Search Results (79)

This work examines how well a Negative Derivative Feedback (NDF) controller suppresses vibration in a nonlinear electromechanical oscillator that is subjected to mixed excitations. Coupled nonlinear ordinary differential equations are used to model the system and show how mechanical and electrical components interact. The method of multiple scales (MMS) is used to develop analytical approximate solutions up to the second order, specifically for the primary resonance scenario. This study’s main contribution is a thorough bifurcation analysis and proof of the NDF controller’s high efficacy, which effectively lowers the first and second mode resonance amplitudes by roughly $99.8\%$ and $98\%$., respectively, with impressive reported effectiveness values of roughly 590 and 51.5. Additionally, the quantitative error analysis between the numerical simulation and the analytical approximation solution demonstrates a high degree of agreement, with a maximum error of less than ${10}^{-5}\%$ for the second mode and just $0.01\%$ for the first mode. Furthermore, we present the impact of parameters on FRCs. Frequency response curves (FRCs) are used in a thorough comparison analysis to assess the behavior of the system both before and after the controller is activated. A strong degree of connection between the analytical conclusions and numerical simulations carried out using the “fourth-order Runge–Kutta method” rigorously validates the accuracy of the perturbation analysis. Additionally, a performance benchmark between different control techniques, such as the NDF controller, Positive Position Feedback (PPF), and Linear Negative Position Feedback (LNPF), is shown in the paper. When compared to alternative approaches, the NDF controller shows the greatest reduction in oscillation amplitudes and higher robustness, as shown by transient response analysis (time history) at various time intervals. The outcomes validate the NDF approach’s dependability and efficiency in stabilizing intricate nonlinear electromechanical systems. The chaotic response and system periodicity were demonstrated through bifurcation diagrams and Poincaré maps. Full article

This paper proposes a source-level electromagnetic interference suppression strategy for high-voltage inverters that uses a series-connected IGBT topology and discrete staircase voltage shaping. From an information-theoretic perspective, the staircase shaping transforms chaotic wideband switching noise into a deterministic harmonic structure, thereby reducing the spectral entropy of the EMI source. This information optimization is achieved using a CPLD-based sequential gate drive circuit, which eliminates the need for complex active gate profiling algorithms. Experimental results obtained using a 1140 V explosion-proof motor drive platform demonstrate harmonic attenuation of 4–16 dB μV within a 2 MHz band. Importantly, this targeted entropy reduction occurs alongside a 68.7% reduction in active-region switching losses, suggesting a concurrent decrease in local thermodynamic entropy production during switching transients. Increasing spectral determinism and relaxing requirements for subsequent physical filters effectively lower the conditional entropy of the overall electromagnetic environment. Leveraging the structural flexibility of series IGBTs, this method provides a practical, low-complexity solution and establishes a novel framework between power electronics and information theory for electromagnetic compatibility. Full article

Grid-forming virtual synchronous generator control can improve the frequency-support capability of converter-interfaced systems. However, under successive disturbances and varying operating conditions, fixed inertia and damping settings often struggle to balance inertial response, oscillation suppression, and recovery speed. To address this issue, this paper develops an adaptive parameter coordination strategy for grid-forming virtual synchronous generators by using frequency deviation and rate of change of frequency as dynamic indicators. A piecewise regulation law is established to adjust virtual inertia and damping during different transient stages, while an improved parrot optimization algorithm is introduced for the offline coordinated tuning of the adaptive-law parameters. In the proposed optimizer, SPM-chaotic initialization, adaptive probability adjustment, and Cauchy-Gaussian hybrid mutation are incorporated to improve population diversity, convergence efficiency, and local refinement capability. Simulation results obtained in MATLAB/Simulink under successive disturbance events show that the proposed strategy achieves smaller frequency excursions, weaker secondary oscillations, and shorter settling times than fixed-parameter control and standard PO-based tuning. The results demonstrate that the proposed method can effectively enhance the dynamic support capability and disturbance adaptability of grid-forming virtual synchronous generators under complex operating conditions. Full article

This study investigates the reliable numerical analysis of chaotic dynamics in the Glukhovsky–Dolzhansky system, which models convective fluid motion in a rotating ellipsoidal cavity. Hidden and self-excited attractors are localized using the numerical continuation method (NCM), Pyragas time-delayed feedback control, and Leonov’s analytical dimension formula following global stability loss. A critical assessment of Lyapunov exponents and Lyapunov dimensions in a finite-time setting shows that positive values over long but finite intervals may incorrectly indicate sustained chaos due to transient effects and shadowing breakdown. Furthermore, we demonstrate that the fractional order $\gamma$ plays a bidirectional control role: it induces chaotic behavior at $\rho =5$ for $\gamma <0.94$ and suppresses chaos at $\rho =15$ for $\gamma <0.93$. The multifractal spectrum and correlation dimension are used to quantify attractor complexity, where transient chaos exhibits a broader spectrum ($\Delta \alpha \approx 0.67$) compared to sustained chaos ($\Delta \alpha \approx 0.48$). Monte Carlo simulations, Sobol sensitivity analysis, Kaplan–Meier survival analysis, and bootstrap-based hypothesis testing confirm the robustness of the results. Overall, the findings provide a unified framework for analyzing hidden attractors, transient chaos, and fractional-order effects in nonlinear fluid dynamical systems. Full article

In this paper, we propose and numerically investigate a fractional T system. As a fractional generalization of the classical T model, the fractional order serves as a memory parameter governing the system dynamics. By employing the fractional stability criterion, the local stability of the equilibrium points is analyzed, and the existence of Hopf bifurcation is characterized. To efficiently simulate the long-time dynamics induced by fractional memory, a linear semi-implicit numerical scheme accelerated by a sum-of-exponentials approximation of the Caputo derivative is developed. The proposed scheme is shown to be stable and enables a significant reduction in computational cost compared with classical L1 and Grünwald–Letnikov methods. Numerical experiments, including time series, phase portraits, Lyapunov exponent computations, and bifurcation diagrams, demonstrate that varying the fractional order leads to transitions among stable, periodic, and chaotic regimes. In particular, pronounced transient dynamics are observed as the fractional order approaches its critical value, highlighting the memory-induced effects inherent in fractional-order systems. Full article

This study proposes a comprehensive methodology for the experimental characterization and non-linear dynamic modelling of Polycrystalline Diamond (PCD) bearings, establishing a high-fidelity digital twin approach for the condition monitoring of rotating machinery. The research addresses complex rotor–stator interactions through the development of a multibody numerical framework. A structural 1D Finite Element (FE) model of the stator assembly was first calibrated via experimental modal analysis, achieving a high correlation with the first four bending modes and a maximum frequency discrepancy of only 1.4%. This validated structure was integrated into a non-linear multibody environment to simulate transient rub-impact events at rotational speeds up to 5500 rpm across varying clearance configurations. The model successfully captures the transition from stable periodic orbital motion to the stochastic and chaotic regimes observed in high-clearance setups. Frequency-domain validation further confirms the model’s accuracy in identifying supersynchronous harmonics and energy distribution patterns. Quantitative analysis shows that high-clearance configurations generate impact forces exceeding 6000 N, providing critical data for structural health assessment. These results demonstrate that the proposed digital twin serves as a robust physical foundation for diagnostic systems, enabling the identification of contact-induced vibrational signatures that are essential for training prognostic algorithms. This approach facilitates the autonomous monitoring of critical rotating machinery in demanding industrial and subsea applications, supporting the transition toward active balancing and model-based vibration control strategies. Full article

This paper is devoted to the problem of identifying the mechanisms of hard excitation of oscillations in coupled systems of equilibrium neurons. In this study, a system of two coupled Chialvo neurons is used. For the deterministic model, we studied how increased coupling causes an abrupt transformation of the quiescent neurons into complex oscillations, both regular and chaotic. We show that even in the case when the deterministic system is in equilibrium, similar spike oscillations can be generated by noise. The important role of fractal basins of short and long deterministic transients is discussed. The potential of the principal directions and confidence domain methods for analyzing noise-induced excitation is demonstrated. The phenomena of coherence resonance and the global transition from order to chaos are explored. Full article

In response to the problem that sensors cannot be directly installed at key local positions on the surface of ship hull structures during the transient strong shock process of underwater explosions due to spatial constraints or large plastic deformations, this paper investigates the chaotic-like nonlinear transient behavior of structural dynamic response systems under strong shock and proposes a key position structural response reconstruction method based on dynamic inversion. Since the structural response under a transient strong shock exhibits significant non-stationarity and nonlinearity, signals from neighboring measurement points cannot directly characterize the dynamic behavior at key positions. Therefore, the shock response signals are discretized in both time and space dimensions. The phase space reconstruction method is employed to characterize the motion trajectory of acceleration responses in a two-dimensional phase space, establish mapping functions for system motion evolution, and use their control parameters to characterize the system’s nonlinear dynamic behavior. Furthermore, based on the spatiotemporal dynamic equations, a spatiotemporal coupled mapping model for spatial state points is established to achieve the theoretical inversion of acceleration responses at key positions. This method provides theoretical support for analyzing the dynamic characteristics of structures at key positions under strong shock environments, characterizing the shock environment, and assessing and designing equipment for shock safety. However, the current validation is based on high-fidelity numerical simulations rather than physical prototype tests; therefore, the predictive capability of this method in actual physical environments requires further validation through subsequent physical model tests. Full article

Linear integrators are traditionally used in motion control systems to compensate for static effects and suppress low-frequency disturbances. However, their use is inevitably accompanied by phase delays that limit the performance and robustness of control systems, especially in conditions of parametric uncertainty. In this regard, nonlinear integrators have been considered for several decades as a promising alternative that can weaken phase constraints and improve the quality of transients. In this paper, the concept of nonlinear integrators is reinterpreted in the context of self-organizing motion control of precision stages. In contrast to traditional approaches focused primarily on frequency analysis and the method of describing the function, a method is proposed for the synthesis of a self-organizing control system for nonlinear SISO objects based on catastrophe theory, namely in the class of elliptical dynamics with the property of structural stability. The control action is formed in such a way that transitions between stable modes occur due to bifurcation-conditioned self-organization, without using external switching logic. To ensure strict analytical guarantees of stability, the Lyapunov gradient-velocity vector function method is used, which guarantees aperiodic robust stability, suppression of oscillatory and chaotic modes, as well as monotonic convergence of trajectories under conditions of parameter uncertainty. The parameters of the nonlinear integrator are adapted using Self-Organizing Maps (SOM), while any parameter changes are allowed only within the regions that meet the conditions of Lyapunov stability. This approach ensures the alignment of analytical and data-oriented methods without violating the structural stability of the system. The results of numerical experiments demonstrate the superiority of the proposed method in comparison with classical linear and adaptive regulators in problems of controlling the movement of stages, especially near bifurcation boundaries and with significant parametric uncertainty. The results obtained confirm that the integration of nonlinear integrators with catastrophe theory and self-organization mechanisms forms a promising basis for the creation of robust and high-precision motion control systems of a new generation. Full article

On-load tap changers (OLTCs) are critical components of power transformers. In recent years, condition monitoring technologies for OLTCs based on vibration signals have attracted increasing research interest. However, practical applications still face several challenges, including background noise interference, insufficient characterization of transient signals, signal complexity, difficulty in detecting subtle anomalies, and ambiguous associations between fault modes and signal features. To address these issues, this paper proposes an OLTC acoustic fingerprint feature recognition method based on multidimensional phase-space trajectory analysis. First, an OLTC fault simulation platform was established, in which typical mechanical faults—such as fastener loosening, contact wear, and insufficient spring energy storage—were physically simulated. Corresponding vibration signals were then acquired under different operating conditions. Considering the independence of vibration characteristics at different locations of the distribution transformer, a blind source separation method based on endpoint detection was employed to separate OLTC vibration signals from the operational noise of the transformer body. Given the nonlinear and chaotic characteristics of OLTC vibration signals, phase-space reconstruction was introduced for signal analysis. Based on the reconstructed phase space, characteristic patterns and geometric feature parameters corresponding to different mechanical states of the OLTC were extracted. Furthermore, a two-dimensional membership function was constructed using the phase-space trajectories, and fuzzy inference based on predefined fuzzy rules was applied to compute representative feature parameters. A feature parameter database was subsequently established to enable OLTC condition identification. Experimental results demonstrate that the proposed diagnostic model can effectively classify and identify OLTC fault conditions using vibration signals, achieving an average classification accuracy exceeding 91.25%. The proposed method provides an effective non-intrusive approach for online monitoring and mechanical fault diagnosis of OLTCs without interrupting normal transformer operation. Full article

Accurate global irradiance (GI) forecasting is essential for improving photovoltaic (PV) energy management, stabilizing renewable power systems, and enabling intelligent control in solar-powered applications, including electric vehicles and smart grids. The highly stochastic and non-stationary nature of solar radiation, influenced by rapid atmospheric fluctuations and seasonal variability, makes short-term GI prediction a challenging task. To overcome these limitations, this work introduces a new hybrid forecasting architecture referred to as WTX–CBO, which integrates a Wavelet Transform (WT)-based decomposition module, an encoder–decoder Transformer model, and an XGBoost regressor, optimized using the Chaotic Billiards Optimizer (CBO) combined with the Adam optimization algorithm. In the proposed architecture, WT decomposes solar irradiance data into multi-scale components, capturing both high-frequency transients and long-term seasonal patterns. The Transformer module effectively models complex temporal and spatio-temporal dependencies, while XGBoost enhances nonlinear learning capability and mitigates overfitting. The CBO ensures efficient hyperparameter tuning and accelerated convergence, outperforming traditional meta-heuristics such as Particle Swarm Optimization (PSO) and Genetic Algorithms (GA). Comprehensive experiments conducted on real-world GI datasets from diverse climatic conditions demonstrate the outperformance of the proposed model. The WTX–CBO ensemble consistently outperformed benchmark models, including LSTM, SVR, standalone Transformer, and XGBoost, achieving improved accuracy, stability, and generalization capability. The proposed WTX–CBO framework is designed as a high-accuracy decision-support forecasting tool that provides short-term global irradiance predictions to enable intelligent energy management, predictive charging, and adaptive control strategies in solar-powered applications, including solar electric vehicles (SEVs), rather than performing end-to-end vehicle or photovoltaic power simulations. Overall, the proposed hybrid framework provides a robust and scalable solution for short-term global irradiance forecasting, supporting reliable PV integration, smart charging control, and sustainable energy management in next-generation solar systems. Full article

Nonlinear single-input single-output (SISO) systems operating under parametric uncertainty often exhibit bifurcations, multistability, and deterministic chaos, which significantly limit the effectiveness of classical linear, adaptive, and switching control methods. This paper proposes a novel synthesis framework for self-organizing control systems based on catastrophe theory, specifically within the class of elliptic catastrophes. Unlike conventional approaches that stabilize a predefined system structure, the proposed method embeds the control law directly into a structurally stable catastrophe model, enabling autonomous bifurcation-driven transitions between stable equilibria. The synthesis procedure is formulated using a Lyapunov vector-function gradient–velocity method, which guarantees aperiodic robust stability under parametric uncertainty. The definiteness of the Lyapunov functions is established using Morse’s lemma, providing a rigorous stability foundation. To support practical implementation, a data-driven parameter tuning mechanism based on self-organizing maps (SOM) is integrated, allowing adaptive adjustment of controller coefficients while preserving Lyapunov stability conditions. Simulation results demonstrate suppression of chaotic regimes, smooth bifurcation-induced transitions between stable operating modes, and improved transient performance compared to benchmark adaptive control schemes. The proposed framework provides a structurally robust alternative for controlling nonlinear systems in uncertain and dynamically changing environments. Full article

Circuit implementation is a widely accepted method for validating theoretical insights observed in chaotic systems. It also serves as a basis for numerous chaos-based engineering applications, including data encryption, random number generation, secure communication, neuromorphic computing, and so forth. To get feasible, compact, and cost-effective circuit implementations of chaotic systems, the underlying mathematical model may be simplified while preserving all rich nonlinear behaviors. In this framework, this manuscript presents a simplified Hopfield Neural Network (HNN) capable of generating a broad spectrum of complex behaviors using a minimal number of electronic elements. Based on Shil’nikov’s theorem for heteroclinic orbits, the number of non-zero synaptic connections in the matrix weights is reduced, while simultaneously using only one nonlinear activation function. As a result of these simplifications, we obtain the most compact electronic implementation of a tri-neuron HNN with the lowest component count but retaining complex dynamics. Comprehensive theoretical and numerical analyses by equilibrium points, density-colored continuation diagrams, basin of attraction, and Lyapunov exponents, confirm the presence of periodic oscillations, spiking, bursting, and chaos. Such chaotic dynamics range from single-scroll chaotic attractors to double-scroll chaotic attractors, as well as coexisting attractors to transient chaos. A brief security application of an S-Box utilizing the presented HNN is also given. Finally, a physical implementation of the HNN is given to confirm the proposed approach. Experimental observations are in good agreement with numerical results, demonstrating the usefulness of the proposed approach. Full article

This paper presents a nonlinear vertical dynamic model of an electromagnetic suspension (EMS) system in maglev trains regulated by a dual nonlinear saturation controller (DNSC) under simultaneous resonance ($\Omega \cong {\omega }_s, {\omega }_s\cong 2{\omega }_c$). The governing nonlinear differential equations of the system are addressed analytically utilizing the multiple time-scale technique (MTST), concentrating on resonance situations obtained from first-order approximations. The suggested controller incorporates two nonlinear saturation functions in the feedback and feedforward paths to improve system stability, decrease vibration levels, and enhance passenger comfort amidst external disturbances and parameter changes. The dynamic bifurcations caused by DNSC parameters are examined through phase portraits and time history diagrams. The goal of control is to minimize vibration amplitude through the implementation of a dual nonlinear saturation control law based on displacement and velocity feedback signals. A comparative analysis is performed on different controllers such as integral resonance control (IRC), positive position feedback (PPF), nonlinear integrated PPF (NIPPF), proportional integral derivative (PID), and DNSC to determine the best approach for vibration reduction in maglev trains. DNSC serves as an effective control approach designed to minimize vibrations and enhance the stability of suspension systems in maglev trains. Stability evaluation under concurrent resonance is conducted utilizing the Routh–Hurwitz criterion. MATLAB 18.2 numerical simulations (fourth-order Runge–Kutta) are employed to analyze time-history responses, the effects of system parameters, and the performance of controllers. The evaluation of all the derived solutions was conducted to verify the findings. Additionally, quadratic velocity feedback leads to intricate bifurcation dynamics. In the time domain, higher displacement and quadratic velocity feedback may destabilize the system, leading to shifts between periodic and chaotic movements. These results emphasize the substantial impact of DNSC on the dynamic performance of electromagnetic suspension systems. Frequency response, bifurcation, and time-domain evaluations demonstrate that the DNSC successfully reduces nonlinear oscillations and chaotic dynamics in the EMS system while attaining enhanced transient performance and resilience. Full article

During drill-and-blast construction, complex and variable rock masses are frequently encountered. Owing to the transient nature of the explosion process and the randomness of crack propagation, the response of different rock masses to explosive loading is highly intricate. This study primarily investigates the dynamic response of rock masses with varying strengths under two different charge configurations. First, four cement mortar specimens of differing strengths were prepared then subjected to general blasting and slit charge blasting, respectively. High-speed cameras and digital image correlation techniques were employed to capture and analyse stress wave propagation and crack propagation during detonation. Fractal dimension analysis was subsequently employed to quantify and compare the extent of damage in the specimens. Findings indicate that rock strength influences stress wave attenuation patterns: lower-strength rocks exhibit higher peak strains but faster decay rates. Crack propagation velocity was calculated by deploying monitoring points along fracture paths and defining fracture initiation thresholds. Higher rock strength correlates with both peak and average crack propagation velocities. Slit charge blasting effectively optimizes damage distribution, concentrating it within the intended directions while reducing chaotic fracturing. These findings provide scientific justification for blasting operations in complex rock formations. Full article