Search Results (159)

This paper presents, by taking the elastic string vibration problem as the model problem, the space–time reduced element and the corresponding adaptive analysis algorithm. The solution of the space–time reduced element is extracted from the standard two-dimensional (spatial and temporal dimensions) polynomial element of the Galerkin-type by omitting the highest-degree terms, which serve as a built-in pointwise error estimator for the reduced solution. Taking the reduced solution as the final solution, the proposed adaptivity algorithm can produce solutions from the reduced element that satisfy the user-preset error tolerances in the maximum norm. Theoretical analysis and formulation are presented. Representative numerical examples, including forced vibrations with damping on an elastic foundation and moving load problems, validate the feasibility, effectiveness, and reliability of the proposed method. Full article

Deep reinforcement learning (DRL) with self-play has emerged as a promising paradigm for solving combinatorial optimization (CO) problems. The recently proposed Gumbel AlphaZero Plan-to-Play (GAZ PTP) framework adopts a competitive training setup between a learning agent and an opponent to tackle classical CO tasks such as the Traveling Salesman Problem (TSP). However, in complex and multi-constrained environments like the Electric Vehicle Routing Problem (EVRP), standard self-play often suffers from opponent mismatch: when the opponent is either too weak or too strong, the resulting learning signal becomes ineffective. To address this challenge, we introduce Two-Stage Self-Play GAZ PTP (TSS GAZ PTP), a novel DRL method designed to maintain adaptive and effective learning pressure throughout the training process. In the first stage, the learning agent, guided by Gumbel Monte Carlo Tree Search (MCTS), competes against a greedy opponent that follows the best historical policy. As training progresses, the framework transitions to a second stage in which both agents employ Gumbel MCTS, thereby establishing a dynamically balanced competitive environment that encourages continuous strategy refinement. The primary objective of this work is to develop a robust self-play mechanism capable of handling the high-dimensional constraints inherent in real-world routing problems. We first validate our approach on the TSP, a benchmark used in the original GAZ PTP study, and then extend it to the multi-constrained EVRP, which incorporates practical limitations including battery capacity, time windows, vehicle load limits, and charging infrastructure availability. The experimental results show that TSS GAZ PTP consistently outperforms existing DRL methods, with particularly notable improvements on large-scale instances. Full article

As the rotational speed increases, the centrifugal expansion of the rotor will significantly affect the performance of the porous gas bearing. However, this rotor’s centrifugal effect has not been studied thoroughly. In this paper, the rotor centrifugal expansion is simplified as a two-dimensional plane stress problem. The gas flow in the porous bushing and the gas film is governed by Darcy’s law and the modified Reynolds equation, respectively. The perturbation method and the finite difference method are adopted to calculate the bearing load and dynamic coefficients for a high-speed porous gas bearing. Comparisons between the simulated results and the available experimental and theoretical data are carried out to validate the proposed model. On this basis, the influence of rotor centrifugal expansion on the performance and the operational conditions of the high-speed porous gas bearing is studied systematically. The results indicate that rotor centrifugal expansion greatly improves the bearing load and dynamic coefficients of the high-speed porous gas bearing with a large rotor diameter and small bearing clearance, but reduces the allowable eccentricity ratio and titling angle. Full article

Microservices as an emerging architectural approach have been widely applied in the development of online applications. However, in large-scale service systems, frequent data communications, complex invocation dependencies, and strict latency requirements pose significant challenges to efficient microservice orchestration. In addition, microservices need to frequently access the database to achieve data persistence, creating a mutual dependency between the two, and this symmetry further increases the complexity of service orchestration and coordinated deployment. In this context, the strong coupling of service deployment, database layout, and request routing makes effective local optimization difficult. However, existing research often overlooks the impact of databases, fails to achieve joint optimization among databases, microservice deployments, and routing, or lacks fine-grained orchestration strategies for multi-instance models. To address the above limitations, this paper proposes a joint optimization framework based on the Database-as-a-Service (DaaS) paradigm. It performs fine-grained multi-instance queue modeling based on queuing theory to account for delays in data interaction, request queuing, and processing. Furthermore this paper proposes a proximal policy optimization algorithm based on multi-stage joint decision-making to address the orchestration problem of microservices and database instances. In this algorithm, the action space is symmetrical between microservices and database deployment, enabling the agent to leverage this characteristic and improve representation learning efficiency through shared feature extraction layers. The algorithm incorporates a two-layer agent policy stability control to accelerate convergence and a three-level experience replay mechanism to achieve efficient training on high-dimensional decision spaces. Experimental results demonstrate that the proposed algorithm effectively reduces service request latency under diverse workloads and network conditions, while maintaining global resource load balancing. Full article

To address the issues of imprecise user segmentation, inadequate handling of fuzzy evaluation information, and low recommendation accuracy in current electricity retail package recommendations, a novel recommendation method based on K-prototypes clustering and interval-valued intuitionistic fuzzy theory is proposed. First, a multi-dimensional user profile is constructed, incorporating five numerical tags—such as monthly average electricity consumption and monthly load factor—and two categorical tags: industry characteristics and value-added service demand. The K-prototypes algorithm is employed to cluster users, effectively resolving the profile distortion problem caused by the neglect of categorical features in traditional K-means clustering. Second, interval-valued intuitionistic fuzzy numbers are introduced to transform user linguistic evaluations into quantitative indicators. A projection measure-based model is established to objectively determine attribute weights, thereby eliminating subjective weighting bias. Finally, a comprehensive ranking of electricity retail packages is generated by integrating satisfaction levels of similar users and similar measures of new users. The recommendation performance is validated using Root Mean Square Error (RMSE), Kendall’s τ, Normalized Discounted Cumulative Gain (NDCG@5), and Discrimination Index (S). A case study involving users from a region in China demonstrates that the proposed method reduces the Root Mean Square Error (RMSE) to 0.32, which is 31.25% lower than the next best traditional method (K-prototypes + equal weight clustering with RMSE = 0.48), accurately addresses the core demands of diverse user groups, significantly improves recommendation precision and user satisfaction, and exhibits substantial practical application value. Full article

State-of-charge (SoC) balancing across multiple battery energy storage systems (BESS) is a central challenge in renewable-rich mini-grids. Heterogeneous battery capacities, differing states of health, stochastic renewable generation, and variable loads create a high-dimensional uncertain control problem. Conventional droop-based SoC balancing strategies are decentralized and computationally light but fundamentally reactive and limited, whereas model predictive control (MPC) is insightful but computationally intensive and prone to modeling errors. This paper proposes a Hierarchical Predictive–Adaptive Control (HPAC) framework for SoC balancing in mini-grids using deep reinforcement learning. The framework consists of two synergistic layers operating on different time scales. A long-horizon Predictive Engine, implemented as a federated Transformer network, provides multi-horizon probabilistic forecasts of net load, enabling multiple mini-grids to collaboratively train a high-capacity model without sharing raw data. A fast-timescale Adaptive Controller, implemented as a Soft Actor-Critic (SAC) agent, uses these forecasts to make real-time charge/discharge decisions for each BESS unit. The forecasts are used both to augment the agent’s state representation and to dynamically shape a multi-objective reward function that balances SoC, economic performance, degradation-aware operation, and voltage stability. The paper formulates SoC balancing as a Markov decision process, details the SAC-based control architecture, and presents a comprehensive evaluation using a MATLAB-(R2025a)-based digital-twin simulation environment. A rigorous benchmarking study compares HPAC against fourteen representative controllers spanning rule-based, MPC, and various DRL paradigms. Sensitivity analysis on reward weight selection and ablation studies isolating the contributions of forecasting and dynamic reward shaping are conducted. Stress-test scenarios, including high-volatility net-load conditions and communication impairments, demonstrate the robustness of the approach. Results show that HPAC achieves near-minimal operating cost with essentially zero SoC variance and the lowest voltage variance among all compared controllers, while maintaining moderate energy throughput that implicitly preserves battery lifetime. Finally, the paper discusses a pathway from simulation to hardware-in-the-loop testing and a cloud-edge deployment architecture for practical, real-time deployment in real-world mini-grids. Full article

This paper presents a novel algorithm for the dynamic analysis of fractional-order viscoelastic spinning disks in the time domain. The novelty mainly lies in the use of the shifted Legendre polynomial algorithm for the direct time-domain numerical analysis of displacement in two directions for a three-dimensional viscoelastic rotating disk, tackling a more complex and strongly coupled problem than those addressed in previous studies. By using the fractional-order Kelvin–Voigt model to describe the viscoelastic properties of the disk, a system of governing equations with three independent variables is established. For the two ternary unknown functions in the equations, a fractional-order differential operator matrix based on Shifted Legendre polynomials is derived, transforming the original equations into two sets of algebraic equations that are easier to solve. This paper presents an in-depth analysis of the convergence of the Legendre polynomial algorithm, complemented by an investigation of its error characteristics using numerical examples, thereby verifying the method’s accuracy and feasibility. This study can be applied to the dynamic analysis of viscoelastic rotating structures under body force density. The findings provide theoretical support for the optimization and safety assessment of load-bearing rotating components in engineering. And the algorithm demonstrates high accuracy and applicability in handling fractional-order equations in science and engineering. Full article

This study proposes a fast material parameter evaluation method for multilayer thin-film structures based on machine learning technology to solve the problems of long time and low efficiency in the traditional material parameter inversion process. Nanoindentation experiments are first conducted to establish an experimental basis across film stacks. A two-dimensional elasto-plastic model of the indentation process is then built to generate a large set of load–depth curves, which serve as training data for a machine learning model. Trained on simulated curves and validated against measurements, the model enables fast inverse identification of layer-wise plastic parameters and interfacial cohesive properties. The experimental results show that the method has high accuracy and efficiency in the inversion of interlayer cohesion parameters, and the correlation coefficient R² is 0.99 or more. Compared with traditional methods, the pipeline supports batch analysis of multiple datasets and delivers parameter estimates within 1 h, substantially shortening turnaround time while improving result reliability. This method can not only effectively solve the challenges faced by traditional material evaluation, but also provide a new and effective tool for the performance evaluation and optimization design of multilayer thin-film materials. It has broad application prospects and potential value. Full article

We consider an axysimmetric cylindrical vessel grown by surface deposition at the inner boundary. The residual stress in the vessel can vary, e.g., depending on the loading history during growth. Can we represent and characterize a stress-free material (namely, reference) configuration for the vessel? Extending an idea initially proposed for surface growth occurring on a fixed boundary, the material configuration is introduced as a two-dimensional manifold immersed in a three-dimensional space. The problem is first formulated in fairly general terms for an incompressible neo-Hookean material in plane strain and then specialized to material configurations represented by ruled surfaces. An illustrative example using geometric and material parameters of carotid arteries shows the characterization of different material configurations based on their three-dimensional slope and computes the corresponding residual stress fields. Finally, such a slope is shown to be in a one to one relationship with the customary measure of residual stress in arteries, i.e., the opening angle in response to a cut. The present work introduces a novel framework for residual stress and shows its applicability in a special setting. Several generalizations and extensions are certainly necessary in the following sections to further test and assess the proposed method. Full article

This study proposes a novel egg-crate honeycomb core sandwich panel (SP-EHC) that combines the structural advantages of conventional lattice and grid configurations while mitigating their limitations in stability and mechanical performance. The design employs chamfered intersecting grid walls to create a semi-enclosed honeycomb architecture, enhancing out-of-plane stiffness and buckling resistance and enabling ventilation and drainage. To facilitate efficient and accurate structural analysis, a two-dimensional equivalent plate model (2D-EPM) is developed using the variational asymptotic method (VAM). This model significantly reduces the complexity of three-dimensional elasticity problems while preserving essential microstructural characteristics. A Reissner–Mindlin-type formulation is derived, enabling local field reconstruction for detailed stress and displacement evaluation. Model validation is conducted through experimental testing and three-dimensional finite element simulations. The 2D-EPM demonstrates high accuracy, with static analysis errors in load–displacement response within 10% and a maximum modal frequency error of 10.23% in dynamic analysis. The buckling and bending analyses, with or without initial deformation, show strong agreement with the 3D-FEM results, with deviations in the critical buckling load not exceeding 5.23%. Local field reconstruction achieves stress and displacement prediction errors below 2.7%, confirming the model’s fidelity at both global and local scales. Overall, the VAM-based 2D-EPM provides a robust and computationally efficient framework for the structural analysis and optimization of advanced sandwich panels. Full article

In subway stations constructed using the cut-and-cover method, an increasing number of projects are adopting the form of precast components combined with on-site assembly. However, analysis of the novel structural elements within such overlapped subway stations remains inadequate. To simulate the shear failure mechanism at slab–wall joints, the structural behavior of these joints in overlapped subway stations is idealized as a rigid die stamping problem. An admissible failure mechanism is constructed, comprising a rigid wedge zone and a vertical tensile fracture perpendicular to a smooth base. The limit analysis approach is adopted, a two-dimensional velocity field is constructed, and the upper-bound theorem is applied to determine the bearing capacity of these joints under strip loading, utilizing a modified Coulomb yield criterion incorporating a small tensile stress cutoff. The failure mechanism proposed on the basis of an engineering case is validated through analytical calculations and parametric studies. Finally, a parametric analysis is conducted to investigate the influence of factors such as the geometric configuration of the slab–wall joints and the tensile and compressive strengths of concrete on their ultimate bearing capacity. The results obtained can provide an effective reference for the design and construction of precast slab–wall joints in future overlapped subway station projects. Full article

Energy generation from renewable sources has increased exponentially worldwide, particularly wind energy, which is converted into electricity through wind turbines. The growing demand for renewable energy has driven the development of horizontal-axis wind turbines with larger dimensions, as the energy captured is proportional to the area swept by the rotor blades. In this context, the dynamic loads typically observed in wind turbine towers include vibrations caused by rotating blades at the top of the tower, wind pressure, and earthquakes (less common). In offshore wind farms, wind turbine towers are also subjected to dynamic loads from waves and ocean currents. Vortex-induced vibration can be an undesirable phenomenon, as it may lead to significant adverse effects on wind turbine structures. This study presents a two-dimensional transient model for a rigid body anchored by a torsional spring subjected to a constant velocity flow. We applied a coupling of the Fourier pseudospectral method (FPM) and immersed boundary method (IBM), referred to in this study as IMERSPEC, for a two-dimensional, incompressible, and isothermal flow with constant properties—the FPM to solve the Navier–Stokes equations, and IBM to represent the geometries. Computational simulations, solved at an aspect ratio of $\varphi =4.0$, were analyzed, considering Reynolds numbers ranging from $Re=150$ to Re = 1000 when the cylinder is stationary, and $Re=250$ when the cylinder is in motion. In addition to evaluating vortex shedding and Strouhal number, the study focuses on the characterization of space–time symmetry during the galloping response. The results show a spatial symmetry breaking in the flow patterns, while the oscillatory motion of the rigid body preserves temporal symmetry. The numerical accuracy suggested that the IMERSPEC methodology can effectively solve complex problems. Moreover, the proposed IMERSPEC approach demonstrates notable advantages over conventional techniques, particularly in terms of spectral accuracy, low numerical diffusion, and ease of implementation for moving boundaries. These features make the model especially efficient and suitable for capturing intricate fluid–structure interactions, offering a promising tool for analyzing wind turbine dynamics and other similar systems. Full article

Addressing the problem that energy supply and load demand cannot be matched due to the difference in inertia effects among multiple energy sources, and taking into account the thermoelectric load, this paper designs a two-stage operation optimization model of IES considering multi-dimensional thermal inertia and constructs an intelligent adaptive solution method based on a time scale-model base. Validation is conducted through an arithmetic example. Scenario 2 has 15.3% fewer CO₂ emissions than Scenario 1, 19.7% less purchased electricity, and 20.0% less purchased electricity cost. The optimal algorithm for the day-ahead phase is GA, and the optimal algorithm for the intraday phase is PSO, which is able to produce optimization results in a few minutes. Full article

The short-term scheduling of pumped-storage hydropower plants is characterised by high dimensionality and nonlinearity and is subject to multiple operational constraints. This study proposes an intelligent scheduling framework that integrates an Atomic Orbital Search (AOS)-optimised Long Short-Term Memory (LSTM) network with the Deep Deterministic Policy Gradient (DDPG) algorithm to minimise water consumption during the generation period while satisfying constraints such as system load and safety states. Firstly, the AOS-LSTM model simultaneously optimises the number of hidden neurons, batch size, and training epochs to achieve high-precision fitting of unit flow–efficiency characteristic curves, reducing the fitting error by more than 65.35% compared with traditional methods. Subsequently, the high-precision fitted curves are embedded into a Markov decision process to guide DDPG in performing constraint-aware load scheduling. Under a typical daily load scenario, the proposed scheduling framework achieves fast inference decisions within 1 s, reducing water consumption by 0.85%, 1.78%, and 2.36% compared to standard DDPG, Particle Swarm Optimisation, and Dynamic Programming methods, respectively. In addition, only two vibration-zone operations and two vibration-zone crossings are recorded, representing a reduction of more than 90% compared with the above two traditional optimisation methods, significantly improving scheduling safety and operational stability. The results validate the proposed method’s economic efficiency and reliability in high-dimensional, multi-constraint pumped-storage scheduling problems and provide strong technical support for intelligent scheduling systems. Full article

The concept of variable-stiffness composites allows the stiffness properties to vary spatially in the material. In the case of fiber-reinforced composites, the mechanical properties of the composite can be improved by tailoring the fiber orientations in a spatially optimal manner. In this paper, the problem of optimal spatial orientation of fibers in a two-dimensional composite structure under in-plane loading is studied, using the strain energy-minimizing method. The fiber orientation is assumed to be constant within each element of the model but varies from element to element. The optimal design problem is solved numerically using a global optimization method based on a genetic algorithm. Some numerical examples illustrate the efficiency and applicability of the method. Full article