Modelling, Volume 6, Issue 3 (September 2025) – 61 articles

The mixing process of powder materials determines the final quality of industrial products. This study employs the Discrete Element Method (DEM) to numerically characterize the effects of particle shape and mixer structure on mixing performance. Using the superquadratic equation, nine types of particles with regular shape variations are constructed, and mixing models are further simulated. The feasibility of superquadratic-generated particles is validated through a classic drum calibration experiment. To investigate the intrinsic mechanisms of particle shape effects, the motion and contact behaviors of particles are quantified by the diffusion index, proportion of rotational kinetic energy, interparticle compressive force, and contact number. Meanwhile, to examine geometry effects, three supplementary mixing simulations are conducted by varying the plow angle and deactivating the choppers. The results show that Cubic particles exhibited poor mixing performance, while disk-shaped particles outperformed cylindrical ones; Increasing the plow blade inclination angle enhanced particle convection and diffusion, whereas excessively small angles may fail to achieve homogeneous mixing; The auxiliary shear of chopper blades promoted particle diffusion, effectively overcoming dead zones between plow blade intervals. Full article

A novel rolling scheme incorporating an inclined oval-caliber configuration is proposed to enhance plastic deformation mechanisms in the traditional oval–round rolling sequence. Finite Element Method (FEM) simulations were performed using DEFORM-3D to evaluate and optimize this new scheme across multiple objectives: maximizing average effective strain, minimizing strain non-uniformity (captured via the standard deviation of effective strain), and minimizing rolling force. Numerical modeling was conducted for calibration angles of γ = 0°, 25°, 35°, and 45°, from which Pareto-optimal solutions were identified based on classical non-dominance criteria. Pairwise 2D projections of the Pareto front enabled visualization of trade-offs and revealed γ = 35° as the Pareto knee-point, representing the most balanced compromise among high deformation intensity, increased uniformity, and reduced energy consumption. This optimal angle was further corroborated through a normalized weighted sum of the objective functions. The findings provide a validated reference for designing prototype deforming tools and support future experimental validation. Full article

The energy consumption of buildings, the effectiveness of energy-saving measures, and the exploitation of energy-saving potential are strategic issues for improving the energy performance of public assets and limiting their environmental impact. However, small and medium municipalities (SMMs) encounter difficulties in identifying their energy-intensive units, a process that is often lengthy (3 to 18 months), costly, and dependent on traditional methods such as the Real Estate and Energy Master Plan (REMP) promoted by ADEME or the Cit’ergie system. These approaches, although structured, rely on time-consuming manual analyses that require significant technical and human resources. This article proposes an innovative solution, PG2E, based on a combinatorial approach that quickly identifies Energy-Saving Potential Scope (ESPSs) from energy consumption data. Backed by a realistic–critical stance to assess the limitations of existing systems and a constructivist–pragmatic approach to designing a tool adapted to SMMs, the PG2E solution uses simple statistical criteria (average, upper quartile). This study, conducted in the town of Quesnoy-Sur-Deûle, shows that PG2E identifies ESPS with a success rate of 60% to 100% while reducing time and costs. It thus offers an accessible digital alternative for initiating an approach that complies with the ISO 50001 standard. Full article

Within the field of permanent magnet synchronous motor sensorless speed control systems, we present a novel scheme with a Multi-dimensional Taylor Network (MTN)-based nonlinear observer as the core, supplemented by two auxiliary MTN modules to realize closed-loop control: (1) MTN Model Identifier: Provides real-time PMSM nonlinear dynamic feedback for the observer; (2) MTN Adaptive Inverse Controller: Compensates for load disturbances using the observer’s estimated states. The study focuses on optimizing the MTN observer to address key limitations of existing methods (high computational complexity, lack of stability guarantees, and low estimation accuracy). Compared with the neural network observer, this MTN-based scheme stands out due to its straightforward structure and significantly reduced approximately 40% computational complexity. Specifically, the intricate calculations and high resource consumption typically associated with neural network observers are circumvented. Subsequently, by leveraging Lyapunov theory, an adaptive learning rule for the MTN weights is meticulously devised, which seamlessly bridges the theoretical proof of the nonlinear observer’s stability. Simulation results demonstrate that the proposed MTN observer achieves rapid convergence of speed and position estimation errors (with steady-state errors within ±0.5% of the rated speed and ±0.02 rad for rotor position) after a transient period of less than 0.2 s. Even when stator resistance is increased by tenfold to simulate parameter variations, the observer maintains high estimation accuracy, with speed and position errors increasing by no more than 1.2% and 0.05 rad, respectively, showcasing strong robustness. These results collectively confirm the efficacy and practical value of the proposed scheme in PMSM sensorless speed control. Full article

From the perspectives of theoretical design and practical application, the existing fault diagnosis methods with the complex identification process owing to manual feature extraction and the insufficient feature extraction for time series data and weak fault signal is not suitable for AC/DC microgrids. Thus, this paper proposes a fault diagnosis method that integrates a convolutional neural network (CNN) with a long short-term memory (LSTM) network and attention mechanisms. The method employs a multi-scale convolution-based weight layer (Weight Layer 1) to extract features of faults from different dimensions, performing feature fusion to enrich the fault characteristics of the AC/DC microgrid. Additionally, a hybrid attention block-based weight layer (Weight Layer 2) is designed to enable the model to adaptively focus on the most significant features, thereby improving the extraction and utilization of critical information, which enhances both classification accuracy and model generalization. By cascading LSTM layers, the model effectively captures temporal dependencies within the features, allowing the model to extract critical information from the temporal evolution of electrical signals, thus enhancing both classification accuracy and robustness. Simulation results indicate that the proposed method achieves a classification accuracy of up to 99.5%, with fault identification accuracy for noisy signals under 10 dB noise interference reaching 92.5%, demonstrating strong noise immunity. Full article

Classifying study objects into groups is facilitated by fuzzy classifiers based on a set of rules and membership functions. Typically, the characteristics of the study objects are used to establish the criteria for classification. This work arises from the need to design fuzzy classifiers in contexts where real data is scarce or highly random, proposing a design based on statistics and chaotic maps that simplifies the design process. This study introduces the development of a fuzzy classifier, assuming that three features of the population to be classified are random variables. A Mamdani fuzzy inference system and three pseudorandom number generators based on one-dimensional chaotic maps are utilized to achieve this. The logistic, Bernoulli, and tent chaotic maps are implemented to emulate the random features of the target population, and their statistical distribution functions serve as input to the fuzzy inference system. Four experimental tests were conducted to demonstrate the functionality of the proposed classifier. The results show that it is possible to achieve a symmetric and robust classification through simple adjustments to membership functions, without the need for supervised training, which represents a significant methodological contribution, especially because this indicates that designers with minimal experience can build effective classifiers in just a few steps. Real applications of the proposed design may focus on the classification of biomedical signals (sEMG), network traffic, and personalized medical assistance systems, where data exhibits high variability and randomness. Full article

High-performance sports cars rely on aerodynamics for stability and speed, but developing aero packages is challenging when wind tunnel testing is limited. In this study, we employed a simulation-guided design loop to maximize downforce and minimize drag on a sports car using Computational Fluid Dynamics (CFD). Thirteen aerodynamic modifications—including splitters, ducts, diffusers, and a Drag Reduction System (DRS)—were iteratively tested using CFD. To ensure numerical reliability, a mesh independence study and convergence analysis were performed, confirming stable aerodynamic predictions. The final configuration achieved an ~11× increase in downforce at 120 km/h (from about 320 N to 3588 N), meeting the design goal of roughly 2000 kg of downforce at 177 mph when scaled. This extreme downforce came with higher drag ($C_D$ ≈ 0.83), so a dual-mode approach was developed: a DRS configuration provides moderate downforce with 50% less drag ($C_D$ ≈ 0.41) for high-speed efficiency. A 1:12-scale wind tunnel test qualitatively supported the CFD predictions by visualizing wake narrowing and improved flow attachment. While quantitative force validation was not possible due to Reynolds mismatch and facility constraints, the qualitative results increased confidence in the CFD-based findings. Overall, the study demonstrates that substantial aerodynamic gains can be achieved under resource constraints, offering a practical framework for motorsport engineers and manufacturers to optimize aero kits when conventional full-scale testing is not accessible. Full article

Electric vehicles are playing an important role in transport, aided by rapid advances in battery technology. The Faculty of Engineering at the University of Debrecen is also engaged research and development in the field of electric vehicles. To support the development of electric vehicle prototypes, a vehicle dynamics simulation program has been designed. The study presents the modeling and simulation of a permanent magnet synchronous motor (PMSM) in MATLAB/Simulink, which has been integrated into the existing vehicle dynamics simulation framework. The methods used to determine the motor characteristics required for the simulation are described in detail. In addition, the performance of the PMSM is compared with that of a brushless DC (BLDC) motor within the vehicle dynamics simulation program. The developed method allows the selection of the appropriate motor type for the given competition tasks. Full article

In a carsharing organization, vehicle availability is considered as a measure of the quality of service. This paper presents a discrete event simulation model to evaluate the performance of round-trip (return to the same station) vs. one-way (return to any station) fleet management strategies used by carsharing organizations. The proposed model evaluates the customer rejection rate for each fleet management strategy and recommends the one with the least number of rejections. A customer request is deemed to be rejected when a vehicle cannot be made available to the user at the requested time and location. A case study for the carsharing organization Communauto in Montreal is conducted. The simulation results show that the one-way model has a greater request rejection rate of 13%, compared to 8% for the round-trip model. Therefore, a round-trip strategy is recommended to Communauto for managing its current fleet operations. Full article

The problem of extracting bearing weak fault features under variable-speed conditions with strong background noise interference remains challenging due to the limitations of existing feature extraction methods. These methods, especially those that rely on manual parameter tuning and rigid regularization, often struggle with noise suppression and robustness optimization, resulting in inaccurate extraction of weak fault features. To overcome this drawback, this study proposes a novel weak fault feature extraction method based on tensor decomposition model for bearings. First, the time–frequency tensor is constructed based on the short-time Fourier transform. Then, two types of fault properties in tensor are explored and an improved tensor decomposition model is proposed to realize the accurate extraction of weak fault features under variable-speed conditions. In addition, the decomposed feature tensor is conducted by a multichannel global energy-weighted fusion strategy, which significantly improves the robustness in extracting multichannel weak fault features. The effectiveness and superiority of the proposed method are systematically investigated through both simulated and experimental case studies. The results demonstrate that the method effectively eliminates background noise interference in measurements while augmenting the resolution of fault features. Full article

Enhancing the economics of microgrid systems and achieving a balance between energy supply and demand are critical challenges in capacity allocation research. Existing studies often neglect the optimization of electrolyzer efficiency and multi-stack operation, leading to inaccurate assessments of system benefits. This paper proposes a capacity allocation model for wind-PV-hydrogen integrated microgrid systems that incorporates hydrogen production efficiency optimization. This paper analyzes the relationship between the operating efficiency of the electrolyzer and the output power, regulates power generation-load mismatches through a renewable energy optimization model, and establishes a double-layer optimal configuration framework. The inner layer optimizes electrolyzer power allocation across periods to maximize operational efficiency, while the outer layer determines configuration to maximize daily system revenue. Based on the data from a demonstration project in Jiangsu Province, China, a case study is conducted to verify that the proposed method can improve system benefits and reduce hydrogen production costs. Full article

Optimizing the accurate estimation algorithms for the State of Charge (SOC) and State of Health (SOH) of power batteries is crucial for improving the performance of electric vehicles. This paper takes lithium-ion batteries as the research object. The Singular Value Decomposition-Unscented Kalman Filter (SVDUKF) at a micro-time scale is used to estimate the battery’s State of Charge, and the traditional Extended Kalman Filter (EKF) at a macro-time scale is used to estimate impedance parameters and capacity. The two filters operate alternately, with the output of one serving as the input for the other, thereby establishing a joint estimation method for SOC and SOH based on the SVDUKF-EKF under a multi-time scale. The joint estimation method is verified under the Dynamic Stress Test (DST) condition and Federal Urban Driving Schedule (FUDS) condition. The results show that the SOH estimation error is within 2% under the DST condition and within 1% under the FUDS condition. The method exhibits high estimation accuracy and stability under both conditions. Full article

Peridynamics (PD) exhibits inherent advantages in solving solid mechanics problems involving strong discontinuities, such as crack propagation. However, the significant magnitude discrepancy between the micro-modulus and bond stretch in the nonlocal modelling, the extensive accumulation operations during nonlocal interaction integration, and the calculation methods for surface-correction coefficients can all introduce or amplify numerical errors, thereby reducing the confidence in numerical results. To address these sources of error and enhance the numerical accuracy of the PD models, this study derived a dimensionless bond-based PD formulation and proposed computational strategies to mitigate numerical errors during model implementation. The correctness of the dimensionless bond-based PD model was validated through investigating an elastic-wave propagation problem and a crack-branching problem, and comparing the numerical results with that from the finite-element method and the referenced literature. The effectiveness of the dimensionless model and the numerical strategies in enhancing numerical accuracy was verified through comparing the numerical performance of the model while investigating symmetrical mechanical problems under extreme computational conditions and load conditions. This study provides an effective modelling framework and numerical processing strategies for accurate computations in PD. Full article

Active vibration control designs for journal bearings have improved rotordynamic stability and led to advancements in adjustable bearing types that enable precise control of bearing geometry. In this study, optimized machine learning (ML) algorithms were modeled and implemented to accurately predict the static performance envelope of a four-pad active journal bearing with features of controlling the radial and tilt positions of pads in real time. ML models developed for the adjustable bearing system help predict its behavior as a function of three key input parameters such as the eccentricity ratio and radial and tilt positions of pads. Four supervised regression models, such as Random Forest Regression (RFR), Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), and a feedforward Artificial Neural Network (ANN), were chosen for their demonstrated ability to capture complex nonlinear patterns and their robustness against overfitting in such tribological applications. Hyperparameter tuning for each model was performed using the Optuna framework, which applies Bayesian optimization to efficiently determine the best parameter settings. The Optuna-optimized ensemble and neural network models were used to identify the optimal combinations of input variables that maximize the static performance envelope of the active bearing system with geometric adjustments. Full article

The active or adjustable journal bearings are designed with unique mechanisms to reduce the rotor-bearing system lateral vibrations by adjusting their damping and stiffness. The article provides a comprehensive review of the literature, outlining the structure and findings of studies on active bearings. Over the years, various kinds of adjustable bearing designs have been developed with unique operational mechanisms. Such bearing designs include adjustable pad sectors, externally adjustable pads, active oil injection through pad openings, and flexible deformable sleeves. These modifications enhance the turbine shaft line’s performance by increasing the system’s overall stability. The detailed review in this paper highlights the characteristics of bearings, along with the key advantages, limitations, and potential offered by active control across different bearing types. The efficiency of any rotor system can be greatly enhanced by optimally selecting the adjustable bearing parameters. These adjustable bearings have demonstrated a unique capability to modify the hydrodynamic operation within the bearing clearances. Experimental studies and simulation approaches were also utilized to optimize bearing geometries, lubrication regimes, and control mechanisms. The use of advanced controllers like PID, LQG, and Deep Q networks further refined the stability. The concluding section of the article explores potential avenues for the future development of active bearings. Full article

In this article, we study a directed version of Douglas–Rachford splitting method in real Hilbert spaces. By using new, self-contained, and simplified techniques, we prove its weak convergence. The major innovation is that we exploit the firm non-expansiveness of the Douglas–Rachford operator for the first time to derive the best possible upper bounds on direction factors, assuming that the involved factors remain constant. We give a new rare feature selection model equipped with the TripAdvisor hotel-review dataset. Numerical results confirm the user-friendliness and efficiency of directed Douglas–Rachford splitting in solving this model. Full article

Unmanned surface vehicles (USVs) have great application prospects in defense, environmental surveillance and offshore energy due to their cost-effectiveness and long-duration mission ability. The structural safety issues induced by the prolonged cyclic wave loading on such small-sized marine structures, such as fatigue failure mechanism, represent an important research topic. In order to characterize the loading process, a piston-type numerical wave flume with wave absorption setting is constructed using the Arbitrary Lagrangian Eulerian (ALE) formulation, and the fluid–structure interaction (FSI) simulations are performed. Simulated wave profiles are measured and compared with corresponding analytical wave solutions to verify the accuracy of target waves. The wave absorption effect is verified by comparing the velocities of water particles in different water regions. Then, different impact scenarios are performed by applying a range of the applicable target waves. Simulated wave forms, impact scenes along with the computed wave load data are presented, and the impact process is analyzed. As a result, the FSI simulations demonstrate cyclic loading characteristics of small-sized floating structures subjected to wave impacts, and the constructed ALE numerical wave flume possesses the extensibility for the simulation of nonlinear water wave impact scenarios. Full article

Meso-scale combustors face persistent challenges in sustaining stable combustion and efficient heat transfer due to high surface-to-volume ratios and attendant heat losses. In contrast, larger outlet diameters exhibit weaker recirculation and more diffused temperature zones, resulting in reduced combustion efficiency and thermal confinement. The behavior of non-premixed flames in meso-scale combustor has been investigated through a comprehensive numerical study, utilizing computational fluid dynamics (CFD) under stoichiometric natural gas (methane)–air conditions; three outlet configurations (6 mm, 8 mm, and 10 mm) were analysed to evaluate their impact on temperature behaviour, vortex flow, swirl intensity, and central recirculation zone (CRZ) formation. Among the tested geometries, the 6 mm outlet produced the most robust central recirculation, intensifying reactant entrainment and mixing and yielding a sharply localised high-temperature core approaching 1880 K. The study highlights the critical role of geometric parameters in governing heat release distribution, with the 6 mm configuration achieving the highest exhaust temperature (920 K) and peak wall temperature (1020 K), making it particularly suitable for thermoelectric generator (TEG) integration. These findings underscore the interplay between combustor geometry, flow dynamics, and heat transfer mechanisms in meso-scale systems, providing valuable insights for optimizing portable power generation devices. Full article

Numerical simulation of metal forming processes is finding increasingly wide applications in advanced industry for the optimization of material processing conditions and prediction of process parameters, finally delivering a reduction of production costs. This work presents a comparison between simulation results of radial shear rolling (RSR) of VT3-1 titanium alloy (Ti-Al-Mo-Cr-Fe-Si) and results of experimental RSR at 1060 °C, 980 °C, and 900 °C in one, three, and five passes, respectively. The digital model (DM) demonstrates a high convergence of the calculation results (calculation error of less than 5%) with the actual geometric parameters of the experimental bars, their surface temperature, and rolling time during the experiment, which indicates a good potential for its application in the selection of deformation modes. Based on the simulation and experimental data, the conditions providing for the formation of differently sized grains in the bar cross-section have been identified. All of the as-rolled bars exhibit a gradient distribution of macrostructure grain size number (GSN), from the smallest one at the bar surface (2–4) to the greatest one in the center (4–6). The macrostructure GSN correlates with the workpiece temperature, which is the highest in the axial zone of the bars, and with the experimentally observed high plastic strain figures in the surface layers. It was found that, depending on the temperature conditions and reduction ratio per pass, any minor change in the values of process parameters can lead to the formation of macrostructures with different grain size numbers. Full article

The identification of interdependent edges plays a critical role in improving information propagation efficiency and enhancing network robustness in interdependent networks. However, existing methods exhibit significant limitations when identifying interdependent edges between networks with substantial differences in edge density. This paper proposes a greedy module matching-based method for sparse interdependent edge identification in similar-order heterogeneous networks. The method utilizes degree entropy and betweenness centrality as node characteristic values for sparse and dense networks, respectively. It first leverages structural differences between sparse and dense networks to determine the upper bound of interdependent edges. Then, a clustering algorithm is employed to identify modules in both networks that align with the estimated number of interdependent edges. Finally, a greedy algorithm is applied to infer interdependent edges between sparse and dense networks. The proposed method is validated using synthetic networks and power-communication networks, with network robustness and connection efficiency as evaluation metrics. Additionally, further validation is conducted through applications in problem–answer networks. Experimental results demonstrate that the proposed approach significantly improves the prediction of sparse interdependent relationships in heterogeneous complex networks and has broad applicability across multiple domains. Full article

Pile foundations are widely used to support offshore wind turbines. While the p-y curve method is adopted for analysis of pile–soil interactions in popular design specifications, including the American Petroleum Institute (API), its accuracy remains unassessed systematically and quantitatively. This study established a database by collecting 491 sets of pile p-y curves from multiple offshore wind turbine projects. The database was used to statistically evaluate the accuracy of the API p-y curve method for cohesionless soils. The model accuracy is represented by a model factor defined as the ratio of measured to predicted values of soil resistance around the pile. The results showed that accuracy assessment using the field data is significantly different from that using the laboratory model test data. On average, the API p-y curve method overestimates the true soil resistance in the field by about 30%, but underestimates that in the laboratory by about 8%. The dispersions in prediction accuracy of both cases are high. Correction terms are introduced to calibrate the current API p-y curves. The calibrated API methods were shown to be accurate in general and medium dispersive in prediction accuracy. Last, the model factors for the current and calibrated API methods were demonstrated to be lognormal random variables. Full article

We present a simple algorithm for synthesizing volumetric 3D puzzles from a 3D freeform geometric model represented volumetrically as trivariate NURBs functions, $\mathcal{M}$. The construction algorithm is based on the functional composition of puzzle elements, positioned in the domain of $\mathcal{M}$, with $\mathcal{M}$. The puzzle elements can be (heterogeneous) freeform polygonal models or freeform surface or trivariate functions and of arbitrary shape, and can include added joints to neighboring puzzle elements. The proposed approach is demonstrated via several examples of such volumetric puzzles, 3D printed and assembled. Full article

The solid electrolyte interphase (SEI) is a passive layer, typically a few hundred angstroms thick, that forms on the electrode surface in the first few battery cycles when the electrode is in contact with the electrolyte in lithium-metal batteries. Composed of a combination of lithium salts and organic compounds, the SEI plays a critical role in battery performance, serving as a channel for Li-ion shuttling. Its structure typically comprises an inorganic component-rich sublayer near the electrode and an outer organic component-rich sublayer. Understanding heat transport through the SEI is crucial for improving battery pack safety, particularly since the Li-ion diffusion coefficient exhibits an exponential temperature dependence. This study employs first-principles calculations to investigate phonon-mediated temperature-dependent lattice thermal conductivity across the inorganic components of the SEI, including, LiF, Li₂O, Li₂S, Li₂CO₃, and LiOH. This study is also extended to the dependence of the grain size on thermal conductivity, considering the mosaic-structured nature of the SEI. Full article

The Kolmogorov–Arnold network (KAN) is a regression model that is based on a representation of an arbitrary continuous multivariate function by a composition of functions of a single variable. Experimentally obtained datasets for regression models typically include uncertainties, which in some cases, cannot be neglected. The conventional way to account for the latter is to model confidence intervals of the systems’ outputs in addition to the expected values of the outputs. However, such information may be insufficient, and in some cases, researchers aim to obtain probability distributions of the outputs. The present paper proposes a method for estimating probability distributions of the outputs by constructing an ensemble of models. The suggested approach covers input-dependent probability distributions of the outputs and is capable of capturing the multi-modality, as well as the variation of the distribution type with the inputs. Although the method is applicable to any regression model, the present paper combines it with KANs, since their specific structure leads to the construction of computationally efficient models. The source codes are available online. Full article

A novel right-sidewall gas blowing method is proposed to improve the flow behavior in a single-strand tundish. Despite advances in tundish flow control, the impact of slag layers and sidewall gas injection on flow dynamics and tracer transport remains underexplored. This study combines 1:3.57 scale water model experiments and Compuational Fluid Dynamics (CFD) simulations to investigate the effects of gas injection heights (50 mm and 100 mm) on flow structure, mixing efficiency, and slag layer interactions. Particle Image Velocimetry (PIV) and the stimulus-response method are used for quantitative validation. Results show that sidewall gas blowing suppresses short-circuit flow, increases average residence time by up to 37%, and reduces dead zone volume by up to 19%. The 50 mm blowing height induces stronger surface turbulence, while the 100 mm height improves flow uniformity. The presence of a slag layer significantly dampens surface fluctuations and alters vortex formation. These findings fill a critical research gap in tundish metallurgy and offer a practical reference for optimizing gas blowing strategies in industrial applications. Full article

In this paper, a switched model for DC-DC boost converters with modeling uncertainty is considered. Based on the switched model, a continuous switching control law is first designed to guarantee the robust stability of the closed-loop system. Then, to reduce the data transmission amount and ease the communication burden, a sampled-data switching control law is explored, where the switching action is executed based on a state-dependent condition at each sampling time. The proposed control strategies can track a specific reference point and varying reference points in the presence of modeling uncertainty. Finally, the simulation results show that the proposed sampling switch control reduces steady-state errors and the transient response is significantly smoother. These results confirm the effectiveness and practical potential of the proposed approach. Full article

Traditional median filtering with a fixed window easily leads to edge blurring and adaptive median filtering requires manual presetting of the maximum window parameter and has insufficient retention of details when dealing with high-density salt-and-pepper noise. Aiming at these problems, this paper proposes a hybrid decision-making adaptive median filtering algorithm with dual-window detection in collaboration with particle swarm optimization (PSO). The algorithm quickly locates suspected noise points through a 3 × 3 small window and enhances noise identification accuracy by using a PSO dynamically optimized 5–35-pixel large window. Meanwhile, a hybrid decision-making mechanism based on local statistical properties was introduced to dynamically select median filtering, weighted average based on spatial distance, or pixel preservation strategy to balance noise suppression and detail preservation, and the PSO algorithm was used to automatically find the optimal parameters of the large window’s size to avoid the manual parameter-tuning process. Experiments were conducted on standard grayscale and color images and compared with four traditional methods and two more advanced methods. The experiments showed that the algorithm improved the peak signal-to-noise ratio (PSNR) value by 2–4 dB and the structural similarity index measure (SSIM) metric by 0.05–0.2 under high salt-and-pepper noise density compared with the traditional methods, which effectively improved the contradiction between noise suppression and detail retention in traditional filtering algorithms and provided a highly efficient and intelligent solution for image denoising in high-noise scenarios. Full article

In this paper, a predator–prey model with hunting cooperation and maturation delay is studied. Through theoretical analysis, we investigate the existence of multiple stability switches of the positive equilibrium. By applying Hopf bifurcation theory, the conditions for Hopf bifurcation are derived, indicating the emergence of periodic solutions as the maturation delay passes through critical values. Utilizing center manifold theory and normal form analysis, we determine the stability and direction of the bifurcating orbits. Numerical simulations are performed to validate the theoretical results. Furthermore, the simulations vividly demonstrate the appearance of period-doubling bifurcations, which is the onset of chaotic behavior. Bifurcation diagrams and phase portraits are employed to precisely characterize the transition processes from a stable equilibrium to periodic, period-doubling solutions and chaotic states under different maturation delay values. The study reveals the significant influence of maturation delay on the stability and complex dynamics of predator–prey systems with hunting cooperation. Full article

This study conducts numerical analysis of fatigue crack propagation in deck-rib welded joints of orthotropic steel decks (OSDs) using linear elastic fracture mechanics. The stress intensity factor for central surface cracks under constant range bending stress is calculated, and single and multi-crack propagation are simulated by a numerical integration method. The research results show that deck geometry critically influences crack propagation behavior. Wider decks accelerate propagation of cracks after the crack depth exceeds half the deck thickness, thicker decks exhibit linearly faster propagation rates yet retain larger residual section to bear loads, and increased weld penetration reduces fatigue life. Initial defects rapidly converge to a preferred propagation path, stabilizing near $a_f/c_f\approx 0.1$ ($a_f$ is the failure crack depth and $c_f$ is the half surface crack length) regardless of initial aspect ratio. For multi-crack scenarios, defect density dominates merging, doubling density increases final cracks by 45%. Merged cracks adhere closely to the single-crack path, while total section loss escalates with defect density and deck thickness but remains stress range independent. The identified convergence preferred propagation path enables depth estimation from surface-length measurements during real bridge inspections. Full article

In three-dimensional (3D) logistics environments, finding optimal paths for unmanned aerial vehicles (UAVs) is challenging due to positioning inaccuracies that require ground-based corrections. These inaccuracies are exacerbated in harsh environments, leading to a significant risk of correction failure. This research proposes a multi-objective mixed integer programming model (MILP) that transforms dynamic uncertainties into binary constraints, utilizing a hierarchical sequencing strategy in the Gurobi optimizer to efficiently identify optimal paths. Our simulations indicate that achieving an 80% mission success probability necessitates an optimal path of 104,946 m with nine corrections. For a 100% success rate, the path length increases to 105,874 m, with corrections remaining constant. These results validate the model’s effectiveness in navigating environments with probabilistic constraints, highlighting its potential for addressing complex logistical challenges. Full article