This paper investigates the structural response of ice-class propeller blades under ice-loading conditions, focusing on the Canadian R-class icebreaker's propeller. The study aims to analyze static and dynamic behaviors to validate the propeller's strength and provide insights into stress and vibration patterns, supporting the optimization of propeller design and the safety of polar vessel operations. A unified numerical framework is developed that integrates static strength analysis, ice–propeller collision dynamics, ice milling simulations, and dry/wet modal analysis. Static analysis, conducted using the ANSYS commercial software, was employed to evaluate the strength safety margin of the propeller under International Association of Classification Societies -prescribed ice loads. Finite element and SPH-based simulations of ice–propeller collisions and milling are used to compare transient stress and energy responses under different ice–propeller interaction modes, highlighting the governing role of milling loads under extreme conditions. The dry/wet modal analysis quantifies the reduction in natural frequencies and mode shape changes induced by the surrounding water. The results show that the propeller blade maintains sufficient safety margins under prescribed static ice loads. Dynamic simulations indicate that blade stress, deformation, and contact force increase markedly with ice impact velocity. Ice milling generates peak stresses of approximately 200 MPa, significantly higher than those induced by direct impacts, yet still below the allowable material limit, suggesting that milling loads may govern the structural design envelope. Modal analysis reveals that boundary constraints reduce natural frequencies by about 8% in air, while fluid–structure interaction leads to an average frequency reduction of approximately 30% in water. This study presents a comprehensive analysis of ice-class propeller behavior under ice-induced loads, integrating static strength, dynamic impact, ice milling, and modal characteristics in both air and water. The novelty lies in quantifying ice milling as a governing load, showing its significant impact on propeller strength. Additionally, this work introduces the influence of wet modal effects, demonstrating a ∼30% reduction in natural frequencies in water. The findings offer valuable insights for the design, optimization, and reliability assessment of ice-class propellers, addressing key engineering challenges in extreme polar environments.
Purpose This study aims to improve the dynamic modelling accuracy of small unmanned helicopters with multi-input multi-output behaviour, strong coupling, and nonlinear flight characteristics. Existing linear identification methods can capture dominant dynamics but have limited ability to represent nonlinear residual effects caused by aerodynamic coupling and unmodelled disturbances. Design/methodology/approach A three-stage numerical algorithms for subspace state space system identification–prediction error method–gradient boosting decision tree (N4SID-PEM-GBDT) hybrid identification framework is proposed. First, N4SID is used to establish a linear state-space model and extract the dominant system dynamics. Next, prediction error method (PEM) is applied to refine the linear model parameters, thereby obtaining an improved benchmark model. Finally, causal time-series features are constructed from the optimized residuals, and gradient boosting decision tree (GBDT) is employed to learn nonlinear residual compensation for the pitch-rate and roll-rate channels. Findings Time-domain validation using an independent dataset demonstrated that the proposed N4SID-PEM-GBDT framework achieved an R2 of 0.9112 and a root mean square error (RMSE) of 3.4518. Compared with N4SID and N4SID-PEM, the proposed method increased the average R2 by 13.17 and 8.15 percentage points, respectively, while reducing the average RMSE by 33.61% and 26.37%, respectively. Furthermore, compared with N4SID-PEM-RNN, N4SID-PEM-extreme gradient boosting (XGBoost) and N4SID-PEM- Gaussian Process (GP), the proposed method reduced the average RMSE by 4.71%, 6.57% and 8.19%, respectively. These results demonstrate that the proposed method further reduces prediction errors on independent test data while retaining the ability of the linear state-space model to capture the dominant system dynamics. Originality/value This study integrates subspace identification, prediction error optimization, and GBDT-based residual learning into a unified hybrid framework, providing an effective approach for high-precision modelling of strongly coupled small unmanned helicopter systems.
Purpose This study investigates an integrated scheduling problem in automated container terminals (ACTs) for export loading, jointly coordinating quay cranes (QCs), automated guided vehicles (AGVs), and automated stacking cranes (ASCs). It explicitly models two practical buffering resources: limited-capacity block buffer zones at yard blocks and quay-side buffer lanes/buffer locations for AGV queuing. The objective is to minimize total QC idle (waiting) time while satisfying realistic constraints, including equipment non-blocking, handover time windows, predetermined QC loading sequences, exclusive buffer-location occupancy, buffer-location assignment, and the rule that each AGV may park on buffer lanes at most once per job transport. Design/methodology/approach A comprehensive mixed-integer linear programming (MILP) (M1) is formulated to capture ASC retrieval, AGV transport with buffer-lane parking, buffer-location assignment, and QC loading interactions under finite buffer capacities. An equivalent reformulation (M2) replaces the max-type QC idle objective with a QC waiting-time-based objective to improve computational efficiency. Given NP-hardness, an improved genetic algorithm (GA) is developed with long- and short-chromosome (SC) random-key encodings and a model-based evaluation method (MEM) that enforces feasibility via time-window calculations and resource exclusivity checks. Extensive numerical experiments and sensitivity analyses validate performance and scalability. Findings The MILP models solve small-to-medium instances effectively, and the reformulated objective (M2) substantially reduces solution time compared with M1. For large instances (up to 400 jobs), the GA-SC delivers high-quality solutions with strong robustness and significantly outperforms benchmark heuristics in both objective value and stability. Sensitivity results show diminishing returns from increasing AGV fleet size, AGV speed, or block buffer capacity: moderate increases reduce QC idle time, but excessive capacity expansion raises AGV waiting ratios and congestion, yielding limited additional improvement in system-level performance. Research limitations/implications The study assumes deterministic processing/travel times, static job sets, and fixed routes/speeds, and it does not explicitly model stochastic disruptions (e.g. equipment breakdowns, weather impacts) or real-time dynamic arrivals. Buffer-lane effects are represented via buffer-location occupancy and time windows rather than full network-level conflict-free routing. Future work should extend the framework to stochastic/robust or rolling-horizon scheduling, integrate real-time sensing and data-driven prediction, and incorporate richer traffic conflict modeling and multi-objective criteria (e.g. energy use, emissions, service reliability) for mixed loading–unloading and multi-vessel settings. Practical implications The proposed models provide a deployable decision-support framework to co-optimize equipment schedules and buffer-resource coordination, reducing QC idle time and improving operational feasibility. Results indicate that simply adding AGVs or increasing speed is not always effective; beyond certain thresholds, congestion and buffer competition dominate. Terminal managers can use the framework to size AGV fleets, set speed policies, and plan block buffer capacities, while operational control can leverage buffer-location assignment rules to mitigate quay-side queuing and upstream blocking, improving throughput with controlled congestion and cost. Social implications By reducing unproductive waiting, congestion, and empty travel, the integrated scheduling approach can lower energy consumption and emissions, supporting “green” and “smart” port objectives. More reliable QC utilization and smoother vehicle flow can reduce vessel turnaround time and improve supply-chain punctuality, limiting downstream delays and associated economic and environmental costs. The buffering-aware coordination logic is transferable to other tightly coupled logistics systems (e.g. automated warehouses, air cargo terminals, manufacturing intralogistics), enabling broader productivity gains and more sustainable operations through better synchronization under finite buffer capacities. Originality/value This work contributes a unified, implementable QC–AGV–ASC integrated scheduling formulation that simultaneously models finite yard-side block buffer capacity and explicit quay-side buffer-lane/buffer-location occupancy with assignment and exclusivity, including the “park at most once” restriction. The QC waiting-time objective reformulation improves MILP tractability and yields verifiable benchmarks. The improved GA – especially the SC variant with model-based feasibility evaluation – scales to large instances while preserving realism and solution quality. The study bridges a practical modeling gap by tightly linking buffer resource coordination to integrated multi-equipment scheduling.
Purpose This study develops and validates a nonlinear finite element analysis (NLFEA) framework for predicting circular concrete-filled fibre-reinforced polymer (FRP) tube (CFFT) columns under concentric and eccentric axial loading. The framework covers both short and slender columns reinforced with fiber-reinforced polymers (FRP) or steel bars, providing a unified assessment beyond the limited conditions considered in previous studies. It also identifies the key parameters governing column response. Design/methodology/approach NLFEA models were developed and calibrated against experimental results from 17 CFFT column specimens covering different material properties, geometries, slenderness ratios, reinforcement types, and loading eccentricities. Concrete was modeled using the concrete damaged plasticity model, while Hashin’s failure criteria were employed to simulate damage and failure in the FRP tubes. Steel reinforcement was modeled using a bilinear elastoplastic constitutive model, whereas FRP bars were represented as linear elastic materials. Findings The calibrated models accurately reproduced the experimental load-deflection behavior and principal failure patterns of the CFFT columns, demonstrating their capability to capture the nonlinear response of both short and slender columns under concentric and eccentric axial loading. The validated models were subsequently used to conduct a systematic parametric study of FRP tube thickness, load eccentricity, longitudinal FRP reinforcement ratio, and column slenderness ratio. Originality/value The main contribution is a validated NLFEA framework that captures the combined effects of column slenderness, load eccentricity, FRP tube thickness, and reinforcement. Validated against 17 specimens and supported by a systematic parametric study, the framework provides broader insight into CFFT column behavior and supports their assessment and preliminary design.
Purpose This study aims to derive explicit analytical solutions for a wave equation subject to a non-local integral conservation condition and provide benchmark solutions for the validation of computational methods. Design/methodology/approach Two analytical approaches are developed to obtain exact solutions. In the first approach, the governing equation is transformed into its characteristic form, where characteristic variables are determined along characteristic lines and integrated piecewise across subregions. In the second approach, the solution is constructed based on the exact solution in an infinite domain, with boundary and integral conservation conditions incorporated to supply the missing information outside the domain of interest. Findings Explicit analytical solutions are obtained for the wave equation under non-local integral constraints. The results reveal key structural features of the solution, including wave propagation characteristics and periodic behavior. These solutions can serve as benchmark references for verifying numerical simulations. Originality/value This study provides explicit and practically implementable analytical solutions for wave equations with non-local integral conditions. The results offer valuable benchmark solutions for computational modeling and numerical method verification in engineering applications.
