Search Results (475)

As power systems continue to expand and grow in complexity, power flow calculation remains a fundamental task in power system analysis and operation. Conventional methods rely on iterative solvers and detailed grid models, yet are often hindered by non-convergence and unreliable modeling assumptions. To address these limitations, this paper introduces a deep learning-based approach that integrates graph neural networks (GNNs) and recurrent neural networks (RNNs) for power flow calculation. The proposed model captures spatial dependencies through graph convolutional layers and temporal dynamics through recurrent layers, enabling accurate prediction of node voltage magnitudes, phase angles, and branch power flows. To enhance transparency, SHAP (Shapley Additive exPlanations)-based feature attribution and multi-modal visualizations are employed to interpret the model’s predictions. Experimental results on the IEEE 9-bus, 39-bus, and 118-bus systems demonstrate prediction errors within 4% and a computational speedup of approximately 40-fold over traditional Newton–Raphson methods. Beyond technical performance, these results suggest that the proposed method can support more efficient and reliable grid operation, thereby contributing to the integration of renewable energy, enhancement of grid resilience, and advancement of sustainable energy systems. Full article

The paper addresses an inverse problem for a nonlinear Volterra integral equation of the first kind with a piecewise continuous kernel whose discontinuity curves are the unknown functions. Such models arise in the theory of developing systems, power systems with energy storage, and related applications. We develop an iterative scheme based on the Newton–Kantorovich linearisation of the nonlinear integral operator and obtain explicit recurrent formulas for the discontinuity curve. Both the full Newton-like and a modified (simplified) iterative process are constructed, and their local convergence is proved under natural smoothness and smallness conditions. The performance and accuracy of the method are illustrated by several model problems with known and unknown exact solutions. The algorithm demonstrates rapid convergence and is robust with respect to the choice of the initial approximation. Full article

Residual film recovery is a crucial approach to mitigating agricultural “white pollution” and ensuring sustainable land use. Currently, the development of residual film recovery machines relies primarily on theoretical analysis and field performance tests. The lack of support from computational simulation models often leads to suboptimal mechanical performance, severely restricting the design and optimization of recovery equipment. To address this, this study proposes a method for constructing and experimentally validating a discrete element model of plow-layer residual film using EDEM software. First, field tests were conducted to measure soil compaction and residual film distribution at various depths. The ultimate tensile force of the residual film was also evaluated to provide fundamental data for model development. Using the Hertz–Mindlin with bonding contact model in EDEM, the intrinsic parameters of the residual film were selected and optimized. Combined with a Box–Behnken experimental design, a quadratic regression model relating normal stiffness per unit area, critical normal stress, and bond radius to the ultimate tensile force of the film was constructed. The optimal parameter combination was determined as follows: normal stiffness = 1.11 × 10⁶ N·m⁻³, critical normal stress = 2.45 × 10⁶ Pa, and bond radius = 0.03 mm. Under these parameters, the theoretically predicted ultimate tensile force was 1.18 N, and the simulated value yielded a relative error of only 1.69%, validating the effectiveness of the single-film model. Furthermore, using the field-measured data, a coupled film–soil model was established via the “rainfall” method to conduct simulated penetration tests. Parameter calibration was executed using the multivariate Newton–Raphson iteration method. The optimal bonding parameters for soil particles were identified as follows: normal stiffness per unit area = 9.6 × 10⁵ N/m², shear stiffness per unit area = 9.6 × 10⁵ N/m², critical normal stress = 5.38 × 10⁵ Pa, critical shear stress = 5.38 × 10⁵ Pa, and bond radius = 4.3 mm. The average simulated penetration resistance was 59.61 N, showing a relative error of 5.91% compared to the field-measured value of 56.28 N. These results demonstrate that the developed coupled film–soil DEM can be effectively applied to simulate the lifting and throwing processes of plow-layer residual film recovery machines, thereby providing vital modeling support for the design and optimization of residual film recovery mechanisms. Full article

This paper presents new optimal eighth-order families with weight functions for solving nonlinear systems, obtained as a generalization of the first optimal eighth-order CTT8 method introduced by Cordero, Torregrosa and Triguero-Navarro. The proposed schemes are constructed by combining a Newton-type predictor with high-order correction steps whose weight functions are suitably chosen to preserve optimal convergence while keeping a low computational cost. To the best of our knowledge, this work introduces the first family of optimal eighth-order methods for nonlinear systems, in the sense of the Cordero–Torregrosa conjecture, developed through a weight-function technique. A complete local convergence analysis is carried out under standard smoothness assumptions, proving eighth-order convergence for nondegenerate solutions. The computational efficiency of the proposed methods is also studied and compared with several existing high-order iterative schemes. Numerical experiments on nonlinear systems of different dimensions confirm the theoretical order of convergence and show the robustness of the new families. In addition, a Fredholm integral equation is solved, followed by a semilinear elliptic Dirichlet problem, further illustrating the reliability and computational performance of the proposed weight-function-based methods. Full article

In the localization of a distributed radar cluster under far-field and short-baseline conditions with a configuration that varies with time, traditional translational maneuvering strategies have limited capability to expand the observation angle. This makes it difficult to effectively improve the observation geometry, and can easily lead to the amplification of localization errors. Targeting this problem, this work proposes a localization method with configuration adjustment based on Fisher information matrix (FIM) prediction. Without requiring prior information of the true target position, the proposed method predicts the FIMs of candidate configurations based on the current target position estimate. It evaluates these configurations by minimizing the localization uncertainty along the worst direction, thereby enabling adaptive adjustment of the cluster configuration. Furthermore, an in-place rotational strategy is introduced to enhance angular diversity, and a Gauss–Newton iterative solution is developed by incorporating temporal prior information to improve the stability of nonlinear localization. Simulation results show that the proposed method can effectively improve the observation geometry under far-field and short-baseline conditions, and reduce abnormal jumps caused by noise. Compared with the traditional translational maneuvering strategy, the proposed method reduces the localization error by more than 70%. Full article

GNSS signals are extremely weak at the Earth’s surface and are highly vulnerable to in-band interference, particularly high-dynamic linear frequency-modulated (LFM) jamming, which may lead to receiver loss of lock. Existing anti-jamming techniques struggle to balance real-time constraints with high-precision frequency estimation. This paper proposes a Newton-iteration-enhanced three-spectral-line RIFE algorithm implemented on a heterogeneous FPGA platform (Zynq-7000 SoC). The method performs coarse frequency estimation using the three-spectral-line RIFE to mitigate FFT fence effects, followed by Newton-based quadratic refinement, enabling high estimation accuracy with reduced FFT size. A fast–slow loop architecture is adopted, where the FPGA (PL) performs real-time interference suppression and the ARM (PS) handles system control and parameter updates. Experimental results show that, under static interference, the proposed method achieves a 10.9 dB improvement over direct estimation algorithms. Under chirp interference, it significantly outperforms both direct estimation and conventional iterative methods. In GNSS closed-loop tests, the proposed approach extends the anti-jamming margin to 82 dB J/S. Overall, the proposed method effectively balances estimation accuracy and processing latency, providing a practical solution for GNSS anti-jamming in high-dynamic environments. Full article

To address the convergence rate degradation of standard Newton iteration methods for nonlinear equations with multiple roots, this study systematically investigates the dynamic behavior and convergence properties of iterative methods for solving multiple roots. First, under the condition of a countable state space, we analyze, based on existing Markov chain theory, the convergence conditions and rates for nine iterative formats, including the modified Newton method and Halley method. Next, extending the research to general state spaces, we discuss a potential probabilistic analysis framework for probability convergence, first arrival time expectation, and distribution convergence rate using Markov chain and drift analysis tools. Numerical experiments demonstrate that, as the root multiplicity increases from 1 to 7, the convergence probability of the standard Newton method decreases from 0.98 to 0.35, while the average first arrival time increases from 6.2 to 190.3 iterations. The results indicate that the performance of iterative methods for multiple roots strongly depends on explicit utilization of multiple roots information or possession of high-order convergence properties, thereby improving both convergence probability and first arrival time performance. This study provides quantitative evidence and novel insights for theoretical analysis and efficient algorithm design of iterative methods in complex scenarios. In addition, the sensitivity of the iterative method to the initial value is discussed. It is pointed out that the adaptive estimation strategy provides a good compromise between robustness and efficiency compared with high-order methods, such as the Halley method, when the prior information of root weight is not available. Full article

We develop a fast Chebyshev spectral collocation method for a coupled system of nonlinear Klein–Gordon equations augmented by Caputo-type fractional memory integrals. The governing equations retain the classical second-order time derivative as the leading operator and incorporate weakly singular convolution integrals modelling viscoelastic memory damping. The spatial discretisation employs Chebyshev–Gauss–Lobatto collocation, while the temporal integration uses a Newmark scheme (${\beta }_{\mathrm{NM}}=1/4$) combined with an implicit–explicit linearisation in which the linear spatial operator is treated implicitly and the nonlinear terms are treated explicitly through a second-order extrapolation. This linearisation eliminates the need for Newton–Raphson iterations at each time step. To overcome the dense memory bottleneck arising from two distinct fractional orders $\alpha \ne \beta$, the convolution memory kernels are compressed by independent sum-of-exponentials approximations obtained from a double-exponential quadrature of the kernel’s integral representation, which significantly reduces the computational complexity of the history term. A rigorous stability estimate and a global convergence bound are established using a discrete Grönwall inequality. Numerical experiments confirm the theoretical temporal and spatial convergence rates and demonstrate the practical speed-up afforded by the sum-of-exponentials acceleration. A solitary wave collision scenario illustrates the method’s capability to capture asymmetric dispersive wakes generated by the fractional memory. Full article

We extend the modified BFGS algorithm to a limited-memory framework, and propose a self-adaptive limited-memory quasi-Newton method, denoted as LADBFGS, for large-scale unconstrained optimization. The proposed method fully exploits function value information to improve the curvature approximation of the objective function, while enabling dynamic and adaptive adjustment of parameters. We establish the global R-linear convergence of the proposed algorithm for uniformly convex problems. Numerical experiments on 102 standard unconstrained test functions with dimensions of no less than 1000 show that the proposed LADBFGS method outperforms the standard limited-memory BFGS method in terms of iteration count, number of function and gradient evaluations, and computational time, and also achieves a higher success rate for solving the test problems. Full article

We propose the higher-order quasi-Newton (HOQN) method, a hybrid algorithm for unconstrained optimization that combines Newtonian predictors with higher-order correctors derived from vector extensions of the Traub, Chun, and Ostrowski methods, along with quasi-Newton updates of the inverse Hessian using Broyden–Fletcher–Goldfarb–Shanno (BFGS) or Davidon–Fletcher–Powell (DFP) formulas. We demonstrate that the resulting scheme achieves cubic local convergence order, representing a substantial improvement over the superlinear convergence typical of classical quasi-Newton methods, while maintaining a cost of $O\left(n^2\right)$ per iteration. We also analyze variants that incorporate two successive quasi-Newton updates, and show that they retain the same cubic order. Numerical experiments with the benchmark functions of Himmelblau and Freudenstein–Roth confirm the theoretical convergence order and show that the hybrid variants consistently require fewer iterations than BFGS, DFP, and Symmetric Rank-One (SR1). In the case of the Booth function, given its strictly convex quadratic structure, the proposed hybrid methods reach the global minimum in just two iterations and exhibit numerical accuracy superior to that of classical quasi-Newton methods. In addition, limited-memory variants (L-HOQN) are introduced; these are evaluated during the training of a convolutional neural network on the MNIST dataset, where they achieve test accuracies exceeding $99\%$ and outperform L-BFGS and standard stochastic gradient descent (SGD) at all tested learning rates. Full article

The present paper addresses a problem that many traditional analytical calculation methods ignore the coupling relationship between loss and temperature rise. In this paper, a 51.51 MW turbine generator is taken as the research object, and a transient thermal network method coupled with loss and temperature rise for calculating the temperature rise in a stator transposition bar is proposed. Considering the influence of temperature change on the AC loss of strands, a thermal network model coupled with loss and temperature rise is established to complete the calculation of thermal conductivity matrix parameters. A sparse matrix storage method is proposed to reduce the memory usage of the high-order matrix. The linear iterative method is introduced to accelerate the solution of the equation. The Newton Krylov method is used to handle the coupling between loss and temperature rise. In this way, the transient temperature rise in the stator transposition bar is calculated rapidly. The accuracy of the thermal network model coupled with loss and temperature rise is verified by comparing its results with the three-dimensional simulations. Finally, a new combined transposition structure is proposed to suppress the temperature rise in the stator transposition bar. Full article

Injection operations are critical in subsurface energy engineering, where wellbores endure complex thermo-hydro-mechanical (THM) coupling under high-temperature and high-pressure conditions, impacting tubing string stability and wellbore long-term safety. Current tubing string THM research relies on simplified assumptions, focusing on single/dual-field coupling without full-scale modeling, failing to accurately characterize comprehensive multi-field behaviors or actual structural stress distributions. This paper presents a full-scale THM coupled numerical model for actual injection conditions, taking real wellbore structures as the object to realize unified modeling of tubing, packer, casing, cement sheath and formation, covering the entire well section and synergistically describing fluid flow, heat conduction and structural mechanical response. It considers fluid pressure/temperature effects on tubing axial load, thermal stress and deformation, as well as nonlinear boundary conditions like packer-casing contact and friction. The governing equations are discretized via the finite element method and solved by Newton iteration. Benchmark verification shows the maximum relative errors of casing inner/outer wall Mises stress vs. analytical solutions are 2.43% and 4.98%, confirming high accuracy. Systematic analysis of displacement, axial force, stress and temperature responses under typical conditions is conducted, providing reliable theoretical and technical support for wellbore structure optimization, injection parameter regulation and long-term wellbore integrity evaluation. Full article

We develop a high-order space-time spectral method for nonlinear convection–diffusion equations with a Riemann–Liouville time-fractional derivative and a spectrally defined space-fractional Laplacian. The spatial discretization uses a Fourier spectral method that diagonalizes the fractional Laplacian under periodic boundary conditions. The temporal discretization employs a Petrov–Galerkin method based on generalized Jacobi functions which capture the initial singularity exactly. The nonlinear convection term is treated pseudo-spectrally, and the resulting algebraic system is solved with a damped Newton iteration. Rigorous error analysis proves exponential convergence in both space and time. Numerical experiments for various fractional orders confirm the spectral accuracy. Simulations of the fractional Burgers equation demonstrate that increasing the viscosity enhances diffusion and stabilizes the solution, while a nonlinear coefficient that significantly exceeds the viscosity leads to error growth over long time intervals. The method provides an efficient and accurate tool for simulating anomalous transport phenomena. Full article

Prediction of the reachable domain for high-threat unmanned aerial vehicles (UAVs) is critical for enabling cross-domain flight vehicles to perform proactive avoidance maneuvers. To address this challenge, this paper proposes a novel generic framework that integrates a Radau pseudospectral method (RPM) with a BP neural network, supported by information acquired from satellites. The framework begins by estimating a preliminary state vector of the non-cooperative target, including its coarse position and velocity, via a Newton iterative algorithm. To refine this initial estimate and enable continuous tracking, an Extended Kalman Filter (EKF) is fused with a flight vehicle dynamics model. Subsequently, the RPM is employed to solve the trajectory planning problem, generating a comprehensive database for offline training. This database is then used to train a multilayer feedforward neural network within an offline training and online application framework, which drastically reduces computational complexity and time. Finally, numerical simulations demonstrate the method’s high prediction accuracy and strong robustness against tracking uncertainties. Crucially, the neural network predicts the reachable domain in just 0.01 s, making it highly viable for real-time online applications. Full article

This study develops an effective numerical method for addressing the time-fractional gas dynamics equation formulated with the Caputo time-fractional derivative. Novel basis functions are utilized, formulated as particular generalized Fibonacci polynomials contingent on a free parameter. This family generalizes the second kind of Chebyshev family. For the proposed polynomials, we establish basic analytical properties, including closed-form series expansion, inverse relation, moment and linearization formulas, and operational matrices for both integer-order and Caputo fractional derivatives. Using these tools, the fractional model, together with its underlying conditions, can be transformed into a finite system of nonlinear algebraic equations via a collocation strategy. Using Newton’s iterative method, the resulting system can be treated. A full convergence analysis of the double generalized Chebyshev expansion is provided. We demonstrate the accuracy and reliability of the presented method through several numerical simulations. Comparisons with existing numerical methods show that this approach achieves higher accuracy and faster execution. Full article