This paper investigates nonlinear vibration responses and chaos suppression in a bio-inspired vibration isolator with toe-like structures and fractional-order viscoelastic damping. A single-degree-of-freedom dynamic model is established by representing the geometry-induced restoring force of the toe-like structure with a quintic polynomial. A Caputo fractional derivative is introduced to characterize memory-dependent damping in compliant components. Under the steady-state harmonic-balance approximation, the fractional-order damping term is decomposed into equivalent viscous damping and stiffness-correction components, providing a physically interpretable integer-order representation for nonlinear vibration analysis. The equilibrium topology of the unperturbed system is shown to be governed by the effective stiffness, leading to pitchfork bifurcations and transitions among monostable, bistable and tristable configurations. In the bistable regime, explicit homoclinic orbits are obtained, and a Melnikov-based criterion is derived to predict the onset of chaotic vibration. Representative numerical simulations, including bifurcation diagrams, phase portraits with Poincaré-section samples and time histories, together with supplementary transition responses, confirm the analytical prediction for both integer- and fractional-order cases. The results show that fractional-order damping reshapes the instability regions in the excitation-amplitude domain, while reducing the excitation amplitude or tuning the fractional-order parameters can suppress chaotic vibration responses. These results establish a fractional-memory-based mechanism for regulating nonlinear instability and provide a parameter-tuning route for improving the dynamic stability of bio-inspired vibration isolation systems.
Carbody vibration in high-speed vehicles significantly impacts ride comfort and operational safety. Conventional dynamic analyses often simplify passengers as rigid masses, neglecting the influence of body flexibility on carbody dynamics. This study systematically investigates the effect of passenger flexibility on carbody vibration through numerical simulation, mechanistic modeling, and laboratory tests. A validated multi-body dynamics model of a human-vehicle coupling system is established to evaluate vibration responses under various speeds. A simplified analytical model is further developed to reveal the underlying mechanism. Experimental tests are conducted to corroborate the theoretical and simulation results. The results show that passenger flexibility consistently attenuates vertical vibration across all speeds, whereas laterally, it suppresses vibration at low speeds but amplifies it at high speeds. Mechanism analysis reveals that the passenger acts as an additional mass functioning like a dynamic vibration absorber. The difference in modal frequencies between lateral and vertical directions defines distinct vibration absorption bands. While vertical excitation remains within this band, ensuring continuous attenuation, lateral excitation at high speeds exceeds it, reducing the equivalent carbody mass and amplifying vibration. This study enhances the understanding of passenger dynamics in railway vehicles and refines the comprehension of human-vehicle interaction mechanisms.
To address the aerodynamic performance challenges caused by cavity flow in the pantograph area of high-speed trains, this study investigates a three-car train set using the improved delayed detached eddy simulation method based on the SST (Shear Stress Transport) k-ω turbulence model to systematically simulate active flow control with varying blowing angles and speeds. The results indicate that blowing control disturbs the airflow beneath the pantograph, significantly altering both the magnitude and distribution of positive and negative pressures in this region, this is the primary mechanism behind the reductions in pantograph drag and tail car lift. Blowing control also optimizes the flow-field structure and effectively weakens vortex intensity. At a train speed of 350 km/h, with a blowing angle of 45° and a blowing speed equal to 0.30 times the train speed, the overall train drag reduction reaches 5.79% during pantograph lifting with the pantograph drag reduced by 28.98% and the tail car lift decreased by 11.63%. During pantograph lowering, the overall train drag reduction is 6.96%, the pantograph drag decreases by 29.56%, and the tail car lift is reduced by 13.2%.
Functionally graded material (FGM) plates are widely used in aerospace, marine, nuclear and civil engineering applications due to their customisable material properties. In practical structures, such plates often carry attached mass in the form of functional components; however, the combined effect of material gradation, attached mass, and plate geometry on dynamic behaviour remains insufficiently explored. In this study, the free vibration and transient response of sigmoidal skew FGM plates carrying attached mass are investigated using a third-order shear deformation theory-based finite element formulation. The plate domain is discretized using a rapidly convergent nine-node isoparametric element. Newmark’s time integration scheme is employed for transient analysis. The results reveal a strong coupling between geometric configuration and attached mass, with frequency reductions reaching up to 71% for a mass ratio of unity at large skew angles, compared to only 54% at small skew angles. Transient response analysis further shows that the presence of attached mass increases the peak deflection and vibration period, particularly when the mass is located in dynamically active regions of the plate. In addition to parametric analysis, uncertainty quantification and data-driven sensitivity analyses are performed. A Gaussian process regression (GPR)-based permutation feature importance approach (PFI) is employed to identify influential parameters. The results indicate that the mass ratio, attachment size ratio, and location have significantly higher influence on vibration characteristics than the material gradient index within the investigated range. This study provides useful insights into the vibration behaviour and parameter sensitivity of FGM plates carrying attached masses.
This paper presents a new non-recursive robust adaptive control method, utilizing a non-recursive finite-time state observer, designed to minimize payload oscillations and accurately track payload trajectories for 3D tower cranes despite parameter uncertainties and external disturbances during lifting and transportation. This model-independent state observer is designed to estimate states, such as the payload’s swing angle velocity, which are challenging or impossible to measure directly with sensors. To bypass the complexities of parameter estimation and handle model uncertainties, the novel non-recursive robust adaptive controller is designed to function without prior model knowledge, using only a time-varying control gain that adapts online. Lyapunov stability theory is utilized to analyze and validate the closed-loop control system’s stability. The control law, known for its computational efficiency and strong sway suppression, guarantees that the payload trajectory tracking error and all closed-loop system parameters remain bounded and ultimately converge to zero. The feasibility and effectiveness of the proposed controller are validated through a quasi-physical simulation. The results are qualitatively compared with those of (i) a second-order sliding mode control using an adaptive finite-time extended state observer and (ii) an adaptive sliding mode control based on time-delay estimation utilizing a non-recursive finite-time state observer.
Sliding mode control (SMC) has been extensively investigated for the stability control of active suspension systems in high-speed trains due to its robustness and rapid response to complex disturbances. However, existing studies remain largely performance-oriented, with insufficient focus on the underlying nonlinear dynamical mechanisms and a notable lack of theoretical analysis from a bifurcation perspective. Since the Hopf bifurcation essentially determines the critical speed and the post-instability vibration characteristics, it represents a core dynamical issue for ensuring the global stability of high-speed vehicle systems. In this study, the Hopf bifurcation characteristics of a high-speed railway bogie under regularized SMC are investigated by establishing an analytical relationship between control parameters and the first Lyapunov coefficient. The analysis shows that although all SMC parameters can significantly increase the linear critical speed, their effects on the Hopf bifurcation type differ fundamentally. In particular, the proportional gain k not only enhances the linear critical speed but also converts the Hopf bifurcation from subcritical to supercritical, thereby improving the stability and safety of the system. In contrast, the switching gain k st , the sliding surface parameter c , and the regularization parameter ε , while also elevating the linear critical speed, tend to promote subcritical bifurcation behavior and thus increase the potential risk of abrupt instability. This study reveals the intrinsic connection between SMC parameters and the underlying bifurcation mechanisms, providing a bifurcation-oriented theoretical foundation for the safe design and parameter optimization of active suspension systems in high-speed railway vehicles.
Human–machine shared control is a critical transitional paradigm toward safe and trustworthy vehicle automation, which fundamentally depends on accurate intention understanding and adaptive authority allocation. To this end, this paper proposes an intention-aware human–machine shared control framework for integrated lateral–longitudinal path tracking. Firstly, a liquid neural network (LNN)-based driver intention predictor is developed to jointly capture dynamically coupled steering and acceleration intentions, where continuous-time, input-modulated neuron dynamics enable adaptive representation of nonlinear and time-varying driving behavior. Then, an intention-aware reinforcement learning-based authority allocation strategy is designed to explicitly regulate lateral and longitudinal control authority in a closed-loop manner. Finally, the proposed framework is validated through driver-in-the-loop experiments under representative driving scenarios. The experimental results show that the proposed shared control strategy significantly improves the human–machine cooperation quality, and achieves a balanced performance among tracking accuracy, driving efficiency, ride comfort, and personalization across drivers with different skills.
This work presents a mathematical model for Rayleigh wave propagation in a piezoelectric fiber-reinforced composite (PFRC) layer resting on a viscoelastic half-space, with the PFRC surface subjected to fluid loading. The interfacial condition is modeled as a sliding contact to represent imperfect bonding. Using analytical techniques, the displacement fields in each region are derived and connected through physically consistent boundary and interface conditions. The governing equations yield a complex dispersion relation that captures both propagation and attenuation dynamics of the Rayleigh wave. Limiting cases are considered to validate the formulation against established results in the literature. Numerical computations are also performed to investigate the influence of interfacial sliding, composite volume fractions, viscoelastic parameters, and the fluid-to-layer thickness ratio on phase velocity and attenuation. The results show that these effects play a significant role in wave transmission and energy dissipation. The study provides useful insight into wave behavior in layered smart composites and has potential applications in nondestructive testing.
Long-term operation of industrial equipment results in the continuous accumulation of monitoring data for emerging fault types. This phenomenon leads to catastrophic forgetting in intelligent diagnostic models and degrades overall performance. A semantic-guided orthogonal subspace network (SOSN) is proposed for class-incremental continual intelligent fault diagnosis. The architecture utilizes lightweight adapters to construct task-specific orthogonal subspaces within a frozen pre-trained backbone. These subspaces ensure that gradient updates for novel tasks remain theoretically isolated from historical parameters. To reduce the dependency on historical raw data, a semantic-guided prototype synthesis mechanism is developed. This mechanism reconstructs historical class centers by leveraging feature similarity across different task subspaces. Extensive evaluations are performed on rolling bearing datasets and a joint heterogeneous dataset comprising wheelset bearings and elevator door systems. Experimental results demonstrate that SOSN significantly outperforms mainstream class-incremental learning approaches in diagnostic accuracy. The framework effectively balances representational plasticity and diagnostic stability across diverse mechanical systems.
Acoustic-vibration coal-gangue recognition is required for intelligent top-coal caving, but non-stationary underground equipment noise can induce distribution shifts between calibration and operating conditions. This paper formulates the task as a noise-scenario generalization problem and proposes RAAF-BiPAC-Mamba, a roughness-guided bidirectional Mamba framework for noise-robust recognition. The framework uses an efficient bidirectional selective state-space backbone to encode 2048-point acoustic-vibration impact responses and introduces two robustness mechanisms. Roughness-aware adaptive fusion (RAAF) uses latent vibration roughness as a modality-reliability cue, whereas the physics-aware constraint with gradient reversal (PAC-GRL) combines gradient-reversal alignment with a label-conditioned, one-sided roughness regularizer. The method is evaluated on a controlled-platform dataset under source-event-disjoint validation, leave-one-noise-scenario-out (LONSO) evaluation, and synthetic held-out equipment-noise overlay testing. Under the primary source-event-disjoint protocol, RAAF-BiPAC-Mamba achieves 93.74% average accuracy across seven noise scenarios and 91.18% under severe mixed noise (S6), improving over Bi-Mamba by +3.25 and +3.75 percentage points and over the adapted HMBCNN-style implementation by +4.00 and +4.20 percentage points, respectively. It also obtains 89.54% Avg-LONSO accuracy and 86.00% accuracy in the held-out mixed-equipment overlay at −6 dB, while using 0.234 M parameters and 0.063 G FLOPs. These results support noise-shift robustness under the evaluated controlled-platform and held-out noise-overlay settings; they do not establish transfer across mine sites, sensor hardware or calibration, geological conditions, or installation configurations.
Magnetorheological (MR) semi-active suspensions suffer from inherent challenges including damper nonlinear hysteresis, feedback control delay, and laborious manual parameter tuning. To address these issues, this paper proposes a preview fuzzy feedforward Lfal-based active disturbance rejection control (PreFuzzy-LADRC) strategy, where the Lfal-based active disturbance rejection control (LADRC) serves as the feedback core with a smoothed nonlinear function to suppress control chattering. An opposition-based learning and differential evolution enhanced particle swarm optimization (OBL-DE-PSO) algorithm is developed for offline tuning of the controller’s key feedback gains. The overall system integrates a Spencer forward damper model and an adaptive neuro-fuzzy inference system (ANFIS) inverse damper model, a two-degree-of-freedom (2-DOF) quarter-vehicle model, and a YOLOv8-enabled binocular vision system for road preview information acquisition. Simulations are conducted under ISO Class-B random roads and discrete impact roads. Compared with the empirically tuned PreFuzzy-LADRC, the OBL-DE-PSO-optimized controller reduces the root mean square (RMS) values of sprung mass vertical acceleration, suspension deflection, and tire deflection by 19.7%, 15.1%, and 22.5% under random road conditions, and by 9.3%, 19.3%, and 17.0% under discrete impact conditions, respectively. Hardware-in-the-loop (HIL) experiments validate the simulation results, with maximum relative deviations below 11%. Notably, the parameter optimization is performed offline, and the total online latency of visual perception and control computation satisfies the requirements of real-time applications. The results demonstrate that the proposed vision preview fusion framework and intelligent parameter tuning method can effectively improve the vibration suppression performance of MR semi-active suspensions.
Controlling spherical robots is challenging due to their nonlinear dynamics, underactuated characteristics, and non-holonomic constraints. These challenges become more pronounced in the presence of parameter variations and external disturbances. To address these issues, this paper proposes an Adaptive Dynamic Programming (ADP)-based control framework for spherical robot dynamics. The stability properties of the proposed method are analyzed using Lyapunov theory. The kinematic control layer is designed based on the feedback linearization approach, while the dynamic controller employs ADP to compensate for uncertainties and disturbances. The effectiveness of the proposed method is evaluated through two simulation case studies involving trajectory-tracking tasks under parametric uncertainties and external disturbances. The simulation results show that the proposed controller is capable of achieving accurate trajectory tracking while maintaining stable system performance. To provide a comparative assessment, a Sliding Mode Control (SMC) scheme is also implemented under the same conditions. The obtained results indicate that the ADP-based controller can reduce tracking errors and power consumption compared with the considered SMC approach. In one case study, the tracking error integral achieved by the ADP controller is approximately 36% lower than that of SMC, while the corresponding power consumption is reduced by about 23%. These results demonstrate the potential of the proposed ADP framework for improving trajectory-tracking performance in spherical robots under uncertain operating conditions.
Limited by their inherent structural characteristics, conventional piezoelectric stack actuators only produce micro-scale output displacements, which fail to satisfy the large-stroke working demands of precision mechanical systems. To overcome this technical limitation, this paper proposes a flexible hinge actuator integrating the lever and triangular amplification principles. The symmetric structural configuration is designed to combine the high displacement gain of lever mechanisms and the high linearity advantage of triangular structures, effectively resolving the inherent trade-off among output stroke, motion trajectory accuracy and structural stiffness in traditional displacement amplification designs. Based on the elastic mechanics theory, theoretical models for the displacement amplification ratio and equivalent stiffness of the proposed actuator are established. Finite element simulation is conducted to further validate its structural strength and dynamic performance. A prototype of the actuator is manufactured through wire electrical discharge machining, and systematic experimental tests are performed for performance verification. The test results demonstrate that the actuator achieves an output displacement of 85.360 μm under a driving voltage of 80 V, with a measured amplification gain of approximately 4.500. The experimental data exhibits a consistent variation trend with the theoretical value of 5.400 and the simulated value of 4.774. Benefiting from the advantages of large output stroke and superior structural stiffness, the proposed actuator provides a promising technical approach for high-precision actuation and vibration suppression applications.
In a compound power-split hybrid system, engaging and braking the power-split device and power components can improve performance and fuel efficiency. However, the resulting mode transitions introduce abrupt changes in torque path, equivalent inertia, and equivalent stiffness. These changes may intensify driveline torsional vibration during engine start/stop and clutch engagement, leading to degraded NVH performance and potential damage to key components. In this study, an 18-degree-of-freedom (18-DOF) nonlinear powertrain model was established to investigate the torsional vibration behavior of a compound power-split hybrid commercial-vehicle powertrain during mode transitions. The results show that the natural frequencies associated with the power-split device vary significantly with operating mode. During the EV1-to-HEV1 transition, the natural frequencies of torsional damper1 mode, torsional damper2 mode, and input shaft mode decrease by 23.8%, 36.2%, and 43.8%, respectively. To address the torsional vibration issue under wide-open-throttle (WOT) HEV1 operation, a variance-based Sobol global sensitivity analysis was further conducted. The Saltelli sampling results show that flywheel inertia dominates both the peak and mean second-order speed oscillations; EM2 inertia mainly affects the peak response, whereas the third-stage damper stiffness and hysteresis torque mainly affect the mean response. Based on these sensitivity results, a parameter optimization scheme was proposed and validated through numerical simulations and bench tests. The optimized design reduced the second-order peak amplitude of the input shaft speed oscillation by 50.8% and the root mean square (RMS) value of the output shaft angular acceleration by 30.6%, preventing spacer pins impact and improving mode switching comfort and system stability.
This paper presents a decentralized finite-horizon suboptimal control approach for uncertain interconnected nonlinear systems based on the decentralized finite-horizon state-dependent Riccati equation (DF-SDRE). The proposed method extends the classical state-dependent Riccati equation framework to large-scale nonlinear systems composed of multiple interconnected subsystems and affected by structured parametric uncertainties. A Lyapunov-based stability analysis using a quadratic function is developed to derive a new sufficient condition ensuring the global asymptotic stability of the overall interconnected system. The proposed control strategy preserves the decentralized structure while explicitly accounting for uncertainty effects. The effectiveness of the (DF-SDRE) controller is evaluated through numerical simulations on a system of three interconnected inverted pendulums. The obtained results show that the proposed approach ensures robust stabilization and improved transient performance compared with a decentralized LQR (D-LQR) controller.
Rolling bearings are core components of rotating machinery, unexpected faults cause economic losses and safety risks. To solve problems of poor feature discriminability and blind parameter selection in traditional fault diagnosis, this paper proposes a method based on refined composite multi-scale attention entropy (RCMAE) and Beluga whale optimization (BWO) for multi-classification support vector machines (SVM). For feature extraction, RCMAE (avoiding hyper-parameter optimization and capturing subtle multi-scale fault information) is fused with time-domain features to form a discriminative multi-dimensional feature vector. For the diagnostic model, BWO optimizes SVM’s key parameters ( c and g ) to eliminate blind selection impacts, establishing the BWO-SVM model. Verification on Jiangnan University and Huazhong University of Science and Technology bearing datasets shows diagnostic accuracies of 99.2% and 100%, respectively. Comparative experiments with DT, RF, KNN, and LSTM confirm its superior accuracy, stability, and generalization. This study provides a reliable technical solution for engineering applications, supporting condition monitoring and predictive maintenance of rotating machinery in manufacturing, wind power, etc., to reduce costs and improve system reliability.
Constrained layer damping (CLD) is widely used for structural vibration attenuation; however, its effectiveness in the low-frequency range remains limited. To address this issue, an acoustic black hole (ABH)-profiled constrained layer damping (ABH-CLD) configuration is proposed, in which the damping layer is designed with ABH profiles to enhance low-frequency vibration attenuation. Finite element simulations of beam structures demonstrate that, compared with uniform CLD, the proposed ABH-CLD configuration reduces the first two resonance peak levels by 3.6 dB and 3.7 dB, respectively. Further investigations on plate structures confirm that ABH-CLD can achieve more pronounced attenuation of low-order resonant responses in two-dimensional configurations, with reductions of 3.5 dB and 1.7 dB in the first two resonance peak levels, respectively. The enhanced low-frequency performance is attributed to ABH-induced flexural-wave energy localization and increased viscoelastic shear dissipation in the damping layer, enabling more effective energy dissipation while maintaining comparable overall broadband attenuation performance. In addition, a differential evolution method is employed to optimize the structural and material parameters to improve damping and vibration attenuation.
Aiming at the problem that various parameter uncertainties and disturbances degrade the tracking control performance in the direct-drive electro-hydrostatic actuator, an improved sliding mode control based on adaptive neural network is proposed in this paper. First, a new sliding mode reaching law is designed. On the basis of the exponential reaching law, a variable gain term based on system state variables, a piecewise function with power terms of the sliding surface and a new switching function are introduced, which improves the response speed, enhances the anti-disturbance capability and suppresses chattering. Secondly, a new adaptive radial basis function neural network observer based on the minimum learning parameter is designed. The outputs of the high-gain observer are taken as the inputs of the radial basis function neural network. An adaptive learning rate dynamically varying with the observation error is developed and incorporated into the weight updating law of the neural network, which improves the real-time nonlinear approximation accuracy for unknown disturbances. The stability was proved through the Lyapunov function. The results demonstrate that the proposed control method outperforms the other control methods in terms of both response speed and control accuracy.
Slope entropy (SlE) is a recently proposed effective metric for quantifying the complexity of nonlinear signals. However, its representation of fine-grained features and dynamic information remains incomplete, primarily due to rigid hard-threshold slope symbolic segmentation and inadequate characterization of the state transition information in symbol patterns. To address these issues, transition fuzzy slope entropy (TFuSlE) is proposed, which for the first time integrates fuzzy sign partitioning of the slopes derived from two consecutive data samples with the dynamic transition probabilities of the resulting symbol mode sequences into the SlE framework. This integration enables TFuSlE to capture more detailed dynamic information from nonlinear signals, thereby yielding more accurate and comprehensive entropy estimates. Through experiments on simulated data, the optimal parameter configuration for TFuSlE is first determined, and the superiority of its multiple performance metrics in accurately characterizing signal complexity is validated. Finally, TFuSlE is evaluated on two real-world datasets related to mechanical components. The experimental results demonstrate that the health-state features extracted from vibration signals using TFuSlE exhibit well-separated visual distributions and achieve superior classification accuracy and noise robustness compared to other entropy methods.
To address heavy data reliance and poor cross-working condition generalization of rolling bearing remaining useful life (RUL) prediction models under small-sample scenarios, this paper proposes a novel method integrating meta-learning, parallel temporal modeling and the domain adversarial mechanism. Firstly, feature extraction is performed on vibration signals of rolling bearings under multiple working conditions to obtain a feature set including time domain, frequency domain, and trigonometric features. Then, a novel prediction network named MGMD under the Model-Agnostic Meta-Learning (MAML) framework is constructed. Through the parallel structure of Gated Recurrent Unit (GRU) and Mamba, the local dynamic changes and long-range acceleration trends of the degradation process are captured, respectively, forming comprehensive features with both details and global information. Domain Adversarial Neural Networks (DANN) are introduced to alleviate cross-working condition distribution shift, enabling efficient cross-domain adaptation under small-sample conditions. The initial parameters of the network are optimized by means of the inner-loop and outer-loop meta-update mechanisms of MAML to improve small-sample rapid adaptation ability. Experimental verification on the IEEE PHM 2012 bearing dataset shows that the proposed method achieves a significant improvement in prediction accuracy. It provides a feasible solution for cross-working RUL prediction of rolling bearings under small-sample conditions.
