Search Results (245)

A nonlinear ultrasonic time-domain identification method based on chaos sensitivity was proposed in this study. The Duffing chaotic system was introduced into the weak second harmonic identification to realize early detection and quantitative evaluation of fatigue damage in U71Mn steel. First, to ensure the reliability of nonlinear ultrasonic testing, a probe-pressure monitoring device was designed. Through pressure-stability experiments, 16 N was determined as the optimal pressure, which effectively suppresses contact nonlinearity interference and ensures coupling stability. Subsequently, the Duffing chaos detection system was established. The signal-system frequency-matching problem was resolved through time-scale transformation. Simultaneously, the issue of unknown initial phases was resolved using phase traversal compensation. Based on the chaotic system’s sensitivity to specific frequency signals and immunity to noise, the amplitudes of the fundamental wave and second harmonics in the target signals were quantified to calculate the nonlinear coefficient. Experimental results demonstrate that the proposed method can extract these amplitudes directly in the time domain, thereby effectively overcoming the spectral leakage inherent in traditional frequency-domain methods. The nonlinear coefficient of U71Mn steel exhibits a “double-peak” characteristic as fatigue damage increases. Specifically, the first peak appears at approximately 50% of fatigue life, while the second occurs at approximately 80%. This phenomenon is closely correlated with the distinct stages of internal fatigue crack propagation, reflecting a complex damage-evolution mechanism. This study not only provides a novel method for the precise extraction of weak nonlinear signals but also establishes a critical theoretical and experimental foundation for accurate fatigue life prediction for U71Mn rail steel. Full article

We develop a fast numerical method for solving nonlinear diffusion equations with memory phenomena, a class of problems arising within viscoelastic materials, anomalous transport, and hereditary systems. The primary computational problem is the nonlocal temporal dependence captured by Volterra-type memory operators, which makes direct evaluation scale quadratically with the number of time steps ($O\left(N_t^2\right)$), rendering prolonged simulations prohibitively expensive. To address this bottleneck, we develop a novel synthesis that combines a high-order spectral method for spatial discretization with a fast memory algorithm based on a sum-of-exponentials approximation. The spectral method obtains exponential spatial convergence for smooth solutions. At the same time, the fast memory algorithm reduces memory usage and computational complexity to $O\left(N_t\right)$, yielding computational speedups exceeding 414x for prolonged simulations. We rigorously prove that the proposed scheme preserves the discrete energy dissipation law of the continuous system under mild assumptions on the memory kernel, thereby ensuring unconditional stability. Error analysis verifies spectral accuracy in space and first-order temporal convergence. Extensive numerical experiments using exponentially decaying and weakly singular kernels validate the theoretical results and illustrate the method’s effectiveness for modeling viscoelastic transport phenomena and irregular diffusion in complex systems. Full article

This paper develops a structured analytical framework and a robust numerical methodology for the spectral stability of time-varying bilateral quaternion differential equations of the form $\dot{q}=A\left(t\right)q+qB\left(t\right)$. By systematically extending classical real matrix theory to non-commutative dynamical systems via exact isometric real representations, this study utilizes the Kronecker product of real adjoint matrices to rigorously elucidate the underlying tensor structure of the bilateral evolution operator. This tensor-based reformulation proves that the Floquet multipliers of the bilaterally coupled system can be strictly decoupled into the product of the spectra corresponding to the left and right unilateral subsystems. Second, a “Scalar-Vector Stability Separation Principle” based on logarithmic norms is proposed, demonstrating that the transient energy evolution of the system is governed exclusively by the Hermitian real parts of the coefficient matrices, remaining entirely independent of the anti-Hermitian imaginary parts (rotation terms). Furthermore, for constant-coefficient and slowly varying systems, the Riesz projection from holomorphic functional calculus is introduced to establish algebraic criteria for exponential dichotomies, thereby revealing a cubic scaling law that relates the robustness threshold to the spectral gap (${\epsilon }_0\propto {\beta }^3$). Numerically, a Quaternion Chebyshev Spectral Collocation Method (Q-CSCM) is embedded within this exact vectorization framework to ensure that the algebraic symmetries of the bilateral system are strictly preserved through the isomorphic mapping. By explicitly constructing the fully discrete Kronecker product matrix via the exact real vectorization isomorphism, discrete energy estimates are utilized to rigorously prove that the numerical scheme successfully inherits the intrinsic spectral accuracy of the Chebyshev approximation. Comprehensive numerical experiments demonstrate that, within the low-dimensional regime, this methodology exhibits substantial temporal approximation efficiency advantages and superior numerical robustness compared to an alternative Legendre spectral baseline, as well as traditional explicit and state-of-the-art implicit symplectic Runge–Kutta methods, particularly when solving stiff and critically stable problems such as nonlinear Riccati oscillators. Full article

This paper introduces a new explicit integration method for second-order ordinary differential equations (ODEs) commonly encountered in engineering applications. Traditionally, these problems are solved either by reformulating them as first-order systems to apply one-step methods such as Runge–Kutta schemes, or by using direct second-order approaches widely adopted in linear dynamics, including the generalized-α, central difference, and Newmark methods. The proposed method is derived from a Taylor series expansion truncated at the third derivative, resulting in a fully explicit algorithm that requires only one function evaluation per time step. Similar to Newmark’s formulation, it includes adjustable parameters that allow the user to balance accuracy and stability. For a specific parameter choice, the method exhibits convergence and stability properties comparable to those of the central difference scheme. An important advantage is that it remains explicit even when nonlinearities depend on first-derivative terms. The paper presents a theoretical analysis covering stability, local truncation error, spectral properties, numerical damping, and period elongation. The method is validated through four test cases from multibody dynamics, including linear and nonlinear problems. Results demonstrate that the Explicit Integration Grade 3 (EIG-3) method achieves accuracy comparable to existing explicit second-order integrators while significantly reducing computational cost, particularly in nonlinear applications. Full article

Estimating the position and orientation of a camera with respect to an observed scene remains a fundamental problem in computer vision, particularly in calibration procedures and multi-sensor vision systems. This paper revisits the planar Perspective–n–Point (PnP) problem with emphasis on rotation representation, initialization strategy, and optimization behavior. We propose the PnP-ProCay78 algorithm, which combines analytical elimination of translation via quadratic reconstruction error with nonlinear least-squares minimization of projection residuals in Cayley parameter space. A deterministic initialization scheme based on canonical directions of the reconstruction matrix eliminates the need for spectral search over the full solution space. Experimental evaluation on heterogeneous datasets acquired from high-resolution RGB cameras and low-resolution thermal cameras demonstrates that the proposed method achieves reprojection accuracy comparable to state-of-the-art OpenCV implementations such as SQPnP and IPPE. Convergence analysis in Cayley space reveals stable and rapidly contracting optimization trajectories, with consistent behavior across sensors of significantly different resolution and noise characteristics. The results indicate that a carefully chosen rotation parameterization combined with a transparent optimization framework can yield competitive numerical performance while maintaining geometric interpretability and structural simplicity. Full article

Recent advances in physics-informed neural networks (PINN) have highlighted the need for systematic criteria for selecting appropriate algorithms to solve differential equations. This paper presents a numerical comparison between standard PINNs and gradient-enhanced PINNs (gPINNs) used to solve a high-order partial differential equations (PDE). To verify the accuracy and convergence behavior of all the methods, we solve a fourth-order PDE whose analytical solution is known. gPINN is recommended for problems requiring high accuracy in gradient fields or operating with sparse data, whereas standard PINN is advised for strongly nonlinear or computationally constrained scenarios. We synthesize our findings into a practical selection guide; gPINN is recommended for problems requiring high accuracy in gradient fields or operating with sparse data, whereas standard PINN is advised for strongly nonlinear or computationally constrained scenarios. This framework provides a clear, evidence-based policy for algorithm choice in SciML. Beyond numerical comparison, we provide an analytical interpretation linking solver performance to the spectral and stiffness properties of each PDE class, offering a principled basis for algorithm selection. Full article

To address the issue of low closed-loop feedback bandwidth caused by the long latency of Carrier-Envelope Phase (CEP) measurement systems for amplified femtosecond laser pulses, and to meet the requirements for real-time single-shot measurement in 10 kHz repetition rate systems, this paper proposes a microsecond-level low-latency CEP measurement technique based on a Field-Programmable Gate Array (FPGA). To tackle the problem of non-uniform spectral sampling resulting from nonlinear wavelength-frequency mapping, the system implements a real-time linear interpolation algorithm for the interference spectrum. This approach effectively suppresses computational spurious peaks introduced by non-uniform sampling and significantly reduces measurement errors. Adopting a fully pipelined parallel processing architecture, the system achieves a CEP processing latency of approximately 89 μs, representing an improvement of 2–3 orders of magnitude compared to traditional Central Processing Unit (CPU)-based solutions. Hardware-in-the-loop testing, conducted by injecting a known sinusoidal phase modulation into the interference spectrum of a 10 kHz laser amplification system, demonstrates that the computational error of the proposed algorithm is less than 30 mrad. This work paves the way for achieving single-shot CEP feedback locking in high-repetition-rate laser amplification systems. Full article

Aiming at the challenges of complex spatial-temporal correlation and strong nonlinearity in the power prediction of large-scale wind farm clusters, this study proposes a short-term wind power prediction method that combines a dynamic graph structure and a Kolmogorov–Arnold Network (KAN) enhanced neural network. Firstly, a spectral embedding fuzzy C-means (FCM) cluster partition method combining geographic location and numerical weather prediction (NWP) is proposed to solve the problem of insufficient spatio-temporal representation ability of traditional methods. Secondly, a dynamic directed graph construction mechanism based on a stacked wind direction matrix and wind speed mutual information is designed to describe the directional correlation between stations with the evolution of meteorological conditions. Finally, a prediction model of dynamic graph convolution and Transformer based on KAN enhancement (DGTK-Net) is constructed to improve the fitting ability of complex nonlinear relationships. Based on the cluster data of 31 wind farms in Gansu Province of China and the cluster data of 70 wind farms in Inner Mongolia, a case study is carried out. The results show that the proposed model is significantly better than the comparison methods in terms of key evaluation indicators, and the root mean square error is reduced by about 1.16% on average. This method provides a prediction tool that can adapt to time and space changes for engineering practice, which is helpful to improve the wind power consumption capacity and operation economy of the power grid. Full article

The determination of brain age based on electroencephalography (EEG) data has become widely developed with the spread of machine learning in recent years. In this research paper, we analyzed 21 articles published no earlier than 2015, focusing particularly on features, machine learning and deep learning models, and the validation process. The studies reviewed presented model performance on EEG data using machine learning or deep learning techniques. Deep convolutional and transformer-based models trained on well-curated features forecasted chronological age most precisely. In newborns, time–frequency and entropy-based characteristics showed good predictive power for the brain age index (BAI) and functional brain age (FBA). Consistently, spectral and nonlinear descriptors ranked among the most informative characteristics. Methodological rigor, meanwhile, differed: only a small number of studies used bias correction techniques, addressed statistical assumptions, or reported external validation. Preprocessing techniques also showed significant variation. Although EEG-based models have good accuracy, problems of interpretability and generalizability restrict their clinical and developmental use. Advancing this discipline will call for biologically based outcome definitions, uniform evaluation systems, and open source processing pipelines. Full article

To address the problem that transformer inrush currents under no-load and energization conditions can easily trigger misoperations of differential protection, this paper proposes a multi-feature identification method for transformer inrush current based on adaptive variational mode decomposition. Traditional methods typically rely on fixed physical features or single criteria, making them sensitive to operating condition variations and prone to misclassification or missed detection under complex disturbances, with limited generalization capability. The proposed method first performs adaptive VMD decomposition of current waveforms under different operating conditions. On this basis, time-domain, frequency-domain, and nonlinear features are extracted to comprehensively characterize the signal’s amplitude, spectral, and complexity information. Then, by combining the ReliefF algorithm with forward stepwise feature selection, the method reduces feature dimensionality while maintaining high discriminative power and low redundancy. Using the VMD-ReliefF-EEFO-SVM classification model, the approach achieves efficient and accurate discrimination between inrush currents and fault currents. Simulation results demonstrate that the proposed identification method adapts well to various operating conditions and exhibits strong robustness and versatility. Full article

Direction of arrival (DOA) estimation is a fundamental problem in array signal processing, with extensive applications in radar, communications, sonar, and other fields. Traditional DOA estimation methods, such as MUSIC and ESPRIT, rely on eigenvalue decomposition or spectral peak search, which suffer from high computational complexity and performance degradation under conditions of low signal-to-noise ratio (SNR), coherent signals, and array imperfections. Cylindrical arrays offer unique advantages for omnidirectional sensing due to their circular structure and three-dimensional coverage capability; however, their nonlinear array manifold increases the difficulty of estimation. This paper proposes a circular-attention residual network (CA-ResNet) for DOA estimation using uniform cylindrical arrays. The proposed approach achieves high accuracy and robust angle estimation through phase difference feature extraction, a multi-scale residual network, an attention mechanism, and a joint output module. Simulation results demonstrate that the proposed CA-ResNet method delivers superior performance under challenging scenarios, including low SNR (−10 dB), a small number of snapshots (L = 5), and multiple sources (1 to 4 signal sources). The corresponding root mean square errors (RMSE) are 0.21°, 0.45°, and below 1.5°, respectively, significantly outperforming traditional methods like MUSIC and ESPRIT, as well as existing deep learning models (e.g., ResNet, CNN, MLP). Furthermore, the algorithm exhibits low computational complexity and a small parameter size, highlighting its strong potential for practical engineering applications and robustness. Full article

Directional flying ad hoc networks (FANETs) equipped with phased array antennas are pivotal for applications demanding high-capacity, low-latency communications. While directional beamforming extends the communication range, it necessitates the intricate joint optimization of the beam direction, power, and time-slot scheduling under hardware constraints. Existing resource allocation schemes predominantly follow two paradigms: (i) conventional physical-layer multiple access (CPMA) approaches, which enforce strict orthogonality within each beam and thus limit spatial efficiency; and (ii) advanced physical-layer techniques like rate-splitting multiple access (RSMA), which have been applied to terrestrial and omnidirectional UAV networks but not systematically integrated with the beam-based scheduling constraints of directional FANETs. Consequently, jointly optimizing the beam direction, intra-beam rate-splitting-based node pairing, transmit power, and time-slot scheduling remains largely unexplored. To bridge this gap, this paper introduces an intra-beam rate-splitting-based resource allocation (IBRSRA) framework for directional FANETs. This paper formulates an optimization problem that jointly designs the beam direction, constrained rate-splitting (CRS)-based node pairing, power control, modulation and coding scheme (MCS) selection, and time-slot scheduling, aiming to minimize the total number of time slots required for data transmission. The resulting mixed-integer nonlinear programming (MINLP) problem is solved via a computationally efficient two-stage algorithm, combining greedy scheduling with successive convex approximation (SCA) for non-convex optimization. Simulation results demonstrate that the proposed IBRSRA algorithm substantially enhances spectral efficiency and reduces latency. Specifically, for a network with 16 nodes, IBRSRA reduces the required number of transmission time slots by more than 42% compared to the best-performing baseline scheme. This confirms the significant practical benefit of integrating CRS into the resource allocation design of directional FANETs. Full article

This work focuses on solving the singularly perturbed generalized Hodgkin-Huxley (HH) problem. The HH equation is numerically solved by a collocation approach using third-degree splines. The forward difference technique is utilized for time discretization, while $\theta$-weighted schemes are employed for space discretization. Solving non-linear models using discretization and quasi-linearization results in a set of linear algebraic equations, which are solved using matrices. Furthermore, Von Neumann’s (VN) stability and Spectral Radius (S.R) reveal that the suggested technique is unconditionally stable. To assess the performance and accuracy of this method, absolute error (AE), $L_2$, and $L_{\infty }$ norms are offered. The results align with the literature. Simulation results show that the proposed strategy produces accurate results. Full article

This paper investigates the long-term asymptotic behavior of solutions to the initial-boundary value problem for the three-dimensional incompressible viscous magnetohydrodynamic (MHD) equations in general unbounded domains. Addressing the difficulty that traditional analytical methods (such as Fourier separation techniques and semigroup estimates for the Stokes operator) fail in unbounded domains, we introduce the operator regularization technique to construct a sequence of approximate solutions. By combining spectral analysis skills and the theory of analytic semigroups, a unified estimation method applicable to the nonlinear terms in the system is proposed. Through energy estimates and the theory of weak convergence, the existence of global weak solutions is proven, and the algebraic decay rate of the solutions is further derived. The results show that the decay behavior of the weak solutions is mainly dominated by the corresponding linear part (i.e., the semigroup solution of the Stokes equations). The estimation method established in this paper is applicable to general smooth unbounded domains, which generalizes the existing results that were only applicable to special domains. Full article

Aiming to improve the currently low accuracy of fault diagnosis due to the difficulty of extracting the non-stationary and nonlinear features of rolling bearing fault signals, a multi-condition fault diagnosis method for rolling bearings was proposed based on enhanced singular spectrum decomposition (ESSD), optimized multi-scale mean permutation entropy (MMPE), and support vector machine (SVM). Firstly, aiming to address the problem of singular spectrum decomposition (SSD) producing false components and signals with low energy proportions that cannot be accurately decomposed when the residual energy ratio is used as the final iteration termination condition, an enhanced singular spectral decomposition method is proposed. Secondly, the effect of the MMPE extraction of fault features depends on the selection of parameters, and after comprehensively considering the interaction between MMPE parameters, a method to optimize MMPE based on the particle swarm optimization (PSO) algorithm is proposed to maximize the performance of the extracted features. Finally, considering that the classification performance of SVM is affected by the penalty factor c and kernel function g, the fault characteristics proposed by ESSD + PSO - MMPE are identified by an SVM classifier model that is optimized by the particle swarm algorithm, so as to realize the effective diagnosis of multi-condition faults in rolling bearings. Using rolling bearing simulation signals, the Case Western Reserve University bearing dataset, and the online monitoring signal from the front bearings of a wind farm’s 1.5 MW wind turbine, the proposed method is compared with EMD + MMPE + SVM, SSD + MMPE + PSO - SVM, ESSD + MMPE + PSO - SVM, and other methods, and the results show that the proposed method can effectively identify multi-working faults in rolling bearings. Full article