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Keywords = whale optimization algorithm (WOA)

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20 pages, 1656 KB  
Article
Design and Evaluation of a Flexible Substrate-Based Microstrip Sensor for Partial Discharge Detection in High-Voltage Equipment
by Shuhao Dong and Xiao Hu
Sensors 2026, 26(11), 3304; https://doi.org/10.3390/s26113304 - 22 May 2026
Abstract
Partial discharge (PD) detection effectively identifies insulation defects in power equipment. Radio frequency (RF) methods for PD detection offer promising advantages due to their non-invasive measurement capability and ability to locate discharge sources. However, microstrip antennas used as RF sensors for PD detection [...] Read more.
Partial discharge (PD) detection effectively identifies insulation defects in power equipment. Radio frequency (RF) methods for PD detection offer promising advantages due to their non-invasive measurement capability and ability to locate discharge sources. However, microstrip antennas used as RF sensors for PD detection suffer from narrow bandwidth and limited installation flexibility. To address these limitations, this paper presents a novel flexible microstrip antenna design. By incorporating a partial ground plane and oblique-cut meandering techniques and optimizing the structural parameters using an improved whale optimization algorithm (I-WOA), the operating bandwidth is expanded from 0.612–0.625 GHz to 0.346–2.0 GHz, while the overall size is reduced to 75.3% of its original dimensions. The antenna’s performance was validated through GTEM cell measurements and PD calibration pulse tests, confirming its suitability for RF detection of PD in power equipment such as transformers and cable joints. Notably, when the antenna was conformally wrapped around a cable joint, the response amplitude increased by 14%. This study contributes to the development of a low-cost, broadband, and flexibly installable RF sensor for partial discharge detection. Full article
(This article belongs to the Special Issue Feature Papers in Fault Diagnosis & Sensors 2026)
24 pages, 8161 KB  
Article
Oil Slick Detection in X-Band Marine Radar Imagery: Leveraging a Boundary-Aware SBR Feature and an Improved Whale Optimization Algorithm
by Jianxun Rui, Jin Xu, Jianbin Yuan, Zekun Guo, Shuo Zhang, Yiteng Zhang, Qiuyu Fu, Boxi Yao, Yulong Yang and Wenhui Li
J. Mar. Sci. Eng. 2026, 14(10), 935; https://doi.org/10.3390/jmse14100935 (registering DOI) - 18 May 2026
Viewed by 120
Abstract
Marine oil spills pose a persistent threat to marine ecosystems and coastal economies, and their rapid and unpredictable spread requires timely and reliable monitoring. In X-band marine radar images, oil slicks usually appear as low-contrast dark targets embedded in heterogeneous sea clutter, making [...] Read more.
Marine oil spills pose a persistent threat to marine ecosystems and coastal economies, and their rapid and unpredictable spread requires timely and reliable monitoring. In X-band marine radar images, oil slicks usually appear as low-contrast dark targets embedded in heterogeneous sea clutter, making accurate segmentation particularly challenging. To address this problem, this study proposes a training-free two-stage oil slick detection framework that combines an improved Slick Boundary Ratio (SBR) feature with an improved Whale Optimization Algorithm (WOA). First, the improved SBR feature is used to extract the oil slick region of interest (ROI). Then, the improved WOA is employed to determine the global threshold for oil slick segmentation. Experimental results show that the proposed method achieves accurate and spatially coherent oil slick segmentation in complex radar backgrounds, with an Accuracy of 99.36%, a Precision of 85.73%, a Recall of 84.42%, an F1-score of 85.07%, and an Intersection over Union (IoU) of 74.01%. These results indicate that the proposed framework can effectively suppress false positives while maintaining strong detection sensitivity, thereby improving segmentation robustness in low-contrast marine radar scenes. Owing to its training-free design, the proposed method shows potential for shipborne and coastal oil spill monitoring applications. Full article
(This article belongs to the Section Marine Ecology)
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31 pages, 2240 KB  
Article
A Routing Mechanism for Low-Power and Lossy Networks in Asymmetric Environments: Leveraging Digital Twin-Enabled Computing Power Networks
by Yanan Cao, Guang Zhang and Yuxin Shen
Symmetry 2026, 18(5), 841; https://doi.org/10.3390/sym18050841 (registering DOI) - 14 May 2026
Viewed by 181
Abstract
Asymmetry is a prevalent phenomenon in low-power and lossy networks (LLNs) due to resource constraints and unstable links. The routing protocol for the low power and lossy network (RPL), standardized by the Internet Engineering Task Force (IETF), is specifically designed for LLNs with [...] Read more.
Asymmetry is a prevalent phenomenon in low-power and lossy networks (LLNs) due to resource constraints and unstable links. The routing protocol for the low power and lossy network (RPL), standardized by the Internet Engineering Task Force (IETF), is specifically designed for LLNs with characteristics of resource constraints, lossy links, and complex communication environments. However, its performance is fundamentally limited by node capabilities and unstable links, a contradiction exacerbated by the stringent QoS demands of emerging applications like IIoT or precision agriculture. Consequently, new RPL routing technologies based on the digital twin-enabled computing power network, called RPL-DTCP, were designed to improve network QoS and support practical applications. First, a low-power and lossy network architecture based on twin-enabled computing network was proposed, considering LLN requirements and computing twin services. Second, in response to the requirements of the digital twin, computing power network and LLNs for low synchronization latency, high data accuracy, efficient computing resource utilization, and energy conservation, several routing metrics were designed, including the data processing model, model deployment rate, end-to-end delay, node remaining energy, and ETX. Then an initial matrix and a comprehensive objective function were formulated to comprehensively evaluate these metrics. Third, to solve the multi-objective optimization problem, an enhanced whale optimization algorithm (E-WOA) was developed. E-WOA improved upon the standard version by using improved Tent chaotic mapping for population initialization, nonlinear adaptive convergence factor, and Cauchy variation mutation operator for solution perturbation, thereby enhancing its global search capability and convergence speed, enabling it to effectively identify the optimal routing path. Simulations confirmed that RPL-DTCP outperforms benchmark algorithms, achieving significant reductions in end-to-end delay, higher packet delivery ratios, extended network lifetime, etc. These findings demonstrate that RPL-DTCP effectively addresses the resource-performance contradiction in LLNs, providing a reliable and efficient routing framework for emerging compute-intensive IoT applications. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Wireless Communication and Sensor Networks II)
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33 pages, 4464 KB  
Article
A Novel Algebraic Saturation-Based PID Controller Optimized by Animated Oat Algorithm for Ultra-Fast Dynamic Response of Automatic Voltage Regulation
by Ömer Türksoy
Biomimetics 2026, 11(5), 343; https://doi.org/10.3390/biomimetics11050343 - 14 May 2026
Viewed by 281
Abstract
This paper presents a novel algebraic saturation-based Proportional–Integral–Derivative (ASB-PID) controller for achieving ultra-fast and well-damped dynamic response in automatic voltage regulator (AVR) systems. The proposed controller incorporates an algebraic saturation-based nonlinear transformation applied to both the error signal and its derivative, enabling adaptive [...] Read more.
This paper presents a novel algebraic saturation-based Proportional–Integral–Derivative (ASB-PID) controller for achieving ultra-fast and well-damped dynamic response in automatic voltage regulator (AVR) systems. The proposed controller incorporates an algebraic saturation-based nonlinear transformation applied to both the error signal and its derivative, enabling adaptive control sensitivity across different operating regions. This formulation preserves high sensitivity near the equilibrium point while effectively limiting excessive control action under large transient deviations, thereby overcoming the inherent trade-off between response speed and overshoot observed in conventional PID-based controllers. To address the highly nonlinear and multimodal tuning problem, the controller parameters are optimally determined using the Animated Oat Optimization Algorithm (AOOA), which provides strong global exploration capability and stable convergence behavior. The effectiveness of AOOA is first validated through comparative analysis with widely used metaheuristic algorithms, including Particle Swarm Optimization (PSO), Gray Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), and Sine Cosine Algorithm (SCA). Furthermore, the proposed controller is benchmarked against recently developed high-performance AVR control strategies, including Gudermannian-PID (G-PID), fractional-order PID (FOPID), and higher-order PID-based controllers. Simulation results demonstrate that the proposed AOOA-optimized ASB-PID controller achieves a rise time of 0.0215 s and a settling time of 0.0383 s with zero overshoot and negligible steady-state error, significantly outperforming both competing optimization algorithms and state-of-the-art control designs. Comprehensive benchmarking further confirms that the proposed method consistently delivers superior performance in terms of speed, stability, and robustness, indicating that it provides an effective, computationally efficient, and scalable solution for high-performance AVR systems and broader nonlinear control applications. Unlike conventional nonlinear PID designs based on hyperbolic or sigmoid mappings, the proposed algebraic formulation provides a more explicit and effective saturation mechanism, enabling a superior balance between transient speed and overshoot suppression without increasing controller complexity. Full article
(This article belongs to the Section Bioinspired Sensorics, Information Processing and Control)
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25 pages, 14530 KB  
Article
Symplectic Geometry Matrix Machine Controlled by the Whale Optimization Algorithm and Its Application in Bearing Fault Diagnosis
by Yonghua Jiang, Zhiqiang He, Zhilin Dong, Jianjie Zhang, Hongkui Jiang, Chao Tang, Jianfeng Sun, Xiaohao Chen and Weidong Jiao
Vibration 2026, 9(2), 34; https://doi.org/10.3390/vibration9020034 - 13 May 2026
Viewed by 174
Abstract
In the field of industrial equipment condition monitoring, accurate rolling bearing fault diagnosis is critical yet challenging due to high-dimensional vibration signals and complex operating conditions. Traditional machine learning methods often struggle with insufficient feature separability and sensitivity to model parameters, leading to [...] Read more.
In the field of industrial equipment condition monitoring, accurate rolling bearing fault diagnosis is critical yet challenging due to high-dimensional vibration signals and complex operating conditions. Traditional machine learning methods often struggle with insufficient feature separability and sensitivity to model parameters, leading to fluctuating diagnostic accuracy. To address these challenges, this study introduces the whale optimization algorithm-guided symplectic geometry matrix machine (WOA-SGMM) and proposes the application of the whale optimization algorithm (WOA) to optimize the symplectic geometry matrix machine (SGMM), forming a WOA-SGMM diagnostic framework. (1) The symplectic geometry spectral transformation (SGST) effectively converts high-dimensional vibration signals into low-dimensional feature matrices while preserving intrinsic geometric and topological structures, enhancing noise robustness. (2) Leveraging WOA, we adaptively search for the optimal hyperparameters of the proposed SGMM, specifically addressing the limitations of traditional SMM, to mitigate the risk of overfitting. (3) Experimental validation on three benchmark datasets demonstrates that WOA-SGMM achieves superior multi-class fault diagnosis accuracy (up to 100%) under varying operating conditions. Compared to traditional methods, the proposed WOA-SGMM demonstrates improved classification accuracy and enhanced robustness against noise interference in the tested experimental scenarios, highlighting its potential for real-world industrial applications. Full article
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27 pages, 7414 KB  
Article
Research on Bidirectional Prediction Model Between Drying Process Parameters and Quality of Fritillaria ussuriensis Maxim Based on WOA-PSO-RF
by Liguo Wu, Xiangquan Meng, Yueyuan Ren, Yucheng Ding, Liping Sun, Sanping Li and Haogang Feng
Appl. Sci. 2026, 16(10), 4773; https://doi.org/10.3390/app16104773 - 11 May 2026
Viewed by 135
Abstract
During the drying of Fritillaria ussuriensis, complex nonlinear interactions occur between process parameters and quality attributes. Conventional approaches rely on empirical trial-and-error, limiting precise control and inverse optimization. This study proposes a hybrid optimization framework combining the whale optimization algorithm (WOA) and [...] Read more.
During the drying of Fritillaria ussuriensis, complex nonlinear interactions occur between process parameters and quality attributes. Conventional approaches rely on empirical trial-and-error, limiting precise control and inverse optimization. This study proposes a hybrid optimization framework combining the whale optimization algorithm (WOA) and particle swarm optimization (PSO) to establish a bidirectional mapping between process variables and quality indicators. The WOA is applied for global optimization of the random forest (RF) hyperparameters, followed by PSO for local refinement. The resulting model enables both forward prediction (from temperature, heating air velocity, dehumidification air velocity, and infrared power to quality indicators) and inverse optimization (from target quality to process parameters). The model achieves high predictive performance, with mean R2 values of 0.9739 (forward) and 0.9736 (inverse), outperforming WOA-RF, PSO-RF, and conventional RF models in accuracy, stability, and generalization. Industrial validation shows prediction errors below 10%, meeting engineering requirements. These results provide an effective approach for drying optimization and support intelligent modeling of rhizome-based medicinal materials. Full article
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31 pages, 4212 KB  
Article
AQGTO: Adaptive Q-Learning-Guided Gorilla Troops Optimizer for 3D UAV Path Planning in Precision Agriculture
by Tahar Bendouma, Saida Sarra Boudouh, Chaker Abdelaziz Kerrache and Jorge Herrera-Tapia
Drones 2026, 10(5), 357; https://doi.org/10.3390/drones10050357 - 8 May 2026
Viewed by 220
Abstract
Unmanned Aerial Vehicles (UAVs) have become a key technology in precision agriculture, enabling efficient monitoring, inspection, and targeted interventions. However, effective UAV path planning in such environments requires the generation of safe, energy-efficient, and smooth trajectories in complex three-dimensional spaces. This paper proposes [...] Read more.
Unmanned Aerial Vehicles (UAVs) have become a key technology in precision agriculture, enabling efficient monitoring, inspection, and targeted interventions. However, effective UAV path planning in such environments requires the generation of safe, energy-efficient, and smooth trajectories in complex three-dimensional spaces. This paper proposes an Adaptive Q-Learning Guided Gorilla Troops Optimizer (AQGTO) for 3D UAV path planning. The proposed method integrates a state-aware Q-learning mechanism into the Gorilla Troops Optimizer (GTO), enabling the optimizer to adaptively select exploration, exploitation, and diversification strategies according to the current optimization state. A multi-objective cost function is formulated to simultaneously minimize path length, an energy-related surrogate cost, obstacle proximity, path smoothness, and altitude variation. In addition, a feasibility repair mechanism is introduced to ensure collision-free trajectories in environments with cylindrical obstacles. The proposed approach is evaluated in three representative agricultural scenarios: row-crop fields, orchard environments, and hilly terrains. Experimental results show that AQGTO achieves competitive and improved performance compared with classical A*, Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), and the original GTO in terms of trajectory cost, path efficiency, and stability. Furthermore, an ablation study confirms that the integration of Q-learning significantly enhances optimization performance. These results suggest that AQGTO provides an effective and robust solution for UAV path planning in complex agricultural environments. Full article
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19 pages, 3564 KB  
Article
Hybrid Whale-Optimized Quantum Particle Swarm Optimization for Maximum Power Tracking in Multi-Peak PV Arrays Under Varying Light Intensities
by Jia Chi, Qiuyan Liang, Chuanhua Yang, Shuangyin Han and Mengyuan Jia
Appl. Sci. 2026, 16(10), 4596; https://doi.org/10.3390/app16104596 - 7 May 2026
Viewed by 306
Abstract
In different light intensities, photovoltaic (PV) arrays with multi-peak characteristics encounter numerous challenges in maximum power point tracking (MPPT) control, such as low computational efficiency, slow convergence speed, and susceptibility to local optima. To address these issues, this study proposes an improved quantum [...] Read more.
In different light intensities, photovoltaic (PV) arrays with multi-peak characteristics encounter numerous challenges in maximum power point tracking (MPPT) control, such as low computational efficiency, slow convergence speed, and susceptibility to local optima. To address these issues, this study proposes an improved quantum particle swarm optimization (QPSO) algorithm that combines the advanced features of the Whale Optimization Algorithm (WOA) with the concept of Lévy flight, thereby forming a novel mechanism. The convergence of this algorithm, together with the particle swarm optimization (PSO) and quantum particle swarm optimization (QPSO) algorithms, was simulated and evaluated using 10 single-peak and multi-peak test functions, and then applied to a simulation model of PV array partial shading. The results show that, compared with the traditional PSO method, the tracking accuracy of this algorithm is improved by 2.80% and the convergence speed is increased by 57.14%. Under both static and sudden shading conditions, this algorithm can effectively enhance the tracking ability of the maximum power point of the PV array and achieve stable maximum power output. The average tracking accuracy of this algorithm reaches 99.71% and the average tracking speed is 0.06 s in simulation, showing an obvious advantage over both the PSO and QPSO algorithms. This simulation-based validation confirms the algorithm’s effectiveness, though hardware validation remains for future work. These results fully demonstrate the unique advantages and innovation of this algorithm in dealing with complex optimization problems, laying a solid foundation for improving the efficiency and reliability of PV systems and providing strong support for related research in this field. Full article
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38 pages, 13926 KB  
Article
A Brown Bear Optimization Driven RGB–Sobel Histogram Fusion Approach for Robust Color Image Segmentation
by Dussa Sudha Mohan and Kothapelli Punnam Chandar
Symmetry 2026, 18(5), 795; https://doi.org/10.3390/sym18050795 - 6 May 2026
Viewed by 192
Abstract
Image segmentation is the first step of image processing. It allows us to comprehend and extract information from the digital image. Multilevel thresholding is one of the most commonly used image segmentation techniques because of its simplicity and effectiveness. However, with the higher [...] Read more.
Image segmentation is the first step of image processing. It allows us to comprehend and extract information from the digital image. Multilevel thresholding is one of the most commonly used image segmentation techniques because of its simplicity and effectiveness. However, with the higher threshold level required, the more complex the process of finding the optimal threshold values becomes more complex. In this research, an effective optimization-based image segmentation technique using Otsu’s multilevel thresholding technique as the objective function to overcome the difficulties of finding the best threshold values is proposed. Instead of using the exhaustive search process, which requires more time, the best threshold values are obtained using different optimization techniques based on the nature of the image. In this study, the optimized threshold values are computed based on Otsu’s scheme, Sobel filter with Brown Bear Optimization Algorithm (BBOA), which is compared with thresholds computed based on the Artificial Bee Colony (ABC) algorithm, Jaya Algorithm (JA), Moth Flame Optimization (MFO) algorithm, Whale Optimization Algorithm (WOA) algorithm, and Particle Swarm Optimization (PSO) algorithm for segmentation. The objective function includes the sum of the variances of all four channels, namely, Red, Green, Blue, and Gray (Sobel). The superiority of the proposed method (BBOA_S) is tested on ten natural color benchmark images to verify results, and the quality of the suggested method is evaluated quantitatively by applying popular image quality assessment parameters, including PSNR, SSIM, and FSIM. The experimental results clearly show the efficiency of the suggested method of segmentation. In fact, the suggested method of segmentation has a higher PSNR value, up to 26.11, compared to other optimization methods, which have lower values. Similarly, the suggested method has a high value of structural similarity, up to 0.988, indicating that it performs a great job in terms of structural similarity. The proposed method also highly minimizes the reconstruction error, as indicated by the minimum values of the MSE, which are close to 194. This is better compared to the results of most of the other methods, which were carried out on the same images. Although the FSIM values of the proposed method are comparable to the values of the other methods, it is evident that the proposed method is good and reliable, as indicated by the overall quantitative and visual assessment. Therefore, it is clear that the use of Otsu’s multi-layer thresholding and the Sobel filter effect in combination with BBOA is effective and good. Full article
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26 pages, 2936 KB  
Article
Design, Optimization, and Field Evaluation of an Automatic Steering System for Agricultural Tractors Using Metaheuristic PID Tuning
by Ali Karamolachab, Saman Abdanan Mehdizadeh and Yiannis Ampatzidis
Agriculture 2026, 16(9), 1004; https://doi.org/10.3390/agriculture16091004 - 3 May 2026
Viewed by 1063
Abstract
This paper presents the design and field evaluation of a low-cost automatic steering system for agricultural tractors. The system employs a PID controller whose gains are tuned using a metaheuristic optimization method. Core hardware includes an ESP32 microcontroller, an MPU9250 inertial measurement unit, [...] Read more.
This paper presents the design and field evaluation of a low-cost automatic steering system for agricultural tractors. The system employs a PID controller whose gains are tuned using a metaheuristic optimization method. Core hardware includes an ESP32 microcontroller, an MPU9250 inertial measurement unit, a GPS module, and a servo motor for closed-loop yaw angle control, with a complementary filter fusing gyroscope and magnetometer data for robust heading estimation. Nine optimization algorithms were systematically compared: Grid Search, Random Search, Bayesian Optimization, Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), Moth-Flame Optimization (MFO), Sine Cosine Algorithm (SCA), Whale Optimization Algorithm (WOA), and Salp Swarm Algorithm (SSA). A cost function combining overshoot and settling time was used. Step response analysis showed that WOA achieved the best performance, with an integral absolute error of 6.31°·s, a settling time of 2.15 s, and a minimal overshoot of 0.08°. In field tests on asphalt and farmland, the WOA-tuned system reduced lateral deviation by 69% (from 12.4 cm to 3.8 cm) and 67% (from 18.7 cm to 6.2 cm), respectively, compared to manual steering. Repeated-measures ANOVA and paired t-tests confirmed statistically significant improvements (p < 0.001) with large effect sizes (Cohen’s d > 2.7). The core components cost under $150 USD. The study offers a reproducible pipeline for comparative metaheuristic evaluation in agricultural vehicle guidance. Full article
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26 pages, 6834 KB  
Article
Optimization for Urban Low-Altitude Logistics Using an Improved Whale Optimization Algorithm
by Song Yang, Yaxuan Huang and Hongmei Zhou
Appl. Sci. 2026, 16(9), 4385; https://doi.org/10.3390/app16094385 - 30 Apr 2026
Viewed by 220
Abstract
Urban low-altitude logistics is increasingly constrained by obstacle-rich city morphology and wind-induced flight disturbances, which makes conventional path-planning methods insufficient for simultaneously ensuring efficiency, feasibility, and robustness. To address this issue, this study proposes an improved whale optimization algorithm (IWOA) for wind-field-coupled three-dimensional [...] Read more.
Urban low-altitude logistics is increasingly constrained by obstacle-rich city morphology and wind-induced flight disturbances, which makes conventional path-planning methods insufficient for simultaneously ensuring efficiency, feasibility, and robustness. To address this issue, this study proposes an improved whale optimization algorithm (IWOA) for wind-field-coupled three-dimensional UAV path planning in urban environments. A voxel-based urban model is established, and the planning objective integrates flight time, energy consumption, wind-field penalty, and path smoothness. On the basis of the original whale optimization algorithm, the proposed method introduces a wind-field-guided local adjustment operator, adaptive convergence control, elite preservation, large-scale mutation, and feasibility repair. The proposed method is evaluated through a structured simulation framework comprising four scenarios: a baseline case, urban density variation, complex wind-field variation, and multi-destination delivery. The results show that IWOA consistently yields the lowest composite cost among the compared algorithms and exhibits better path smoothness, stronger wind adaptation, and earlier convergence stability. In the baseline case, the total cost of IWOA is reduced by 17.3%, 13.1%, and 6.7% relative to A*, GA, and WOA, respectively. Under the high-density urban environment and the complex wind field, IWOA also maintains the best performance, indicating stronger robustness under increased environmental difficulty. Sensitivity analyses further show that wind speed and wind direction have pronounced effects on the total cost, while the energy coefficient mainly affects the energy-related component. These results demonstrate that the proposed framework provides an effective and practically relevant solution for urban low-altitude UAV logistics path planning. Full article
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37 pages, 64444 KB  
Article
A WTD-WOA-SVMD-Based Signal Processing Method for Stress Distortion Zones in Coiled Tubing
by Xu Luo, Huan Yang, Wenbo Jiang, Luqi Lin, An Mao and Li Kou
Processes 2026, 14(9), 1404; https://doi.org/10.3390/pr14091404 - 28 Apr 2026
Viewed by 343
Abstract
As critical equipment in the petroleum industry, coiled tubing is prone to safety hazards, including stress concentrations and fatigue failure, under complex operating conditions. An online enhanced metal magnetic memory detection method was employed to reduce noise in surface magnetic field signals from [...] Read more.
As critical equipment in the petroleum industry, coiled tubing is prone to safety hazards, including stress concentrations and fatigue failure, under complex operating conditions. An online enhanced metal magnetic memory detection method was employed to reduce noise in surface magnetic field signals from tubing subjected to 35 MPa of internal pressure across different fatigue cycles. Conventional signal processing methods have difficulty effectively extracting characteristic magnetic field signals in high-noise environments; therefore, a comprehensive comparison of the noise reduction effectiveness of five common signal processing techniques in stress-distorted regions was conducted, an in-depth analysis of the limitations of different methods was performed, and a hybrid noise reduction framework combining wavelet threshold denoising (WTD) and sequential variational modal decomposition (SVMD) was established. Concurrently, the whale optimization algorithm (WOA), which possesses global search capabilities and demonstrates good adaptability to multi-parameter coupling issues in hybrid denoising frameworks, was innovatively proposed for key parameter optimization. Using fuzzy entropy (FE) as an evaluation metric, the experimental results demonstrated that magnetic field signals in all directions achieved at least a 1.03% reduction in FE and a minimum increase of 33.1% in integrated side lobe ratio (ISLR). This provided effective technical support for reliably detecting stress-distortion zones on coiled-tubing surfaces and established the engineering necessity of implementing preventive maintenance. Full article
(This article belongs to the Section Process Control, Modeling and Optimization)
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29 pages, 1564 KB  
Article
Product Structure Optimization of Coal Preparation Plants Based on GPSOM–WOA
by Gan Luo, Ranfeng Wang, Xiang Fu, Mingzhang Yang, Longkang Li, Xinlei Li, Shunqiang Wang and Hanchi Ren
Processes 2026, 14(9), 1366; https://doi.org/10.3390/pr14091366 - 24 Apr 2026
Viewed by 215
Abstract
Coal preparation plants pursue maximum economic benefit, yet product structure optimization under fluctuating coal quality and changing market demand is a coupled decision-making problem involving the organization of primary products such as lump clean coal, clean coal, raw fine coal, coal slime, and [...] Read more.
Coal preparation plants pursue maximum economic benefit, yet product structure optimization under fluctuating coal quality and changing market demand is a coupled decision-making problem involving the organization of primary products such as lump clean coal, clean coal, raw fine coal, coal slime, and gangue, together with commercial coal blending and process-scheme selection. Conventional optimization methods that focus on a single stage are often insufficient to address such complex coordinated decisions. To this end, a GPSOM–WOA nested optimization model was developed to achieve the coordinated optimization of primary product separation, commercial coal blending, and process-scheme selection under the objective of economic benefit maximization. In the outer layer, where process-scheme selection and primary product structure adjustment involve both discrete decisions and continuous variables, a simplified Group-based Particle Swarm Optimization with Multiple Strategies (GPSOM) was employed to search the primary product structure parameters and generate engineering-feasible primary product balance tables. In the inner layer, where the commercial coal blending problem is subject to multiple constraints, including ash content, moisture, calorific value, and supply demand, the Whale Optimization Algorithm (WOA) was adopted to optimize blending ratios within a restricted feasible region. A piecewise penalty function was introduced for quality-limit violations to support profit-oriented constrained optimization. Subject to commercial coal quality constraints on ash content, moisture, and calorific value, a case study of a coal preparation plant in Inner Mongolia was conducted to compare product structures and economic benefits under different process conditions. The results show that the proposed model can realize the joint optimization of primary product structure and commercial coal blending, and can provide a quantitative basis for product structure optimization and process selection in coal preparation plants. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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28 pages, 3847 KB  
Article
Optimal Reactive Power Compensation in Rural Distribution Systems Through a Neuroscience-Based Optimization Approach
by Juan M. Lujano-Rojas, Rodolfo Dufo-López, Jesús S. Artal-Sevil and José L. Bernal-Agustín
Energies 2026, 19(8), 1968; https://doi.org/10.3390/en19081968 - 18 Apr 2026
Viewed by 240
Abstract
Improving the efficiency of distribution systems (DSs) through reactive power compensation using shunt capacitor banks is a widely applied practice, as it enhances the voltage profile and reduces operating costs. Owing to the nonlinear nature of DSs, heuristic algorithms—along with other optimization tools—are [...] Read more.
Improving the efficiency of distribution systems (DSs) through reactive power compensation using shunt capacitor banks is a widely applied practice, as it enhances the voltage profile and reduces operating costs. Owing to the nonlinear nature of DSs, heuristic algorithms—along with other optimization tools—are frequently employed to support techno-economic decision-making in DS design. In this study, we employ the neural population dynamics optimization algorithm (NPDOA), a recently developed heuristic approach inspired by brain neuroscience. The simulation and optimization model adopted in this research is based on quasi-static time-series analysis, which enables the planning problem and DS constraints to be examined from a probabilistic perspective. A comparative analysis with the genetic algorithm (GA) and the whale optimization algorithm (WOA) indicates that NPDOA provides a similar solution with comparable computational time. Specifically, the results show that NPDOA produces a solution only 0.02% higher than GA, with improvement probabilities of 27.42% and 10.94%, respectively. In comparison with WOA, NPDOA yields a solution that is 0.05% lower, with a corresponding probability of improvement of 10.76%. Furthermore, the installation of shunt capacitor banks optimized using NPDOA reduces the net present cost by 33%. Full article
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29 pages, 4784 KB  
Article
Incipient Fault Diagnosis in Power Cables Based on WOA-CEEMDAN and a TCN-BiLSTM Network with Multi-Head Attention
by Yuhua Xing and Yaolong Yin
Appl. Sci. 2026, 16(8), 3908; https://doi.org/10.3390/app16083908 - 17 Apr 2026
Viewed by 233
Abstract
Incipient faults in power cables are difficult to diagnose because their transient signatures are weak, non-stationary, and easily masked by background noise, while labeled real-world samples are often scarce. To address these challenges, this paper proposes an offline diagnosis framework that integrates Whale [...] Read more.
Incipient faults in power cables are difficult to diagnose because their transient signatures are weak, non-stationary, and easily masked by background noise, while labeled real-world samples are often scarce. To address these challenges, this paper proposes an offline diagnosis framework that integrates Whale Optimization Algorithm (WOA)-guided CEEMDAN with a TCN-BiLSTM-Multi-HeadAttention network. The proposed method has three main features. First, WOA is explicitly mapped to the CEEMDAN parameter optimization problem and is used to adaptively optimize the noise amplitude and ensemble number, thereby improving decomposition quality and enhancing weak fault-related components. Second, the optimized intrinsic mode functions are reconstructed into a multi-channel representation that preserves complementary fault information across different frequency bands. Third, a hybrid deep architecture combining Temporal Convolutional Networks, Bidirectional Long Short-Term Memory, and multi-HeadAttention is designed to jointly capture local transient characteristics, bidirectional temporal dependencies, and fault-sensitive feature interactions. Experimental results on both PSCAD/EMTDC simulation data and real-world measured data show that the optimized WOA-CEEMDAN achieves superior decomposition performance, with an RMSE of 0.097 and an SNR of 8.42 dB. On the real-world test dataset, the proposed framework achieves 96.00% accuracy, 97.25% precision, 96.84% recall, an F1-score of 0.970, and an AUC of 0.97, outperforming several representative baseline models. Additional ablation, noise-robustness, small-sample, confusion-matrix, and cross-cable validation results further demonstrate the effectiveness and robustness of the proposed framework for incipient cable fault diagnosis. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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