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Search Results (8,068)

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Keywords = vibration modelling

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19 pages, 5614 KB  
Article
CNN-BiLSTM-CA Model with Visualized Bayesian Optimization for Structural Vibration Prediction During Flood Discharge
by Guojiang Yin and Shuo Wang
Vibration 2026, 9(2), 23; https://doi.org/10.3390/vibration9020023 (registering DOI) - 30 Mar 2026
Abstract
Accurate prediction of vibration responses in hydraulic structures during flood discharge is essential for ensuring safe and stable operation. This study develops a hybrid deep learning model that combines Convolutional Neural Networks (CNN), Bidirectional Long Short-Term Memory (BiLSTM), and a Channel Attention (CA) [...] Read more.
Accurate prediction of vibration responses in hydraulic structures during flood discharge is essential for ensuring safe and stable operation. This study develops a hybrid deep learning model that combines Convolutional Neural Networks (CNN), Bidirectional Long Short-Term Memory (BiLSTM), and a Channel Attention (CA) mechanism, optimized through Bayesian Optimization (BO), to predict dam gantry crane beam displacements. Time-lagged Pearson correlation and Maximum Information Coefficient (MIC) are applied to select the informative input features. The CNN-BiLSTM-CA model captures both spatial patterns and temporal dependencies in vibration signals. BO tunes model hyperparameters, while Partial Dependence (PD) analysis provides insight into how these parameters affect prediction accuracy. The model is validated using vibration data from an arch dam in Southwest China during flood discharge. Results show that CNN parameters have a greater impact on prediction accuracy than BiLSTM parameters, underscoring the importance of spatial feature extraction. Ablation studies confirm each component’s contribution. Compared with existing methods, the proposed model achieves superior accuracy with a Root Mean Square Error (RMSE) of 5.49, Mean Absolute Error (MAE) of 4.34, and correlation coefficient (R) of 99.42%. This framework provides a reliable and interpretable tool for predicting structural vibrations in hydraulic engineering under complex discharge conditions. Full article
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16 pages, 4855 KB  
Proceeding Paper
Modeling and Simulation of Active Suspension System for Road Vehicles and Sensitivity to Design Criteria for Energy Efficiency
by Maurizio Guadagno, Lorenzo Berzi, Marco Pierini and Massimo Delogu
Eng. Proc. 2026, 131(1), 17; https://doi.org/10.3390/engproc2026131017 - 30 Mar 2026
Abstract
Active suspensions in automotive applications are designed to improve vehicle stability and comfort and reduce vibration transmission from the road surface. Active systems often include a dedicated actuator, and, to reduce their mass and energy absorption, it is a typical choice to rely [...] Read more.
Active suspensions in automotive applications are designed to improve vehicle stability and comfort and reduce vibration transmission from the road surface. Active systems often include a dedicated actuator, and, to reduce their mass and energy absorption, it is a typical choice to rely on brushless electric motors with permanent magnets containing Critical Raw Materials such as Neodymium, a Rare Earth Element (REE), offering favorable power density values. Although these systems offer clear advantages in terms of ride quality and performance, their direct and indirect energy requirements, combined with their dependence on resource-intensive materials, raise concerns about life cycle sustainability: in other words, there is a trade-off between production impact (relevant for REE) and use impact (reduced by REE adoption). To address this issue, the research proposes a method to estimate energy consumption during the use phase of a vehicle through a dedicated parametric modeling and simulation framework; the aim is to evaluate the energy performance of active suspension systems under different road and driving conditions. The analysis explores how design parameters and operational choices affect energy consumption and efficiency. The simulation results reveal a marked sensitivity of system performance to road profiles and driving scenarios, highlighting the importance of holistic assessments during the early stages of design. The proposed framework represents a first step toward integrating circular design principles into the development of active suspensions. By combining technical and environmental perspectives, it supports the development of next-generation automotive components that balance comfort, performance, and sustainability. Full article
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21 pages, 1482 KB  
Article
Multi-Degree-of-Freedom Tuned Mass Damper for Vibration Suppression of Floating Offshore Wind Turbine
by Zhendong Yang, Haoran He, Faxiang Zhang and Jing Na
J. Mar. Sci. Eng. 2026, 14(7), 634; https://doi.org/10.3390/jmse14070634 (registering DOI) - 30 Mar 2026
Abstract
Stable wind resources in far-reaching sea areas are important direction for the development of renewable energy, making floating offshore wind turbine (FOWT) a focus of current research. However, the working environment of FOWT is severe. Under the condition of changeable wind and waves, [...] Read more.
Stable wind resources in far-reaching sea areas are important direction for the development of renewable energy, making floating offshore wind turbine (FOWT) a focus of current research. However, the working environment of FOWT is severe. Under the condition of changeable wind and waves, the floating platform exhibits various motion responses, which may reduce power generation efficiency and even lead to structural damage with unpredictable consequences. In this paper, the National Renewable Energy Laboratory (NREL) 5 MW OC4-DeepCwind semi-submersible wind turbine is considered, and a multi-degree-of-freedom (M-DOF) tuned mass damper (TMD) system is designed to simultaneously suppress its roll and pitch motion responses. A multi-objective optimization problem is formulated to unify the frequency tuning accuracy, damping ratio constraints, and mass ratio limits through penalty functions. Then an improved Particle Swarm Optimization algorithm with time-varying acceleration coefficients (TVAC-PSO) is employed to determine the optimal TMD parameters, which dynamically adjusts exploration and exploitation capabilities to overcome the limitations of standard PSO in handling the strongly coupled parameter space. A high-fidelity aero-hydro-servo-elastic simulation model is established using OpenFAST to verify the vibration suppression performance under various sea state conditions. Simulation results demonstrate that the proposed M-DOF TMD system can effectively reduce the roll and pitch motion responses and significantly suppress the resonant peak energy, substantially improving the dynamic performance of FOWT. Full article
(This article belongs to the Special Issue Control and Optimization of Marine Renewable Energy Systems)
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12 pages, 1211 KB  
Article
Non-Relativistic Closed-Form Energy Spectrum of a Hyperbolic Molecular Potential Through the Asymptotic Iteration Method
by Hasan Fatih Kisoglu
Symmetry 2026, 18(4), 586; https://doi.org/10.3390/sym18040586 (registering DOI) - 30 Mar 2026
Abstract
In this study, we consider a potential expressed as a hyperbolic-sine function aiming to achieve the energy eigenvalues in a closed form, that is, as an analytical expression. Based on this, the Schrödinger equation is constructed within the framework of non-relativistic quantum mechanics [...] Read more.
In this study, we consider a potential expressed as a hyperbolic-sine function aiming to achieve the energy eigenvalues in a closed form, that is, as an analytical expression. Based on this, the Schrödinger equation is constructed within the framework of non-relativistic quantum mechanics and is tackled by using the Asymptotic Iteration Method. The potential in question was previously addressed in the literature. As an alternative, we obtain the complete energy spectrum in a closed form for the single-well regime of the potential function, by way of the quasi-exact solvability where the system has analytical energy eigenvalues once a certain condition is met, or a relation between the potential parameters is satisfied. This is provided by the applicability of the Asymptotic Iteration Method to both quasi-exact and numerical solutions. Thus, the effects of the potential parameters on the energy spectrum can be seen separately. We conclude that the accuracy of the obtained closed-form energy spectrum is quite high as evidenced by the strong agreement with the numerically obtained ones. Furthermore, it is seen that this consistency improves as the energy level increases. The obtained analytical expression can also be used as a simple analytical model for vibrational spectrum of molecular systems described by anharmonic single-well potentials. Full article
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40 pages, 6696 KB  
Article
Aluminum Surface Quality Prediction Based on Support Vector Machine and Three Axes Vibration Signals Acquired from Robot Manipulator Grinding Experiment
by Khairul Muzaka, Liyanage Chandratilak De Silva and Wahyu Caesarendra
Automation 2026, 7(2), 55; https://doi.org/10.3390/automation7020055 (registering DOI) - 30 Mar 2026
Abstract
This research presents a machine learning-based vibration signal acquired from aluminum grinding experiment for potential application in smart and intelligent manufacturing. The study addresses the challenges of traditional surface finishing quality inspection by integrating vibration sensing and support vector machine (SVM). A robot [...] Read more.
This research presents a machine learning-based vibration signal acquired from aluminum grinding experiment for potential application in smart and intelligent manufacturing. The study addresses the challenges of traditional surface finishing quality inspection by integrating vibration sensing and support vector machine (SVM). A robot manipulator lab grinding experiment consist of a four-axis DOBOT Magician with a handheld cylindrical grinding tool attached on the end-effector of the DOBOT Magician. This customized lab grinding experiment was designed to perform consistent surface finishing experiment for different aluminum work coupon and time duration. Triaxial accelerometer was used to collect the vibration signal and to investigate the most relevant vibration signal direction (x, y, and z) to the surface quality prediction of the aluminum work coupon. The vibration signal was acquired via LabVIEW and NI data acquisition (DAQ) system. The vibration features were extracted and analyzed using Python programming in Google Colab. The SVM algorithm in Python (3.11 and 3.12) is used to classify surface roughness quality into coarse, medium, and fine categories based on the extracted vibration features. Vibration feature parameters such as root mean square (RMS), Peak to RMS, Skewness, and Kurtosis were also investigated to determined which feature pairs are most critical for effective surface roughness monitoring and prediction using SVM classification. The classification model achieved high accuracy across all three vibration axes (x, y, and z), with the z-axis yielding the most consistent results. The proposed system has potential applications in real-time surface quality prediction within smart manufacturing practices aligned with Industry 4.0 principles. Full article
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4 pages, 159 KB  
Editorial
Control and Optimization of Ship Propulsion System
by Xin Hu
J. Mar. Sci. Eng. 2026, 14(7), 630; https://doi.org/10.3390/jmse14070630 (registering DOI) - 30 Mar 2026
Abstract
Marine vessels operate in highly dynamic and uncertain marine environments, where propulsion systems are continuously influenced by multiple-source disturbances induced by waves, wind, ocean currents, structural vibration, mechanical friction, and modeling uncertainties [...] Full article
(This article belongs to the Special Issue Control and Optimization of Ship Propulsion System)
20 pages, 1910 KB  
Article
A Self-Propelled Traveling-Wave Linear Ultrasonic Motor Based on End Excitation
by Danhong Lu, Wenjian Qian, Nan Sun, Yao Chen, Xiaoxiao Dong and Bowen Chang
Micromachines 2026, 17(4), 418; https://doi.org/10.3390/mi17040418 (registering DOI) - 29 Mar 2026
Abstract
Ultrasonic motors have attracted considerable attention in precision actuation applications because of their advantages over conventional electromagnetic motors, such as compact structure, high positioning accuracy, immunity to electromagnetic interference, noise-free operation, and suitability for low-temperature environments. However, conventional traveling-wave linear ultrasonic motors usually [...] Read more.
Ultrasonic motors have attracted considerable attention in precision actuation applications because of their advantages over conventional electromagnetic motors, such as compact structure, high positioning accuracy, immunity to electromagnetic interference, noise-free operation, and suitability for low-temperature environments. However, conventional traveling-wave linear ultrasonic motors usually rely on boundary constraints to establish stable traveling waves, which may limit their structural flexibility and self-propelled capability. To address this issue, this paper proposes a free-boundary traveling-wave linear ultrasonic motor capable of realizing self-propelled motion. The motor features a projection structure at each end of the stator. Two piezoelectric ceramics are placed at one end for excitation, while a damping material is arranged at the other end for energy absorption. This design enables the motor to generate traveling waves without requiring fixed boundary conditions. The motor operates in the B(3,1) out-of-plane vibration mode to enhance the energy absorption capacity of the non-excited end and reduce its standing wave ratio (SWR). A finite element model of the motor is established to investigate its vibration characteristics. In addition, a novel method for estimating the standing wave ratio is proposed by using piezoelectric ceramics attached to the motor surface, replacing the traditional calculation approach. A prototype is fabricated to verify the feasibility of the proposed design. Experimental results show that the prototype achieves a minimum SWR of 1.81, a no-load speed of 42.1 mm/s, and a maximum output force of 0.465 N. These results confirm the feasibility of the proposed scheme and provide a new approach for the design of free-boundary traveling-wave linear ultrasonic motors. Full article
24 pages, 1545 KB  
Article
PMSDA: Progressive Multi-Strategy Domain Alignment for Cross-Scene Vibration Recognition in Distributed Optical Fiber Sensing
by Yuxiang Ni, Jing Cheng, Di Wu, Qianqian Duan, Linhua Jiang, Xing Hu and Dawei Zhang
Photonics 2026, 13(4), 334; https://doi.org/10.3390/photonics13040334 - 29 Mar 2026
Abstract
Distributed optical fiber vibration sensing (DVS) has shown strong potential in perimeter security, pipeline leakage monitoring, transportation safety, and structural health diagnostics owing to its high sensitivity, long-range coverage, and immunity to electromagnetic interference. However, severe cross-scene distribution mismatch is often encountered in [...] Read more.
Distributed optical fiber vibration sensing (DVS) has shown strong potential in perimeter security, pipeline leakage monitoring, transportation safety, and structural health diagnostics owing to its high sensitivity, long-range coverage, and immunity to electromagnetic interference. However, severe cross-scene distribution mismatch is often encountered in real-world deployments: indoor, outdoor, and pipeline environments exhibit markedly different noise patterns and time–frequency characteristics, thereby degrading the generalization ability of models trained in a single scene. To address this challenge, we propose a Progressive Multi-Strategy Domain Alignment (PMSDA) framework for label-disjoint cross-scene vibration recognition. PMSDA uses a compact expansion–compression encoder together with complementary alignment mechanisms—maximum mean discrepancy (MMD), correlation alignment (CORAL), and adversarial domain discrimination—to learn a scene-robust latent space from a labeled indoor source and two unlabeled target domains (outdoor and pipeline) within a single alternating-training model. Because the fine-grained source and target label spaces are disjoint, PMSDA is formulated as a representation-transfer framework rather than a standard label-shared unsupervised domain adaptation method; target-domain recognition is therefore performed through domain-specific prototype clustering in the aligned latent space. On three representative scenes with nine event classes in total, PMSDA achieved 89.5% accuracy, 86.7% macro-F1, and 0.93 AUC for Indoor→Outdoor, and 85.8%, 84.7%, and 0.87, respectively, for Indoor→Pipeline, outperforming traditional feature+SVM/RF pipelines, CNN/ResNet baselines, and representation-transfer baselines adapted from DANN/CDAN/SHOT under the same evaluation protocol. These results indicate that PMSDA is a promising and effective framework for offline cross-scene DVS evaluation under disjoint target event sets. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence for Optical Networks)
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9 pages, 596 KB  
Data Descriptor
Curated Vibration Features and an Interpretable Gearbox Health Index (GHI) Baseline for Condition Monitoring Bench-Marking
by Krisztian Horvath
Data 2026, 11(4), 70; https://doi.org/10.3390/data11040070 - 29 Mar 2026
Abstract
This data descriptor provides a standardized and reproducible subsystem-level representation of the NREL wind turbine gearbox condition monitoring benchmarking dataset. The released records are derived from Healthy (H1–H10) and Damaged (D1–D10) measurement files and include subsystem-level standardized indices (KHI_HS, KHI_IMS, KHI_PL) together with [...] Read more.
This data descriptor provides a standardized and reproducible subsystem-level representation of the NREL wind turbine gearbox condition monitoring benchmarking dataset. The released records are derived from Healthy (H1–H10) and Damaged (D1–D10) measurement files and include subsystem-level standardized indices (KHI_HS, KHI_IMS, KHI_PL) together with a calibrated 0–1 Gearbox Health Index (GHI). The indices are generated using a fully specified and deterministic feature extraction and aggregation workflow based on established vibration indicators and healthy-referenced normalization. The Zenodo deposit contains machine-readable CSV tables intended to support transparent benchmarking across supervised classification and anomaly detection studies. The proposed GHI is introduced as an interpretable and reproducible reference baseline rather than an optimized diagnostic model. Technical validation demonstrates condition-level separability within the analyzed dataset while emphasizing the descriptive nature of the index. By releasing structured derived records and a documented regeneration procedure, this work enables an implementation-independent comparison of gearbox condition monitoring approaches and supports reproducible evaluation of alternative health index formulations. Full article
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21 pages, 1675 KB  
Article
Thermoelastic Vibration of Functionally Graded Porous Euler–Bernoulli Beams Using the Differential Transformation Method
by Selin Kaptan and İbrahim Özkol
Appl. Sci. 2026, 16(7), 3271; https://doi.org/10.3390/app16073271 - 27 Mar 2026
Viewed by 111
Abstract
Functionally graded porous beams are increasingly used in lightweight engineering structures, where thermal effects and material inhomogeneity significantly influence vibration behavior. In this study, the thermoelastic free vibration of functionally graded porous Euler–Bernoulli beams with temperature-dependent material properties is investigated by considering uniform [...] Read more.
Functionally graded porous beams are increasingly used in lightweight engineering structures, where thermal effects and material inhomogeneity significantly influence vibration behavior. In this study, the thermoelastic free vibration of functionally graded porous Euler–Bernoulli beams with temperature-dependent material properties is investigated by considering uniform and symmetric porosity distributions, together with uniform, linear, and nonlinear temperature fields. The governing equations are derived based on classical Euler–Bernoulli beam theory and solved using the Differential Transformation Method, while the accuracy of the semi-analytical formulation is verified through a Hermite-based finite element model. The results show that increasing temperature reduces the bending stiffness due to thermal axial forces and leads to a rapid decrease in natural frequency as the critical buckling temperature is approached. Increasing porosity generally decreases the natural frequency, although a slight increase may occur in symmetric distributions because of the accompanying reduction in mass density. The present study provides a computational framework for the thermo-vibration analysis of functionally graded porous beams in lightweight structural applications. Full article
(This article belongs to the Section Acoustics and Vibrations)
24 pages, 1020 KB  
Article
Research on the Diagnosis of Abnormal Sound Defects in Automobile Engines Based on Fusion of Multi-Modal Images and Audio
by Yi Xu, Wenbo Chen and Xuedong Jing
Electronics 2026, 15(7), 1406; https://doi.org/10.3390/electronics15071406 - 27 Mar 2026
Viewed by 168
Abstract
Against the global carbon neutrality target, predictive maintenance (PdM) of automotive engines represents a core technical strategy to advance the sustainable development of the automotive industry. Conventional single-modal diagnostic approaches for engine abnormal sound defects suffer from low accuracy and weak anti-interference capability. [...] Read more.
Against the global carbon neutrality target, predictive maintenance (PdM) of automotive engines represents a core technical strategy to advance the sustainable development of the automotive industry. Conventional single-modal diagnostic approaches for engine abnormal sound defects suffer from low accuracy and weak anti-interference capability. Existing multi-modal fusion methods fail to deeply mine the physical coupling between cross-modal features and often entail excessive model complexity, hindering deployment on resource-constrained on-board edge devices. To resolve these limitations, this study proposes a Physical Prior-Embedded Cross-Modal Attention (PPE-CMA) mechanism for lightweight multi-modal fusion diagnosis of engine abnormal sound defects. First, wavelet packet decomposition (WPD) and mel-frequency cepstral coefficients (MFCC) are integrated to extract time-frequency features from engine audio signals, while a channel-pruned ResNet18 is employed to extract spatial features from engine thermal imaging and vibration visualization images. Second, the PPE-CMA module is designed to adaptively assign attention weights to audio and image features by exploiting the physical coupling between engine fault acoustic and visual characteristics, enabling efficient cross-modal feature fusion with redundant information suppression. A rigorous theoretical derivation is provided to link cosine similarity with the physical correlation of engine fault acoustic-visual features, justifying the attention weight constraint (β = 1 − α) from the perspective of fault feature physical coupling. Third, an improved lightweight XGBoost classifier is constructed for fault classification, and a hybrid data augmentation strategy customized for engine multi-modal data is proposed to address the small-sample challenge in industrial applications. Ablation experiments on ResNet18 pruning ratios verify the optimal trade-off between diagnostic performance and computational efficiency, while feature distribution analysis validates the authenticity and effectiveness of the hybrid augmentation strategy. Experimental results on a self-constructed multi-modal dataset show that the proposed method achieves 98.7% diagnostic accuracy and a 98.2% F1-score, retaining 96.5% accuracy under 90 dB high-level environmental noise, with an end-to-end inference speed of 0.8 ms per sample (including preprocessing, feature extraction, and classification). Cross-engine and cross-domain validation on a 2.0T diesel engine small-sample dataset and the open-source SEMFault-2024 dataset yield average accuracies of 94.8% and 95.2%, respectively, demonstrating strong generalization. This method effectively enhances the accuracy and robustness of engine abnormal sound defect diagnosis, offering a lightweight technical solution for on-board real-time fault diagnosis and in-plant online quality inspection. By reducing engine fault-induced energy loss and spare parts waste, it further promotes energy conservation and emission reduction in the automotive industry. Quantified experimental data on fuel efficiency improvement and carbon emission reduction are provided to substantiate the ecological benefits of the proposed framework. Full article
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37 pages, 3540 KB  
Article
A Multimodal Time-Frequency Fusion Architecture for FaultDiagnosis in Rotating Machinery
by Hui Wang, Congming Wu, Yong Jiang, Yanqing Ouyang, Chongguang Ren, Xianqiong Tang and Wei Zhou
Appl. Sci. 2026, 16(7), 3269; https://doi.org/10.3390/app16073269 - 27 Mar 2026
Viewed by 145
Abstract
Accurate fault diagnosis of rotating machinery in complex industrial environments demands an optimal trade-off between feature representation capability and computational efficiency. Existing single-modality models relying solely on 1D time-series signals or heavy 2D time-frequency images often fail to simultaneously capture high-frequency transient impacts [...] Read more.
Accurate fault diagnosis of rotating machinery in complex industrial environments demands an optimal trade-off between feature representation capability and computational efficiency. Existing single-modality models relying solely on 1D time-series signals or heavy 2D time-frequency images often fail to simultaneously capture high-frequency transient impacts and long-range degradation trends. CLiST (Complementary Lightweight Spatiotemporal Network), a novel lightweight multimodal framework driven by time-frequency fusion, was proposed to overcome this limitation. The architecture of CLiST employs a synergistic dual-stream design: a LightTS module efficiently extracts global operational trends from 1D vibration signals with linear complexity, while a structurally pruned LiteSwin integrated with Triplet Attention captures local high-frequency textures from 2D continuous wavelet transform (CWT) images. This mechanism establishes explicit cross-dimensional dependencies, effectively eliminating feature blind spots without excessive computational overhead. The experimental results show that CLiST not only achieves perfect accuracy on the fundamental CWRU benchmark but also exhibits exceptional spatial generalization when independently evaluated on non-dominant sensor axes of the XJTUGearbox dataset. Furthermore, validation on the real-world dataset (Guangzhou port) proves that the framework has excellent robustness to the attenuation of the signal transmission path and reduces the performance fluctuation between remote measurement points. Ultimately, CLiST delivers highly reliable AI-driven image and signal-processing solutions for vibration monitoring in industrial equipment. Full article
10 pages, 3571 KB  
Article
Experimental Validation and Integrated Multi-Physics Analysis of High-Speed Interior Permanent Magnet Synchronous Motor for Marine Exhaust Gas Recirculation Blower System
by WonYoung Jo, DongHyeok Son and YunHyun Cho
Energies 2026, 19(7), 1663; https://doi.org/10.3390/en19071663 - 27 Mar 2026
Viewed by 130
Abstract
This study explores an integrated multi-physics design approach for a high-speed Interior Permanent Magnet Synchronous Motor (IPMSM) optimized for marine diesel engine Exhaust Gas Recirculation (EGR) blower systems. To satisfy the rigorous operational demands of marine environments, an IPMSM with a rated output [...] Read more.
This study explores an integrated multi-physics design approach for a high-speed Interior Permanent Magnet Synchronous Motor (IPMSM) optimized for marine diesel engine Exhaust Gas Recirculation (EGR) blower systems. To satisfy the rigorous operational demands of marine environments, an IPMSM with a rated output of 150 kW and a base speed of 9000 rpm was developed. The design validity was rigorously verified through a comprehensive multi-physics framework using the Finite Element Method (FEM), ensuring a balance between electromagnetic, thermal, and mechanical performance. The investigation established a mathematical model for the IPMSM driven by a Space Vector Pulse-Width Modulation (SVPWM) inverter, facilitating a detailed analysis of steady-state characteristics within the EGR system. To guarantee long-term reliability at high rotational speeds, the study performed an integrated thermal analysis based on precise electrical loss separation and a rotor-dynamic evaluation focusing on unbalanced vibration responses of the shaft. Finally, the proposed design was validated by integrating the IPMSM into a full-scale EGR blower system. Experimental evaluations across the entire operating range confirm that the integrated design successfully achieves the high power density and mechanical robustness required for marine diesel applications. Full article
(This article belongs to the Collection Electrical Power and Energy System: From Professors to Students)
18 pages, 1685 KB  
Article
Symmetric Element Stiffness and Symplectic Integration for Eringen’s Integral Nonlocal Rods: Static Response and Higher-Order Vibrations
by Zheng Yao, Changliang Zheng and Lulu Wen
Symmetry 2026, 18(4), 571; https://doi.org/10.3390/sym18040571 - 27 Mar 2026
Viewed by 106
Abstract
Integral-form nonlocal elasticity provides a mechanically meaningful approach to describing size effects, yet it leads to Volterra-type integro-differential equations that are difficult to solve analytically and numerically challenging for boundary layers and high-order modes. In this work, we developed a symplectic numerical integration [...] Read more.
Integral-form nonlocal elasticity provides a mechanically meaningful approach to describing size effects, yet it leads to Volterra-type integro-differential equations that are difficult to solve analytically and numerically challenging for boundary layers and high-order modes. In this work, we developed a symplectic numerical integration framework for Eringen’s two-phase (local/nonlocal mixture) integral model by embedding the constitutive operator into a Hamiltonian formulation and discretizing the influence domain in a belt-wise manner. A step-increase strategy was incorporated to allow flexible spatial marching while preserving the geometric (symplectic) structure of the transfer operation. In addition, a symmetry-explicit, element-level stiffness representation was derived for the discretized integral operator; it exposes a mirrored long-range coupling pattern and enables symmetric, energy-consistent assembly. The resulting kernel-agnostic algorithm accommodates both smooth and finite-range kernels. Static benchmarks and longitudinal vibrations are investigated for exponential, Gaussian, and triangular kernels over representative length ratios and mixture parameters. Comparisons with available analytical and asymptotic solutions show good agreement within their validity ranges, and the method yields stable higher-order eigenfrequencies when asymptotic expansions may be unreliable. The current study is limited to a linear one-dimensional rod setting, and validation is restricted to published analytical/asymptotic solutions rather than experimental calibration. Full article
(This article belongs to the Section Engineering and Materials)
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27 pages, 12956 KB  
Article
Research on Magnetorheological Semi-Active Suspension Control Using RBF Neural Network-Tuned Active Disturbance Rejection Control
by Mei Li, Shuaihang Liu, Shaobo Zhang and Xiaoxi Hu
Actuators 2026, 15(4), 184; https://doi.org/10.3390/act15040184 - 27 Mar 2026
Viewed by 175
Abstract
Magnetorheological (MR) semi-active suspensions offer clear advantages in improving ride comfort and handling stability, yet their engineering applications are often hindered by strong nonlinear hysteresis of the damper, the randomness of road excitations, and the reliance on manual tuning of controller parameters. To [...] Read more.
Magnetorheological (MR) semi-active suspensions offer clear advantages in improving ride comfort and handling stability, yet their engineering applications are often hindered by strong nonlinear hysteresis of the damper, the randomness of road excitations, and the reliance on manual tuning of controller parameters. To address these issues, this paper proposes an integrated framework of “experimental modeling–semi-active implementation–adaptive control.” First, characteristic tests of the MR damper are conducted, based on which a current-dependent Bouc–Wen forward model is established. Tianji’s Horse Racing Optimization (THRO) is then employed for parameter identification to reproduce the hysteresis behavior accurately. Second, a back propagation (BP) neural network-based inverse current model is developed to achieve rapid mapping from “desired damping force” to “driving current,” enabling semi-active actuation. Furthermore, a radial basis function (RBF) neural network is embedded into the active disturbance rejection control (ADRC) structure to estimate the system Jacobian online and to tune key extended state observer (ESO) gains in real time, forming the proposed RBF-ADRC strategy and thereby enhancing disturbance observation and compensation capability. Simulation results under pulse-road and Class-C random-road excitations show that, compared with the passive suspension, the proposed method reduces the root mean square error values of sprung-mass acceleration, suspension dynamic deflection, and tire dynamic load by 25.14%, 18.71%, and 11.61%, respectively, while also outperforming skyhook control and fixed-gain ADRC. Frequency-domain results further show stronger attenuation in the low-frequency band relevant to body vibration. Under pulse excitation, RBF-ADRC yields smaller peak and trough body accelerations and faster post-impact recovery. Under ±30% sprung-mass variations, it achieves the best worst-case and fluctuation-range robustness among the compared strategies and remains close to offline retuning. These results demonstrate that the proposed method improves both control performance and robustness while reducing the need for repeated manual calibration. Full article
(This article belongs to the Section Actuators for Surface Vehicles)
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