vs. 30% MVIC in controls; p < 0.001, d = 1.68), with maximum recruitment at shorter muscle lengths and 24% less activation at optimal length (95% CI: 18.2–29.8%). The lumbar erector spinae and multifidus muscles exhibited the highest activation during asymmetric 20% loading in CLBP participants (0.282 and 0.263%MVIC, respectively), indicating compensatory neuromuscular strategies. Conclusion: Asymmetric load carriage creates disproportionately high mechanical and neuromuscular demands, effects that are greatly amplified in individuals with CLBP. These findings support rehabilitation strategies that improve load distribution and restore motor control, thereby reducing compensatory strain and enhancing trunk stability. Full article
(This article belongs to the Special Issue Biomechanics of Physical Exercise)
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20 pages, 2477 KB  
Article
Quadri-Wave Lateral Shearing Interferometry for Precision Focal Length Measurement of Optical Lenses
by Ze Li, Chi Fai Cheung, Wen Kai Zhao and Bo Wang
Appl. Sci. 2026, 16(2), 757; https://doi.org/10.3390/app16020757 - 11 Jan 2026
Viewed by 215
Abstract
The effective focal length is a critical determinant of optical performance and imaging quality, serving as a fundamental parameter for components ranging from ophthalmic lenses to precision microlens arrays. With the rapid advancement of complex optical systems in microscopy and smart manufacturing, there [...] Read more.
The effective focal length is a critical determinant of optical performance and imaging quality, serving as a fundamental parameter for components ranging from ophthalmic lenses to precision microlens arrays. With the rapid advancement of complex optical systems in microscopy and smart manufacturing, there is an increasing demand for high-precision measurement techniques that can characterize these parameters with low uncertainty. In this paper, a quadri-wave lateral shearing interferometry (QWLSI) measurement system was developed. A novel precision focal length measurement method of optical lenses based on the principle of QWLSI is presented. A theoretical model for solving the focal length of the measured lens from the curvature radius of the wavefront was derived. We also proposed a novel algorithm and subsequently developed a dedicated hardware platform and a corresponding software package for its real-time implementation. Different sets of repeated measurement experiments were carried out for two convex lenses with symmetrical and asymmetrical structures, a large-scale concave lens, and a microlens array, to verify the measurement uncertainty and robustness of the QWLSI measurement system. The expanded uncertainty was also analyzed and determined as 0.31 mm (k = 1.96, normal distribution). The results show that the proposed QWLSI measuring system possesses good performance in measuring the focal lengths of different kinds of lenses and can be widely used in fields such as advanced optics manufacturing. Full article
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34 pages, 7344 KB  
Article
Fitness-Driven Assessment of Mooring-System Designs for 15-MW FOWT in Shallow Waters
by Shun-Wen Cheng, Nai-Chi Chen, Cheng-Hsien Chung and Ray-Yeng Yang
J. Mar. Sci. Eng. 2026, 14(2), 142; https://doi.org/10.3390/jmse14020142 - 9 Jan 2026
Viewed by 167
Abstract
Offshore wind energy is a key enabler of the global net-zero transition. As nearshore fixed-bottom projects reach maturity, floating offshore wind turbines (FOWTs) are becoming the next major focus for large scale deployment. To accelerate this development and reduce construction costs, it is [...] Read more.
Offshore wind energy is a key enabler of the global net-zero transition. As nearshore fixed-bottom projects reach maturity, floating offshore wind turbines (FOWTs) are becoming the next major focus for large scale deployment. To accelerate this development and reduce construction costs, it is essential to optimize mooring systems through a systematic and performance driven framework. This study focuses on the mooring assessment of the Taiwan-developed DeltaFloat semi-submersible platform supporting a 15 MW turbine at a 70 m water depth offshore Hsinchu, Taiwan. A full-chain catenary mooring system was designed based on site specific metocean conditions. The proposed framework integrates ANSYS AQWA (version 2024 R1) and Orcina OrcaFlex (version 11.5) simulations with sensitivity analyses and performance-based fitness metrics including offset, inclination, and line tension to identify key parameters governing mooring behavior. Additionally, an analysis of variance (ANOVA) was conducted to quantitatively evaluate the statistical significance of each design parameter. Results indicate that mooring line length is the most influential factor affecting system performance, followed by line angle and diameter. Optimizing these parameters significantly improves platform stability and reduces tension loads without excessive material use. Building on the optimized symmetric configuration, an asymmetric mooring concept with unequal line lengths is proposed. The asymmetric layout achieves performance comparable to traditional 3 × 1 and 3 × 2 systems under extreme environmental conditions while demonstrating potential reductions in material use and overall cost. Nevertheless, the unbalanced load distribution highlights the need for multi-scenario validation and fatigue assessment to ensure long-term reliability. Overall, the study establishes a comprehensive and sensitivity-based evaluation framework for floating wind mooring systems. The findings provide a balanced and practical reference for the cost-efficient design of floating offshore wind farms in the Taiwan Strait and other shallow-water regions. Full article
(This article belongs to the Section Ocean Engineering)
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46 pages, 1025 KB  
Article
Confidence Intervals for the Difference and Ratio Means of Zero-Inflated Two-Parameter Rayleigh Distribution
by Sasipong Kijsason, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2026, 18(1), 109; https://doi.org/10.3390/sym18010109 - 7 Jan 2026
Viewed by 140
Abstract
The analysis of road traffic accidents often reveals asymmetric patterns, providing insights that support the development of preventive measures, reduce fatalities, and improve road safety interventions. The Rayleigh distribution, a continuous distribution with inherent asymmetry, is well suited for modeling right-skewed data and [...] Read more.
The analysis of road traffic accidents often reveals asymmetric patterns, providing insights that support the development of preventive measures, reduce fatalities, and improve road safety interventions. The Rayleigh distribution, a continuous distribution with inherent asymmetry, is well suited for modeling right-skewed data and is widely used in scientific and engineering fields. It also shares structural characteristics with other skewed distributions, such as the Weibull and exponential distributions, and is particularly effective for analyzing right-skewed accident data. This study considers several approaches for constructing confidence intervals, including the percentile bootstrap, bootstrap with standard error, generalized confidence interval, method of variance estimates recovery, normal approximation, Bayesian Markov Chain Monte Carlo, and Bayesian highest posterior density methods. Their performance was evaluated through Monte Carlo simulation based on coverage probabilities and expected lengths. The results show that the HPD method achieved coverage probabilities at or above the nominal confidence level while providing the shortest expected lengths. Finally, all proposed confidence intervals were applied to fatalities recorded during the seven hazardous days of Thailand’s Songkran festival in 2024 and 2025. Full article
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16 pages, 3991 KB  
Article
Study on Wind Load Distribution and Aerodynamic Characteristics of a Yawed Cylinder
by Xinxin Yuan, Zetao Li, He Yang, Fei Wang, Wenyong Ma, Qiaochu Zhao and Yong Yang
Buildings 2025, 15(23), 4390; https://doi.org/10.3390/buildings15234390 - 4 Dec 2025
Viewed by 319
Abstract
The flow mechanism around a yawed cylinder is highly complex. While previous research has confirmed the limitation of the Independence Principle at high yaw angles, the specific flow phenomena beyond 20° yaw remain poorly understood, particularly concerning the spanwise development of the critical [...] Read more.
The flow mechanism around a yawed cylinder is highly complex. While previous research has confirmed the limitation of the Independence Principle at high yaw angles, the specific flow phenomena beyond 20° yaw remain poorly understood, particularly concerning the spanwise development of the critical regime and the mechanism behind asymmetric surface pressure. Most studies have focused on spatially averaged forces or specific angles, lacking a systematic investigation of the inherent flow characteristics in the intermediate region of finite-length cylinders. To bridge this gap, the present study conducts a detailed wind tunnel test on a yawed cylinder across a wide range of yaw angles (0–60°). By analyzing the pressure distribution and aerodynamic forces in the mid-span region, this study yields the following core findings of universal significance: (1) As the yaw angle increases, the critical flow regime in the intermediate section occurs prematurely. This leads to a decrease in the Reynolds number at which the critical region begins, resulting in the formation of separation bubbles and consequent localized negative-pressure zones on either the upper or lower windward surface of the cylinder. (2) When the yaw angle β ≤ 17.4°, the mean drag and lift in the middle region resemble those of a straight cylinder. However, as the yaw angle increases further, the drag coefficient decreases beyond a certain critical Reynolds number, which itself decreases with increasing yaw angle. (3) At β = 0°, the circumferential mean pressure distribution is symmetric about the cross-sectional axis and remains largely uniform along the span. High yaw angles disrupt this symmetry and uniformity, leading to complex three-dimensional flow structures. These findings have critical implications for the design of structures like inclined bridge towers and cables under oblique winds. Full article
(This article belongs to the Special Issue Innovations in Composite Material Technologies and Structural Design)
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14 pages, 2582 KB  
Article
The Effect of the Axial Plasma Electron Density Distribution on the Effective Length and Radiation Pattern of a Plasma Antenna
by Nikolai N. Bogachev, Vyacheslav P. Stepin, Vsevolod I. Zhukov, Sergey E. Andreev, Dmitry M. Karfidov, Maksim S. Usachonak, Evgeny M. Konchekov and Namik G. Gusein-zade
Plasma 2025, 8(4), 49; https://doi.org/10.3390/plasma8040049 - 28 Nov 2025
Viewed by 907
Abstract
This study investigates the axial electron density distribution in two plasma antenna configurations excited by a surface wave microwave discharge and its influence on the radiation pattern of antennas. The axial plasma electron density profiles were characterized using two non-invasive diagnostic techniques: the [...] Read more.
This study investigates the axial electron density distribution in two plasma antenna configurations excited by a surface wave microwave discharge and its influence on the radiation pattern of antennas. The axial plasma electron density profiles were characterized using two non-invasive diagnostic techniques: the resonant cavity measurements in the TM110 mode and the waveguide transmission analysis. A linear decrease in the plasma electron density along the antenna was observed. The effective electrical length of the plasma antennas, accounting for this density distribution, is found to be approximately half the physical plasma column length. Numerical simulations employing COMSOL Multiphysics based on the Drude model revealed that a realistic nonuniform axial plasma electron density distribution markedly modifies the antenna radiation characteristics. For the wave-type plasma monopole antenna, this results in a shift in the emission maximum, a reduction in the main lobe amplitude, a nearly twofold broadening of the main lobe, and the disappearance of the side lobe. For the quarter-wave-type plasma asymmetric dipole antenna, there is a reduction in the main lobe amplitude without a shift in the maximum and a broadening of the main lobe due to an increase in the side-lobe level and its merging with the main lobe. Full article
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19 pages, 2083 KB  
Article
A Robust TEWMA–MA Control Chart Based on Sign Statistics for Effective Monitoring of Manufacturing Processes
by Piyatida Saesuntia, Yupaporn Areepong and Saowanit Sukparungsee
Mathematics 2025, 13(23), 3789; https://doi.org/10.3390/math13233789 - 26 Nov 2025
Viewed by 368
Abstract
A nonparametric control chart is a type of control chart that does not rely on assumptions regarding the underlying distribution of the data. This characteristic provides greater flexibility and robustness, particularly when handling non-normal data, skewed distributions, or datasets containing outliers. The primary [...] Read more.
A nonparametric control chart is a type of control chart that does not rely on assumptions regarding the underlying distribution of the data. This characteristic provides greater flexibility and robustness, particularly when handling non-normal data, skewed distributions, or datasets containing outliers. The primary objective of this study is to propose a nonparametric TEWMA–MA control chart based on the sign statistic, designed to operate under both symmetric and asymmetric distributions for effective process monitoring. This chart aims to enhance the ability to quickly detect shifts in the production process. The run-length characteristics obtained through Monte Carlo simulation (MC) were employed as performance measures. In addition, overall efficiency was assessed using AEQL, RMI, and PCI. The proposed control chart was compared against MA, TEWMA, MA–TEWMA, TEWMA–MA, and MA–TEWMA sign charts. The findings indicate that the proposed chart is effective for process control and demonstrates superior detection capability compared to competing charts, particularly in identifying small to moderate shifts. Furthermore, to validate its practical utility, the proposed control chart was applied to real-world data. Full article
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28 pages, 4652 KB  
Article
Research on the Influence of Span on Wind Deflection Angle of Insulator Strings in Stochastic Wind Fields
by Guanghui Liu, Zhongbin Lv, Bo Zhang, Chuan Wu, Zhan Huang, Xiaohui Liu and Jinze He
Symmetry 2025, 17(11), 1968; https://doi.org/10.3390/sym17111968 - 14 Nov 2025
Viewed by 398
Abstract
This paper presents an independently developed finite element analysis software built on the QT and VTK platforms. Its core innovation is the integration of the analytical solution from catenary theory with nonlinear finite element methods. The software accurately predicts the initial configuration and [...] Read more.
This paper presents an independently developed finite element analysis software built on the QT and VTK platforms. Its core innovation is the integration of the analytical solution from catenary theory with nonlinear finite element methods. The software accurately predicts the initial configuration and tension distribution of conductors based on catenary theory, utilizing these results as high-precision initial values for static equilibrium iterations. This approach overcomes the convergence difficulties commonly encountered in traditional commercial software when analyzing such flexible cable structures. Using this software, we systematically investigated the nonlinear effects of asymmetric span arrangements on the mean value and standard deviation of wind deflection angles, and subsequently established a practical wind deflection calculation model that accounts for span asymmetry. The study reveals that higher wind speeds lead to larger wind deflection angles, with static wind deflection angles approximating the mean values under pulsating wind conditions. When one span length is fixed, the wind deflection angle first increases and then decreases as the adjacent span length increases. Symmetrical span arrangements were found to amplify the fluctuation range of the wind deflection angles. The research further developed polynomial regression models to systematically analyze the influence of wind speed and span length on dynamic amplification factors and elucidate their interactions and nonlinear relationships. Finally, based on symbolic regression and least squares methods, three expressions for the dynamic amplification factor in terms of span length and wind speed were derived. These formulas all demonstrate certain engineering applicability for predicting the dynamic amplification factor. Full article
(This article belongs to the Section Engineering and Materials)
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17 pages, 1520 KB  
Article
Development of an Efficient CUSUM Control Chart for Monitoring the Scale Parameter of the Inverse Maxwell Distribution in Asymmetric, Non-Normal Process Monitoring with Industrial Applications
by Gul Nisa, Mahmoud M. Abdelwahab, Aamir Sanaullah, Mediha Maqsood, Mohamed A. Abdelkawy and Mustafa M. Hasaballah
Symmetry 2025, 17(11), 1819; https://doi.org/10.3390/sym17111819 - 29 Oct 2025
Viewed by 852
Abstract
Control charts are commonly practical as diagnostic tools in statistical applications to recognize probable changes in a process. Control charts find general use as diagnostic tools in statistics in the detection of probable shifts in a process. Among the variety of methods of [...] Read more.
Control charts are commonly practical as diagnostic tools in statistical applications to recognize probable changes in a process. Control charts find general use as diagnostic tools in statistics in the detection of probable shifts in a process. Among the variety of methods of detection of smaller shifts in processes, the cumulative sum (CUSUM) chart is the most useful in general use. The standard CUSUM chart is often based on the normal distribution, an assumption that does not often align with the quality characters of the majority of real processes. However, many real-world processes exhibit asymmetric and heavy-tailed behavior, which limits the performance of traditional symmetric control chart models. This study presents a new CUSUM control chart based on the inverse Maxwell (IM) distribution and terms it the IMCUSUM chart. The proposed chart’s performance is assessed based on run-length (RL) metrics, which comprise the RL average, the standard deviation of RL, and the median RL. Comparison with the existing IM exponentially weighted moving average (IMEWMA) chart is performed. The results reveal that the proposed IMCUSUM chart performs better compared with the existing IMEWMA chart, especially in the detection of small and moderate shifts in processes. The practical application of the proposed IMCUSUM chart is demonstrated with the application of the proposed and existing control charts in the survival analysis of the lifetimes of brake pads of cars. This real application example highlights the practical application of the proposed IMCUSUM chart in real processes. Full article
(This article belongs to the Section Mathematics)
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23 pages, 3161 KB  
Article
Characterizing Hydraulic Fracture Morphology and Propagation Patterns in Horizontal Well Stimulation via Micro-Seismic Monitoring Analysis
by Longbo Lin, Xiaojun Xiong, Zhiyuan Xu, Xiaohua Yan and Yifan Wang
Symmetry 2025, 17(10), 1732; https://doi.org/10.3390/sym17101732 - 14 Oct 2025
Viewed by 604
Abstract
In horizontal well technology, hydraulic fracturing has been established as an essential technique for enhancing hydrocarbon production. However, the complex architecture of fracture networks challenges conventional monitoring methods. Micro-seismic monitoring, recognized for its superior resolution and sensitivity, enables precise fracture morphology characterization. This [...] Read more.
In horizontal well technology, hydraulic fracturing has been established as an essential technique for enhancing hydrocarbon production. However, the complex architecture of fracture networks challenges conventional monitoring methods. Micro-seismic monitoring, recognized for its superior resolution and sensitivity, enables precise fracture morphology characterization. This study advances diagnostic capabilities through integrated field–laboratory investigations and multi-domain signal processing. Hydraulic fracturing experiments under varied geological conditions generated critical micro-seismic datasets, with quantitative analyses revealing asymmetric propagation patterns (total length 312 ± 15 m, east wing 117 m/west wing 194 m) forming a 13.37 × 104 m3 stimulated reservoir volume. Spatial event distribution exhibited density disparities correlating with geophone offsets (west wing 3.8 events/m vs. east 1.2 events/m at 420–794 m distances). Advanced time–frequency analyses and inversion algorithms differentiated signal characteristics demonstrating logarithmic SNR (Signal-to-Noise Ratio)–magnitude relationships (SNR 0.49–4.82, R2 = 0.87), with near-field events (<500 m) showing 68% reduced magnitude variance compared to far-field counterparts. Coupled numerical simulations confirmed stress field interactions where fracture trajectories deviated 5–15° from principal stress directions due to prior-stage stress shadows. Branch fracture networks identified in Stages 4/7/9/10 with orthogonal/oblique intersections (45–65° dip angles) enhanced stimulation reservoir volume (SRV) by 37–42% versus planar fractures. These geometric parameters—including height (20 ± 3 m), width (44 ± 5 m), spacing, and complexity—were quantitatively linked to micro-seismic response patterns. The developed diagnostic framework provides operational guidelines for optimizing fracture geometry control, demonstrating how heterogeneity-driven signal variations inform stimulation strategy adjustments to improve reservoir recovery and economic returns. Full article
(This article belongs to the Special Issue Feature Papers in Section "Engineering and Materials" 2025)
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32 pages, 5558 KB  
Article
Research on Urban UAV Path Planning Technology Based on Zaslavskii Chaotic Multi-Objective Particle Swarm Optimization
by Chaohui Lin, Hang Xu and Xueyong Chen
Symmetry 2025, 17(10), 1711; https://doi.org/10.3390/sym17101711 - 12 Oct 2025
Viewed by 865
Abstract
Research on unmanned aerial vehicle (UAV) path planning technology in urban operation scenarios faces the challenge of multi-objective collaborative optimization. Currently, mainstream path planning algorithms, including the multi-objective particle swarm optimization (MOPSO) algorithm, generally suffer from premature convergence to local optima and insufficient [...] Read more.
Research on unmanned aerial vehicle (UAV) path planning technology in urban operation scenarios faces the challenge of multi-objective collaborative optimization. Currently, mainstream path planning algorithms, including the multi-objective particle swarm optimization (MOPSO) algorithm, generally suffer from premature convergence to local optima and insufficient stability. This paper proposes a Zaslavskii chaotic multi-objective particle swarm optimization (ZAMOPSO) algorithm to address these issues. First, three-dimensional urban environment models with asymmetric layouts, symmetric layouts, and no-fly zones were constructed, and a multi-objective model was established with path length, flight altitude variation, and safety margin as optimization objectives. Second, the Zaslavskii chaotic sequence perturbation mechanism is introduced to improve the algorithm’s global search capability, convergence speed, and solution diversity. Third, nonlinear decreasing inertia weights and asymmetric learning factors are employed to balance global and local search abilities, preventing the algorithm from being trapped in local optima. Additionally, a guidance particle selection strategy based on congestion distance is introduced to enhance the diversity of the solution set. Experimental results demonstrate that ZAMOPSO significantly outperforms other multi-objective optimization algorithms in terms of convergence, diversity, and stability, generating Pareto solution sets with broader coverage and more uniform distribution. Finally, ablation experiments verified the effectiveness of the proposed algorithmic mechanisms. This study provides a promising solution for urban UAV path planning problems, while also providing theoretical support for the application of swarm intelligence algorithms in complex environments. Full article
(This article belongs to the Section Computer)
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27 pages, 358 KB  
Article
Re-Examining Confidence Intervals for Ratios of Parameters
by Zaka Ratsimalahelo
Econometrics 2025, 13(3), 37; https://doi.org/10.3390/econometrics13030037 - 20 Sep 2025
Viewed by 984
Abstract
This paper considers the problem of constructing confidence intervals (CIs) for nonlinear functions of parameters, particularly ratios of parameters a common issue in econometrics and statistics. Classical CIs (such as the Delta method and the Fieller method) often fail in small samples due [...] Read more.
This paper considers the problem of constructing confidence intervals (CIs) for nonlinear functions of parameters, particularly ratios of parameters a common issue in econometrics and statistics. Classical CIs (such as the Delta method and the Fieller method) often fail in small samples due to biased parameter estimators and skewed distributions. We extended the Delta method using the Edgeworth expansion to correct for skewness due to estimated parameters having non-normal and asymmetric distributions. The resulting bias-corrected confidence intervals are easy to compute and have a good coverage probability that converges to the nominal level at a rate of O(n1/2) where n is the sample size. We also propose bias-corrected estimators based on second-order Taylor expansions, aligning with the “almost unbiased ratio estimator” . We then correct the CIs according to the Delta method and the Edgeworth expansion. Thus, our new methods for constructing confidence intervals account for both the bias and the skewness of the distribution of the nonlinear functions of parameters. We conduct a simulation study to compare the confidence intervals of our new methods with the two classical methods. The methods evaluated include Fieller’s interval, Delta with and without the bias correction interval, and Edgeworth expansion with and without the bias correction interval. The results show that our new methods with bias correction generally have good performance in terms of controlling the coverage probabilities and average length intervals. They should be recommended for constructing confidence intervals for nonlinear functions of estimated parameters. Full article
16 pages, 1551 KB  
Article
Probabilistic Estimation of During-Fault Voltages of Unbalanced Active Distribution: Methods and Tools
by Matteo Bartolomeo, Pietro Varilone and Paola Verde
Energies 2025, 18(18), 4791; https://doi.org/10.3390/en18184791 - 9 Sep 2025
Viewed by 613
Abstract
In low-voltage (LV) distribution networks, system operating conditions are always unbalanced due to the unpredictability of the load demand in each phase, coupled with a potentially asymmetrical network structure due to different phase conductors’ sizes and lengths. The widespread diffusion of distributed generators [...] Read more.
In low-voltage (LV) distribution networks, system operating conditions are always unbalanced due to the unpredictability of the load demand in each phase, coupled with a potentially asymmetrical network structure due to different phase conductors’ sizes and lengths. The widespread diffusion of distributed generators (DGs) among network users has significantly contributed to reducing the overall load of the electrical system, but at the cost of making voltages slightly more unbalanced. In this article, an LV distribution test network equipped with several single-phase DGs has been considered, and all During-Fault Voltages (DFVs) have been studied, according to each possible type of short circuit. To provide a measure of the asymmetry of unsymmetrical voltage dips, three different indices based on the symmetrical components of the voltages have been considered; moreover, the Monte Carlo simulation (MCS) method has allowed for studying faults and asymmetries in a probabilistic manner. Through the probability density functions (pdfs) of the DFVs, it has been possible to assess the impact of single-phase DGs on the asymmetry of bus voltages due to short-circuits. Full article
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