Search Results (65)

The digital integration of existing industrial equipment (retrofitting) is a central element of the Industry 4.0 paradigm, wherein the energy efficiency of Internet of Things (IoT) gateways is a decisive design consideration. This research aims to experimentally compare various wireless and wired communication protocols—ESP-NOW, Bluetooth Low Energy (BLE), Bluetooth Classic (Serial Port Profile, SPP), Message Queuing Telemetry Transport (MQTT), and S7 Protocol—within a legacy Programmable Logic Controller (PLC)-based environment. A dedicated testbed was developed using Siemens S7-300 PLCs and ESP32-based gateway devices to ensure measurement reproducibility. Energy consumption was determined using a high-precision power profiler with payloads ranging from 50 to 15,000 bytes, applying the trapezoidal rule while considering both active transaction and standby states. The specific energy consumption metric (μJ/byte) introduced in this study highlights the distinct scaling limitations of the protocols. While ESP-NOW proved highly efficient for small telemetry packets, Bluetooth Classic exhibited superior scalability for bulk data volumes. Furthermore, a critical energetic crossover point was identified for ESP-NOW due to hardware fragmentation limits, whereas MQTT demonstrated massive energetic overhead for small payloads. Standby measurements confirmed that the continuous baseline consumption of the wired Ethernet interface significantly dominates the energy budget compared to wireless alternatives. These empirical findings are synthesized into a formal Qualitative Decision Matrix to help engineers optimize protocol selection based on the expected duty cycle, facilitating the development of sustainable industrial digitalization solutions. Full article

Accurate stockpile volume estimation is crucial for material quantification and inventory management in civil engineering, directly affecting cost assessment and on-site decision-making. Traditional manual methods suffer from subjective bias and limitations in handling irregular geometries, resulting in reduced accuracy and efficiency. This study presents a Light Detection and Ranging (LiDAR)-based workflow integrated with Robot Operating System (ROS) for point cloud processing, enabling accurate volume estimation of irregular stockpiles. The core innovation lies in the integration of multi-station scanning, point cloud registration, boundary extraction, layered slicing, and numerical integration using the trapezoidal rule, thereby enabling geometrically precise volume estimation of irregular stockpiles. The proposed system was validated through three experimental scenarios: (1) controlled experiments, showing strong agreement with theoretical volumes; (2) verification experiments, demonstrating high stability and consistency; and (3) field experiments, yielding a volume of 124.93 m³ compared to 130–135 m³ obtained by manual measurement. The results indicate that the proposed approach reduces processing time by over 80% while significantly decreasing labor requirements and improving operational safety. Overall, the proposed method provides a reliable and efficient solution for volume estimation in practical engineering applications. Full article

This paper develops a unified α-cut optimization framework for modular electric vehicle (EV) fast-charging station design under fuzzy uncertainty. Uncertain peak demand, annual delivered energy, electricity price, ambient temperature, arrival rate, and energy per session are represented by triangular or trapezoidal fuzzy numbers and reformulated through α-cut bounds. The resulting design problem is expressed as a hybrid discrete–continuous model in which the number of modules, the selected catalog module rating, installed power, cooling provision, and a station-volume proxy are jointly optimized. An aggregated representation of interchangeable modules is adopted to remove permutation-equivalent descriptions and preserve a compact search space. Three planning views are examined: minimum CAPEX at a prescribed α-cut level, minimum loss-driven OPEX under a CAPEX budget, and a service-oriented admissibility/coverage analysis that avoids interpreting larger α values as greater robustness. The strengthened numerical study includes a deterministic nominal benchmark, peak demand sensitivity regimes, feasibility threshold and budget sweep results, explicit service stress scenarios, and a queueing sensitivity check against Erlang-C and discrete-event simulation indicators. The results show that baseline CAPEX designs may be dominated by catalog thresholds, whereas OPEX and service-oriented conclusions become informative once budget and traffic regimes are varied. The proposed framework is therefore positioned as a tractable α-cut-based design screening and comparative optimization tool for representative modular EV charging station scenarios, rather than as a universally validated operational design rule. Full article

Accurate energy consumption prediction is fundamental for enhancing range estimation and trip planning in battery electric vehicles (BEVs) under real-world conditions. This study develops a route-level benchmark utilizing 1 Hz data acquired via ECU/OBD-II interfaces (CAN 500 kbps) across ten diverse real-world driving routes. The input feature set comprises vehicle speed, longitudinal acceleration, estimated motor torque, road altitude, and accelerator pedal position. Ground truth energy consumption was derived from battery voltage and current, integrated via the trapezoidal rule. We performed a comparative analysis between five memoryless regressors (FNN, SVR, GPR, QRNN, and Bagged Trees) and three sequence models (LSTM, GRU, and BiLSTM) trained on 20-second temporal windows. The results indicate that the GRU model achieved the highest overall performance (mean RMSE = 0.1142 kWh, R² = 0.9545 and MAE = 0.072 kWh), while Bagged Trees emerged as the most robust static model (mean RMSE = 0.1587 kWh). Temporal models outperformed static ones on routes with high dynamic variability, whereas Bagged Trees excelled in five specific scenarios. These findings provide a controlled within-route benchmark for time-resolved cumulative energy estimation and highlight the need for chronological and cross-route validation before drawing deployment-oriented generalization claims. Full article

Accuracy in fractional numerical integration is often limited by the regularity of the integrand. This work proposes a flexible error estimation framework for proportional Caputo-hybrid integral operators based on $\mathfrak{s}$-convexity. We introduce a parametric Newton–Cotes formula ($\nu \in [0,1]$) that bridges the gap between classical quadrature rules, recovering the fractional Trapezoidal, Midpoint, and Simpson’s methods as specific instances. In order to confirm the correctness of our results, we provide an illustrative example with graphical representations. Furthermore, we provide some additional results using Hölder’s and power mean inequalities and employ a verification strategy based on an Artificial Neural Networks (ANNs) model. The ANN approach allows for high-dimensional parameter space exploration, demonstrating that the proposed inequalities provide robust and precise error estimates. Full article

This article investigates the numerical solution of the two-dimensional Poisson equation defined over a rectangular domain subject to a double integral nonlocal boundary condition. We propose a finite difference scheme by discretizing the integral term using the two-dimensional trapezoidal rule. The main difficulty of this problem is that, in the non-classical case, we cannot use the method of separation of variables and decompose the problem into one-dimensional problems. Our approach involves reducing the integral boundary condition from the complete domain to the interior points and strategically partitioning the computational domain into the boundary and interior points. We propose a method that allows us to find a solution by solving the Poisson equation with classical boundary conditions, and using the solutions found to construct a solution to a problem with a nonlocal integral condition. This method requires solving a linear system whose dimension is much smaller than the original. Under certain conditions on the kernel, the proposed method is correct. Full article

Sustainable urban development increasingly depends on understanding how digital activity is distributed across space and time, yet the spatiotemporal dynamics of the urban digital landscape remain poorly mapped by conventional data sources. This study uses Beijing as an empirical testbed, applying a multi-dimensional analytical framework to massive mobile network traffic data to decode the metabolic rhythms, distributional laws, and functional organization of the urban digital landscape. The results reveal three findings. First, the urban digital landscape exhibits a sleepless trapezoidal temporal rhythm characterized by continuous saturation without a midday trough and a quantifiable weekend activation lag, indicating that digital metabolism is structurally decoupled from physical mobility patterns. Second, digital traffic follows a skew-normal distribution consistent with a 20/70 rule of spatial polarization, in which the top 20% of super-connector nodes sustain approximately 70% of total urban digital flow, yielding a Gini coefficient of 0.68 as a measurable indicator of infrastructure inequality and systemic vulnerability. Third, four distinct functional prototypes are identified—ranging from continuously active metropolitan cores to inverse-tidal ecological peripheries—empirically validating Beijing’s polycentric transformation through the lens of digital flows. These findings demonstrate that large-scale mobile network traffic data offers a replicable and structurally distinct lens for sustainable urban digital governance, supporting resilient network planning, equitable allocation of digital resources, and evidence-based monitoring of urban functional transformation in rapidly growing megacities. Full article

This paper presents a reduced-order Legendre–Galerkin extrapolation (ROLGE) method combined with the scalar auxiliary variable (SAV) approach (ROLGE-SAV) to numerically solve the time-fractional Allen–Cahn equation (tFAC). First, the nonlinear term is linearized via the SAV method, and the linearized system derived from this SAV-based linearization is time-discretized using the shifted fractional trapezoidal rule (SFTR), resulting in a semi-discrete unconditionally stable scheme (SFTR-SAV). The scheme is then fully discretized by incorporating Legendre–Galerkin (LG) spatial discretization. To enhance computational efficiency, a proper orthogonal decomposition (POD) basis is constructed from a small set of snapshots of the fully discrete solutions on an initial short time interval. A reduced-order LG extrapolation SFTR-SAV model (ROLGE-SFTR-SAV) is then implemented over a subsequent extended time interval, thereby avoiding redundant computations. Theoretical analysis establishes the stability of the reduced-order scheme and provides its error estimates. Numerical experiments validate the effectiveness of the proposed method and the correctness of the theoretical results. Full article

Variable switching frequency modulation (VSFM) is an easy-to-implement and low-cost method to reduce electromagnetic interference (EMI) of power electronics, yet changes in loss and harmonic behavior make it hard to decide the parameters of the filter and the switching frequency (SF) variation range. In this article, a new VSFM method characterized by evenly distributed SF is proposed, and it is easy to implement. In order to handle the induced variation in loss and current total harmonic distortion (THD) behavior, current dynamics of a full-bridge grid-tied inverter under constant SF modulation (CSFM) are analyzed through multidimensional Fourier decomposition (MFD), and then the results are extended to VSFM. Based on these dynamics, loss of MOSFETs and THD of grid-connected current are estimated through the trapezoidal integral rule, and the analytical expressions of these indexes can be derived. After this, parameters needed for VSFM can be determined while meeting the minimum MOSFET loss and fixed current THD constraint. The performance of EMI, loss, and current harmonic is revealed through simulations and experiments and compared with the CSFM and classical VSFM methods. Full article

Anti-lock braking systems (ABSs) play a vital role in vehicle safety by preventing wheel lockup and maintaining stability during braking. However, their performance is strongly affected by variations in tire–road friction, which often limits the effectiveness of conventional controllers. This research proposes and evaluates a fuzzy logic controller (FLC)-based ABS using a quarter-vehicle model and the Burckhardt tire–road interaction, implemented in MATLAB/Simulink. Two input variables (slip error and slip rate) and one output variable (brake pressure adjustment) were defined, with triangular and trapezoidal membership functions and 15 linguistic rules forming the control strategy. Simulation results under diverse road conditions—including dry asphalt, concrete, wet asphalt, snow, and ice—demonstrate substantial performance gains. On high- and medium-friction surfaces, stopping distance and stopping time were reduced by more than 30–40%, while improvements of up to 25% were observed on wet surfaces. Even on snow and ice, the system maintained consistent, albeit modest, benefits. Importantly, the proposed FLC–ABS was benchmarked against two recent studies: one reporting that an FLC reduced stopping distance to 258 m in 15 s compared with 272 m in 15.6 s using PID, and another where PID outperformed an FLC, achieving 130.21 m in 9.67 s against 280.03 m in 16.76 s. In contrast, our system achieved a stopping distance of only 24.41 m in 7.87 s, representing over a 90% improvement relative to both studies. These results confirm that the proposed FLC–ABS not only demonstrates clear numerical superiority but also underscores the importance of rigorous modeling and systematic controller design, offering a robust and effective solution for improving braking efficiency and vehicle safety across diverse road conditions. Full article

The probability density function (PDF) of the product of two normal random variables remains an open discussion. Researchers have proposed many forms of PDFs. Among these, two notable PDFs are an analytical solution with infinite summation and an integral form with transformation. For practical computation, they must be estimated. The form with infinite summation must be truncated to a finite summation, and the form still in integration must be computed numerically. As a result of this estimation, an error occurs in the value of the estimation. This paper derives upper bounds for the estimation error resulting from truncation and numerical approximation in integral calculations. The upper bound error between the exact PDF and the truncated PDF is expressed as a geometric series using Bessel function inequality and Stirling’s approximation. The geometric formula allows the quantification of the total truncation error to be determined. For the PDF, which is still in integration form, the trapezoidal rule is used for numeric calculation. Hence, the error can be determined using the error-bound formula. The two estimated PDFs have their own advantages and disadvantages. The truncated PDF gives a relatively small upper bound value compared to the numerical calculation integral form PDF for a small value domain. However, the truncated PDF fails to perform for a large value domain, and only the integral form PDF can be used. The error for the estimation is applied to the conventional mass measurement. The results demonstrate that the error can be controlled through an analytical approach. Full article

Singularly perturbed integro-partial differential equations with reaction–diffusion behavior present significant challenges due to boundary layers arising from small perturbation parameters, which complicate the development of accurate and efficient numerical schemes for physical and engineering models. In this study, a uniformly convergent higher-order method is proposed to address these challenges. The approach applies the implicit Euler method for temporal discretization on a uniform mesh and central differences on a Shishkin mesh for spatial approximation, and utilizes the trapezoidal rule for evaluating integral terms; further, extrapolation techniques are incorporated in both time and space to increase accuracy. Numerical analysis demonstrates that the base scheme achieves first-order convergence, while extrapolation enhances convergence rates to second-order in time and fourth-order in space. Theoretical results confirm uniform convergence with respect to the perturbation parameter, and comprehensive numerical experiments validate these analytical claims. Findings indicate that the proposed scheme is reliable, efficient, and particularly effective in attaining fourth-order spatial accuracy when solving singularly perturbed integro-partial differential equations of reaction–diffusion type, thus providing a robust numerical tool for complex applications in science and engineering. Full article

Model predictive control (MPC) has been proven effective in terms of cooperative control for wind turbines (WTs). Previous work was limited to segmented linearization at a specific operating point, which significantly affected the robustness of the MPC performance. Moreover, due to nonlinearity, frequent control switching would result in the instability and fluctuation of the closed-loop control system. To address these issues, this paper proposes a novel cooperative control strategy considering fatigue load suppression for wind turbines, which is named soft switch multiple model predictive control (SSMMPC). Firstly, based on the gap metric, a model bank is constructed to divide the nonlinear WT model into several linear segments. Then, the multiple MPC is designed in a wide range of operating points. To settle the control signal oscillation problem, a soft-switching rule based on the triangular–trapezoidal hybrid membership function is proposed during controller selection. Several simulations are performed to verify the effectiveness and flexibility of SSMMPC in the partial-load region and full-load region. The results confirm that the proposed SSMMPC exhibits excellent performance in both reference operating point tracking and fatigue load mitigation, especially for the main shaft torque and tower bending load. Full article

This paper presents a fully implicit finite difference scheme for the numerical approximation of a wave equation featuring strong damping and a distributed delay term. The discretization employs second-order accurate approximations in both time and space. Although implicit, the scheme does not ensure unconditional stability due to the nonlocal nature of the delayed damping. To address this, we perform a stability analysis based on Rouché’s theorem from complex analysis and derive a sufficient condition for asymptotic stability of the discrete system. The resulting criterion highlights the interplay among the discretization parameters, the damping coefficient, and the delay kernel. Two quadrature techniques, the composite trapezoidal rule (CTR) and the Gaussian quadrature rule (GQR), are employed to approximate the convolution integral. Numerical experiments validate the theoretical predictions and illustrate both stable and unstable dynamics across different parameter regimes. Full article

Aiming at the problem that the whole row of reciprocating seedling picking mechanism is prone to inertial impacts during operation due to its excessive mass, causing seedling damage and positioning errors, this study builds a motion control system with a PLC controller as the core and proposes a composite motion control strategy based on planned S-curve acceleration and deceleration and fuzzy PID to achieve rapid response, precise positioning, and smooth operation of the seedling picking mechanism. By establishing the objective function and constraint conditions and taking into account the dynamic change of the seedling picking displacement, the S-curve acceleration and deceleration control algorithm is planned in six and seven stages to meet the requirements of a smooth transition of the speed and continuous change of the acceleration curve of the seedling picking mechanism during movement. A fuzzy PID positioning control system is designed, the control system transfer function is constructed, and fuzzy rules are formulated to dynamically compensate for the error and its rate of change to meet the requirements of fast response and no overshoot oscillation of the positioning control system. The speed and acceleration of the seedling picking mechanism under the six-segment and seven-segment S-curve acceleration and deceleration motion control conditions were simulated using MATLAB2024a simulation software and compared with the trapezoidal acceleration and deceleration motion control. The planned S-curve acceleration and deceleration control algorithm has a more stable control effect on the seedling picking mechanism when it operates under the conditions of the dynamic change of the displacement, and it meets the design requirements of seedling picking efficiency. The positioning control system was modeled and simulated using the Simulink simulation platform. When KP = 15, KI = 3, and KD = 1, the whole-row seedling picking control system ran stably, responded quickly, and had no overshoot. Compared with the PID control system with fixed parameters, the fuzzy PID control system reduced the time consumption in the rising stage by 24.5% and shortened the overall stabilization process by 17.6%. The zero overshoot characteristic was ensured, and the response speed was faster. When a disturbance signal is added, the overshoot of the fuzzy PID control system is reduced by 2.4%, and the response speed is increased by 6.8% compared with the fixed-parameter PID control system. The dynamic response rate and anti-disturbance performance are better than those of the fixed-parameter PID control system. A bench comparison test was carried out. The results showed that the S-curve acceleration and deceleration motion control algorithm reduced the average mass loss rate of seedlings by 46.19% compared with the trapezoidal acceleration and deceleration motion control algorithm, and the seedling picking efficiency met the design requirements. Fuzzy PID positioning control was used, and the maximum displacement error of the end effector during seedling picking was −1.4 mm, and the average relative error rate was 0.22%, which met the positioning accuracy requirements of the end effector in the X-axis direction and verified the stability and accuracy of the designed control system. The designed control system was tested in the field, and the average comprehensive success rate of seedling picking and throwing reached 96.2%, which verified the feasibility and practicality of the control system. Full article