Search Results (662)

The Sparse Identification of Nonlinear Dynamics (SINDy) method yields compact and interpretable models that preserve physical system properties, offering a superior alternative to black-box models. This work proposes a computationally efficient Model Predictive Control (MPC) algorithm for SINDy models. The algorithm employs a successively obtained online linear Taylor approximation of the model for future prediction, while the full SINDy model captures past dynamics. As a result, the nonlinear MPC problem is reformulated as a tractable quadratic program. The implementation covers three discretization schemes: the first-order Euler and the simplified and full fourth-order Runge–Kutta. Simulation benchmarks for population dynamics and aircraft models show that the algorithm achieves performance comparable to nonlinear MPC with significantly lower complexity, enabling real-time use. Full article

The present computational work investigates the effects of thermal radiation, activation energy, and diffusion-thermo (Dufour) and thermo-diffusion (Soret) effects on 3D doubly diffusive convective rotational streams across a surface contained in a non-Darcian porous structure. The dominating mathematical system is converted into a group of ODEs (ordinary differential equations) by appropriate similarity transformations. The non-dimensional model is solved using the fourth-order Runge–Kutta method with a shooting procedure numerically. For the fields of concentration, temperature, and velocity, the findings are shown visually. The local heat and mass transport rates are given by computed Sherwood and Nusselt numbers. By growing the values of radiation, activation energy parameters, and Soret number, the local rate of heat transfer increases. Nevertheless, as the Soret and activation energy parameter values increase, the mass transfer decreases. The outcome of the present research can be used to model thermal systems. Full article

Studying jet engine vibration (JEV) enhances flight safety and operational reliability through advanced detection, precision modeling, and data-driven techniques. This approach involves complex nonlinear vibration behaviors that often exceed the capabilities of conventional techniques. It facilitates early fault detection, predictive maintenance, and improved engine design. This study employs the non-perturbative approach (NPA) to examine the dynamics of a parametric nonlinear oscillatory system. The formulation is based on He’s frequency formula (HFF), which transforms a nonlinear ordinary differential equation (ODE) into an equivalent linear one. The analytical results are validated using Mathematica software (MS) (v13), showing strong agreement between the original nonlinear ODE and the corresponding linearized equation. To further explore the system behavior, bifurcation diagrams (BDs) are constructed, and the largest Lyapunov exponent (LLE) is utilized to identify stability regions and detect chaotic oscillations. The averaging method is applied to determine the critical resonance conditions and derive the frequency–response relationships; meanwhile, stability near simultaneous primary resonance is examined using the Routh–Hurwitz criterion. Finally, numerical simulations (NSs) based on the fourth-order Runge–Kutta method (RK-4) confirm the effectiveness of the positive position feedback (PPF) control strategy. Full article

Multispectral satellite image segmentation constitutes a challenging optimization problem due to high dimensionality and complex inter-band correlation structures. As the number of thresholds increases, the search space grows exponentially, causing metaheuristic methods to suffer from convergence instability by getting trapped in local optima on highly multimodal landscapes. In this study, a hybrid optimization method is proposed by integrating the Marine Predators Algorithm (MPA) with the Runge–Kutta (RUN) approach. The proposed framework enhances global exploration through Cauchy-based perturbation, while improving exploitation capability via a mutation-based local refinement mechanism, and reduces spectral redundancy using Principal Component Analysis (PCA). The MPA-RUN hybrid structure, combined with a Cauchy-driven exploration strategy and an adaptive local search mechanism, significantly improves the exploration–exploitation balance in multispectral image thresholding problems. Experiments are conducted on Sentinel-2 multispectral images, and the proposed method is evaluated against conventional metaheuristic algorithms over a wide threshold range (2–26), encompassing both low- and high-dimensional configurations. At high threshold levels, the proposed method achieves Peak Signal-to-Noise Ratio (PSNR) = 23.66, Structural Similarity Index Measure (SSIM) = 0.863, and Feature Similarity Index Measure (FSIM) = 0.797, while providing approximately 35% lower computational time at moderate levels, demonstrating superior efficiency. These results demonstrate that a balanced trade-off between accuracy and computational cost is achieved. The proposed approach offers a fast and reliable solution for processing high-dimensional data by effectively balancing segmentation quality and computational complexity. Full article

Structure-preserving numerical methods are well-established for purely conservative or purely dissipative systems but remain underdeveloped for mixed-type equations coupling dispersion, dissipation, and nonlinearity. We investigate the Korteweg–de Vries–Burgers equation as a canonical model of this class. We develop a geometric covering method based on nonlocal symmetries that lifts the equation to an extended manifold, enabling exact conservation law preservation. As a pedagogical counterexample, we also analyze a naive recursive approximation. Both methods are implemented using sixth-order compact finite differences and fourth-order Runge–Kutta (RK4) time integration. Numerical experiments on sinusoidal waves, two-soliton collisions, and perturbed traveling waves show that the covering method reduces numerical dissipation by 50% and phase error by 90% relative to a standard second-order scheme, achieving one to two orders of magnitude higher accuracy. Mass and momentum are conserved to machine precision (below ${10}^{-14}$), and soliton amplitudes are preserved to within 0.3% after collision, with only 15% computational overhead. The framework offers a generalizable template for embedding nonlocal symmetries into high-order numerical methods for nonlinear wave equations. Full article

This study selects five numerical methods: the explicit Leap-Frog scheme, the implicit Crank–Nicolson scheme, the explicit second-order Runge–Kutta scheme, the implicit Newmark-β scheme, and the implicit Bathe scheme. These methods are compared through representative dynamic cases in terms of solution accuracy and computational efficiency. The results demonstrate that implicit schemes maintain numerical convergence even with relatively large time steps. The findings also indicate that, although the actual convergence accuracy of the given schemes varies slightly among motion models of different dimensions, it remains close to the theoretical second-order accuracy. Different time integration schemes exhibit distinct numerical accuracies when applied to multi-dimensional motion problems. Overall, under identical time step sizes, the Bathe time integration scheme demonstrates slightly superior computational accuracy and error stability compared to other schemes considered. The numerical efficiency of time integration schemes also varies across dimensions and problem types. The actual computational time does not scale linearly with the time step size and is partially influenced by the complexity of the solution algorithm employed. In general, when solution accuracy is comparable, the Leap-Frog scheme shows marginally higher efficiency in explicit simulations, whereas the Crank–Nicolson scheme proves more efficient in implicit simulations. Full article

This study presents a numerical and analytical investigation of the nonlinear smooth-discontinuous (SD) oscillator. The nonlinear restoring force is approximated by a fifth-order polynomial using a Taylor series expansion to simplify the governing equation while preserving the essential nonlinear characteristics of the system. To analyze the oscillator dynamics, two analytical approaches are applied, namely the spreading residue harmonic balance method (SRHPM) and the Multiple Scales Method (MSM). The obtained analytical solutions are validated through comparison with numerical simulations carried out using the classical fourth-order Runge–Kutta scheme. The results reveal a strong agreement between the analytical and numerical solutions, confirming the capability of both SRHPM and MSM to accurately describe the nonlinear oscillatory response of the SD system. Full article

This article proposes a novel conservative ConRKDG method for one-dimensional hyperbolic conservation laws with applications in computational fluid dynamics simulations. A DG local solution is reconstructed over each element based on the sub-cell solution averages with a newly proposed set of shape functions. In this virtue, the conservation property of the problem is naturally imposed for the numerical DG solution. In addition, the availability of finite-volume sub-cell solution averages without any DG-to-FV transformation or vice versa facilitates a direct and robust technique for detecting troubled elements, in which the unlimited DG local solution is deemed unstable. A new WENO-type smoothness measurement based on sub-cell solution averages is introduced to assess whether a DG local solution is admissible or unstable, thereby determining whether an element is good or troubled. For the latter case, a secondary finite-volume WENO method is invoked in an a posteriori phase to recalculate the sub-cell averages to sustain numerical stability by essentially suppressing non-physical spurious oscillations in the vicinity of shocks or discontinuities at troubled elements. The performance of the ConRKDG method with different secondary finite-volume WENO methods is compared for both problems with smooth solutions and those with shocks and discontinuities. Full article

Neural ordinary differential equations (Neural ODEs) describe the feature evolution of deep networks by continuous-time dynamical systems and enable end-to-end learning through differentiable numerical solvers. Nevertheless, in closed-loop rolling prediction for small-sample time series, conventional Neural ODEs remain vulnerable to error accumulation and numerical instability. To improve the controllability of long-term evolution, this study proposes a neural ordinary differential equation framework based on fractional-order operators. Rather than directly introducing full-history convolution kernels into the governing dynamics, the proposed approach constructs a fractional effective step size from the closed-form expression of the Riemann–Liouville fractional integral of a constant function and consistently embeds it into all sub-steps of a fourth-order Runge–Kutta solver. In this way, the scale of continuous-depth propagation is regulated by a single tunable parameter. Combined with a residual output structure, the method preserves the interpretability of continuous dynamics while effectively suppressing trajectory drift in closed-loop prediction and improving training stability. To investigate the impact of the fractional-order parameter on fitting and extrapolation, particle swarm optimization is employed to search automatically for the optimal order. Experimental evaluations on the linear spiral system and Lorenz continuous dynamical systems and on a small-sample provincial annual electricity-consumption dataset show that the proposed model achieves lower prediction errors across multiple tasks and exhibits superior trajectory preservation and robustness under long-horizon forecasting. Full article

This paper investigates the dynamic behavior of non-Darcy seepage systems in post-failure rock. A one-dimensional non-Darcy seepage evolution equation is established, and a 6-dimensional nonlinear ordinary differential system is derived via the spectral truncation method. Eigenvalue analysis is adopted to determine the instability and bifurcation conditions, with the bifurcation diagram plotted. The fourth-order Runge–Kutta method is used to obtain phase trajectory patterns under different initial values. The results confirm the existence of transcritical bifurcations and fold bifurcations. The dynamic response of the system is discontinuous with control parameters, and phase trajectory symmetry breaking occurs with the increase in nonlinear terms. The reduced-order model shows diverse phase trajectories including equilibrium, periodic, chaotic attractors and unstable states. The system is sensitive to initial values, which significantly affect phase trajectory behaviors. The system may lose stability and trigger water inrush hazards under critical conditions. The bifurcation diagram and critical parameters obtained can provide a theoretical basis for the early warning, risk assessment and prevention of coal mine water inrush hazards. Full article

Long-distance belt conveyors exhibit significant nonlinear dynamic characteristics due to factors such as the viscoelasticity of the conveyor belt, startup curves, and material loading, which lead to substantial variations in component loads and belt tension. This complexity poses challenges for dynamic analysis and the study of dynamic properties. Based on the Kelvin–Voigt viscoelastic constitutive relation, this paper establishes a discrete model of the conveyor belt and further develops a nonlinear dynamic model for long-distance belt conveyors. The model is numerically solved using the fourth-order Runge–Kutta method. On this basis, the influence of key parameters—such as integration step size, startup curve, operating time, and belt speed—on the dynamic behavior of the belt conveyor is investigated. The results indicate that increasing the counterweight mass effectively suppresses oscillation in the tensioning device and enhances system stability. Prolonging the startup duration and optimizing belt speed also mitigate load impacts. Compared with conventional methods, a composite transitional startup strategy is proposed, which significantly reduces transient tension peaks in the conveyor belt. This study provides a theoretical basis for optimizing control strategies and structural design of long-distance belt conveyors, thereby improving operational safety and reliability. Full article

This paper proposes a hybrid PINN + LSTM framework for the high-precision solution of malware propagation dynamics in wireless sensor networks. A seven-compartment SVEHLQR model is developed to capture this complex transmission process. To overcome the limitations of standard physics-informed neural networks (PINNs) in long-term prediction, including gradient vanishing and error accumulation, we integrate LSTM’s temporal memory capability into the PINN architecture. Comprehensive comparisons are conducted among the proposed PINN + LSTM, standard PINN, and Fourier PINN, using the fourth-order Runge–Kutta method as the benchmark. Experimental results demonstrate that PINN + LSTM significantly outperforms both baseline methods, achieving an average relative error of $3.88\times {10}^{-3}$ compared to $7.20\times {10}^{-2}$ for PINN and $2.81\times {10}^{-1}$ for Fourier PINN, representing a 94.6% accuracy improvement over PINN. These results validate that incorporating LSTM’s recursive memory mechanism enables the accurate and efficient solution of complex time-dependent dynamical systems. Additionally, the model’s robustness is verified under 1%, 5%, and 10% Gaussian noise. PINN + LSTM maintains extremely low relative errors, not exceeding 0.0049, and outperforms PINN and Fourier PINN significantly, confirming its strong noise immunity and stable dynamics learning ability in realistic environments. Full article

This paper studies the reliability and availability of a k-out-of-(M+S) retrial machine repair system with two-way communication, consisting of M primary components and S warm standby components. The system incorporates the retrial behavior of failed components. When the repairman becomes idle, he initiates outgoing calls after a random period either to failed components in the orbit for repair or to components outside the orbit for preventive maintenance. The main contribution of this study is the incorporation of proactive repairman behavior, which more realistically captures operational practices in certain engineering systems. By employing the matrix analytic method together with a recursive approach, the steady-state probabilities of the system are obtained, and several important performance measures are derived. Furthermore, the Runge–Kutta method is used to evaluate the system reliability and the mean time to failure. A sensitivity analysis is conducted to investigate the effects of key system parameters, supported by numerical experiments and graphical illustrations. Finally, a cost–benefit model is formulated, and a genetic algorithm is implemented to determine the optimal values of the decision variables that minimize the cost–benefit ratio. Full article

Consistent control of landing length is critical in cricket spin bowling, yet the sensitivity of landing location to variations in the release velocity components remains unclear. This study quantified the tolerance bands (margin of error) of horizontal (Vy) and vertical (Vz) release velocities required for a ball to land within a 2 m good-length zone (3.37–5.37 m from the batter’s stumps), and examined their dependence on the release height. A six-degree-of-freedom aerodynamic model incorporating gravity, drag, and Magnus forces was used to simulate ball flight for a representative off-spin delivery. The release height was varied between 1.95 and 2.30 m, and the trajectories were solved using a fourth-order Runge–Kutta method with a 0.00001 s time step. Tolerance bands were determined via a bisection search. The results show that the vertical velocity exhibited substantially tighter margins than the horizontal forward velocity. Across release heights, the mean ΔVy was 3.86 ± 0.15 m·s⁻¹ (16.4% of release speed), whereas the mean ΔVz was 1.03 ± 0.03 m·s⁻¹ (4.3%). These findings indicate that pace variation is safer than trajectory variation for achieving consistent ball landings in spin bowling. Full article

DBSCAN is widely used to identify structured regions in unlabeled data, but its performance depends critically on the selection of the neighborhood parameter $\epsilon$. Traditional heuristics for estimating $\epsilon$ often become unreliable in high-dimensional or varying-density settings because they rely heavily on local geometric criteria and may fail under smooth transitions or topological ambiguity. This work presents a three-level perspective on DBSCAN hyperparameter selection. At the algorithmic level, $\epsilon$ controls neighborhood connectivity and structural transitions in clustering. At the modeling level, the ordered k-distance signal is approximated through a surrogate dynamical estimation framework inspired by a mass–spring–damper system. At the causal level, the resulting estimator is interpreted through interventions on its internal threshold-selection mechanism. The proposed method models the variation of $\epsilon$ using ordinary differential equations defined on the ordered k-distance signal, enabling analysis of structural transitions in density organization via a surrogate dynamical representation. System identification is performed using L-BFGS-B optimization on the smoothed k-distance curve, while the system dynamics are solved with the fourth-order Runge–Kutta method. The resulting estimator identifies transition regions that are structurally informative for $\epsilon$ selection in DBSCAN. To analyze the estimator at the intervention level, Pearl’s do-calculus is used to compute the Average Causal Effect (ACE). The method was evaluated on synthetic benchmarks and on the Covtype dataset, including scenarios with multi-density overlap and dimensionality up to ${\mathbb{R}}^{10}$. The resulting ACE values, $+0.9352$, $+0.5148$, and $+0.9246$, indicate that the proposed estimator improves intervention-based $\epsilon$ selection relative to the geometric baseline across the evaluated datasets. Its practical computational cost is dominated by nearest-neighbor search, behaving approximately as $O(NlogN)$ under favorable indexing conditions and degrading toward $O\left(N^2\right)$ in high-dimensional or weak-pruning regimes. Full article