Search Results (1,233)

In classical reliability engineering, failure is a probabilistic structural failure based on lifetime distributions of Weibull models. However, in the control-critical mechanical systems, it is possible that functional failure of the system happens before material failure occurs as a result of control power loss. This paper proposes a Controllability–Reliability Coupling (CRC) model, which redefines the concept of reliability as the stabilizability in the face of progressive degradation. The actuators’ deterioration is modeled using the time-varying input effectiveness factor $\alpha \left(t\right)$, and the actuator is said to be in failure when the minimum singular value of the finite-horizon controllability Gramian becomes less than a stabilizability threshold $\epsilon$. The performance of the simulation indicates that the functional failure is a precursor of structural failure in several degradation conditions. A baseline comparison shows that the CRC metric forecasts loss of controllability at $T_{CRC}=17.0$ s, but the classical Weibull reliability never attains the structural failure threshold even in the time horizon of 20 s. The system retains margins of Lyapunov stability and H infinity robustness are not lost, and it is still stable and attenuates disturbances even when control authority is lost. In practical degradation scenarios, the forecasted CRC failure times are 21.5 s (linear wear), 13.1 s (accelerated fatigue), 23.7 s (intermittent faults), and 24.4 s (shock damage), whereas maintenance recovery abated functional failure completely. In a case study of an industrial robotic joint, at 27.0 s, functional collapse occurred, and at the same time, structural reliability was still above the failure threshold. The findings support the hypothesis that structural survival and functional controllability are distinct concepts. The proposed CRC framework is an approach to control-conscious reliability measure, which can detect early failures and offer proactive maintenance advice in the context of a cyber–physical system. Full article

We develop a local, patchwise geometric framework that embeds a broad class of potential Hamiltonian dynamical systems into a family of Riemannian Hamilton patches built over an underlying Gutzwiller manifold. We adopt a conformal (Jacobi) ansatz and a frame-adapted reconstruction procedure, through which we construct, on each patch, a pulled-back metric, along with a reduced (truncated) connection (not a metric-compatible connection) and a corresponding dynamical curvature tensor governing geodesic deviation in the Hamilton coordinates. Then, using the Poisson–Hodge reconstruction, we reconstruct coordinate potentials, enforcing harmonic obstructions, and along with exactness and Jacobian nondegeneracy conditions, we obtain explicit elliptic bounds that control the connection and curvature residuals. On the basis of this construction, we formalize the notion of a Hamilton manifold such that reparametrized geodesics approximate Newton trajectories with controlled acceleration and tolerances. As a generalized structural framework, to promote the local Jacobi reconstructions to a coherent dynamical evolution and provide a dynamical closure, we introduce a patchwise hyperbolic geometric flow for the pullback metric coupled to a kinetic (Vlasov) closure that controls reconstruction and curvature residuals. Under natural regularity, ellipticity, and overlap-tolerance assumptions, together with precise estimates that control the reconstruction and curvature errors, we establish short-time well-posedness of the coupled Vlasov–hyperbolic geometric flow that defines the patchwise Hamilton manifold. Motivated by this construction of the Hamilton manifold with atlas-dependent time, we propose convergence and stability conjectures for dissipative and conservative (non-dissipative) hyperbolic geometric flows. On a single patch, these conjectures characterize local orbital stability (in the sense of coercivity modulo symmetry) and identify local linear instability when unstable linear modes are present. On a finite atlas (the Hamilton manifold with atlas-dependent time), we state conjectures under which local stability propagates to global stability, provided that overlap residuals remain uniformly sufficiently small. The framework identifies the geometric origin of local instability diagnostics used in Hamiltonian mechanics and outlines a practical strategy for verifying stability or instability, numerically or analytically, on finite coverings of configuration space (the Hamilton manifold). Full article

This paper investigates a finite-time prescribed performance control (PPC) problem for a class of nonlinear engineering systems subject to actuator input saturation. By introducing a performance transformation framework, the tracking error is constrained within predefined bounds with guaranteed finite-time convergence. To address the strict-feedback structure and input constraints simultaneously, a dynamic surface control (DSC) technique is employed to avoid the explosion of complexity. A novel saturation-compensated control law is constructed to ensure closed-loop stability without requiring the persistence of excitation or exact knowledge of system dynamics. Lyapunov-based analysis rigorously proves that all closed-loop signals are bounded and the prescribed performance is achieved within a finite time. The simulation results demonstrate the effectiveness of the proposed approach under actuator saturation, highlighting its applicability to constrained engineering process control systems. Full article

In this article, we explore the possibility of using reinforcement learning to create convective flow approximation schemes that maintain accuracy and stability at high Courant-Friedrichs-Lewy (CFL) numbers in the finite-volume discretization of advection equations. Unlike most existing data-driven discretization methods, which primarily concentrate on spatial grid refinement, this work emphasizes increasing the allowable time step without compromising solution accuracy. This approach reduces the total number of time integration steps, thereby enabling faster computation. A neural network is used as a surrogate model for reconstructing the convective flow, which takes as input local information about the flow, scalars, and geometry and predicts scalar values at node points. Reinforcement learning is used for training and is formulated as a policy optimization problem, where the long-term reward is defined as the difference between the numerical and reference solutions over the entire simulation period. Both the genetic algorithm and the Deep Deterministic Policy Gradient (DDPG) method are investigated. The effectiveness of the approach is evaluated using a one-dimensional nonlinear advection problem with a constant velocity field. Despite the simplicity of the test case, the results demonstrate that the trained convective flux approximation scheme achieves accuracy comparable to or better than the classical second-order linear upwind (LUD) scheme, while operating at CFL numbers 2–50 times higher than the optimal CFL for LUD, thereby reducing the simulation time by the same factor. This allows for a wider range of stability and accuracy in the finite-volume method and the use of larger time steps without compromising the quality of the solution. The study is intentionally limited to a single spatial dimension and serves as a basic analysis of the method’s applicability. The results demonstrate that reinforcement learning can successfully find more convective flow approximation schemes that improve efficiency at high CFL numbers than conventional explicit second-order schemes, establishing a framework that is subsequently extended in our follow-up work to improve training methods and three-dimensional complex transport problems. The proposed method improves the spatial discretization of convective fluxes, which is independent of the choice of time integration scheme. Therefore, the neural reconstruction can in principle be used in both explicit and implicit finite-volume solvers. Full article

Despite its importance in modeling subdiffusion in fractal and heterogeneous media, a rigorous and computational scheme for solving the fractional diffusion equation on generalized comb structures over unbounded domains has remained elusive, mainly due to the nonlocal memory effect and slow spatial decay of solutions. To the best of our knowledge, we address this long-standing gap by presenting a fully integrated framework that simultaneously resolves both challenges. We derive the governing equation from constitutive relations and establish exact absorbing boundary conditions (ABCs) for the multi-skeleton comb model, a result absent in prior work. A transparent Dirichlet-to-Neumann (DtN) map, constructed via Laplace analysis, rigorously handles skeletal Dirac delta singularities and eliminates spurious reflections without empirical parameters. Furthermore, we propose a novel structure-preserving finite difference scheme that applies the sum-of-exponentials (SOE) approximation not only to the interior Caputo derivative but also to the convolution kernels arising from the ABCs. This yields a dramatic reduction in computational complexity, from quadratic $O\left(N_t^2\right)$ to quasi-linear $O(N_{t}log{N}_t)$, while preserving the physics of anomalous transport. We prove the well-posedness, unconditional stability, and convergence of the method. Numerical results confirm theoretical error estimates and show excellent agreement between simulated particle distributions, mean square displacement profiles, and exact asymptotics, validating both accuracy and robustness. The speedup (CPU time ratio Direct/Fast) is about $1.00\times$–$1.23\times$ for $N_t=5000$ in our tests. Our approach sets a new benchmark for simulating anomalous dynamics in fractal-inspired media. Full article

The widespread commercialization of wireless chargers for electric vehicles generally suffers from one main problem, which is the perfect alignment between the two coils, leading to a decrease in mutual inductance, which causes a drop in magnetic coupling and even a failure to transfer power. To address this persistent problem, this work proposes a comprehensive and integrated method for optimizing the coils and control architecture for reliable and safe battery charging. To address the challenges of a complex, nonlinear design space and the need for misalignment-tolerant geometries, we employ a memetic algorithm (MA) that hybridizes Particle Swarm Optimization (PSO) for broad global exploration with Mesh Adaptive Direct Search (MADS) for precise local refinement. This combination effectively avoids poor local solutions—a limitation of standalone PSO or GA approaches reported in recent studies—while efficiently converging to coil geometries that maintain strong magnetic coupling under misalignment. After the coils have been designed, electromagnetic validation is tested using finite element analysis (FEA), which allows the magnetic field distribution to be evaluated, as well as the coupling coefficient under different scenarios of misalignment and variation in the air gap between the ground side and the vehicle side. At the same time, a comprehensive control strategy for the primary side of the system has been developed. This control method ensures power management on the primary side, enabling system interoperability for charging multiple types of vehicles, as well as reducing vehicle weight for greater range. All this is combined with an innovative pulsed current charging method, chosen for its advantages in terms of thermal stability, ensuring safe and efficient recharging that is mindful of battery health. Simulation and experimental validation demonstrate that the proposed framework maintains stable wireless power transfer and achieves over 87% DC–DC efficiency under lateral misalignments up to 100 mm, fully complying with SAE J2954 alignment tolerance requirements. Full article

Dynamic umbilicals, as critical components connecting offshore platforms to subsea production systems, can effectively decouple platform motions through a lazy-wave configuration, thereby reducing top tension and fatigue damage. To address the engineering challenges of numerous configuration design variables and time-consuming dynamic analyses for dynamic umbilicals, an efficient design optimization framework based on surrogate modeling and multi-objective optimization is proposed. An integrated finite-element model of a lazy-wave dynamic umbilical–offshore platform system is developed in OrcaFlex, incorporating environmental loads, material properties, and geometric parameters. The arrangement parameters of clump weights and buoyancy modules are selected as design variables, and the dynamic responses and parameter sensitivities of multiple configurations are investigated. Using simulation data, surrogate models for predicting tension and curvature are constructed via random forest regression, achieving coefficients of determination (R²) of 0.9948 and 0.9121 on the test set, respectively. Based on the surrogate predictors, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to solve a multi-objective optimization problem that minimizes the maximum tension and curvature, yielding a set of Pareto-optimal solutions. The proposed approach effectively improves the stability and reliability of the dynamic umbilical system under complex sea states. Full article

This paper addresses the three-dimensional trajectory tracking problem for underactuated autonomous underwater vehicles subject to external disturbances and model uncertainties in complex ocean environments. A robust control method integrating backstepping dynamic surface control and non-singular terminal sliding mode is proposed. Firstly, based on the kinematic and dynamic models of autonomous underwater vehicle, virtual velocity commands are constructed via backstepping approach to stabilize the position and attitude errors. To circumvent the “differential explosion” problem inherent in conventional backstepping control caused by repeated differentiations of virtual control variables, first-order low-pass filters are introduced to construct dynamic surface control, yielding smooth derivatives of virtual velocity commands. Secondly, to enhance convergence rate and robustness, a non-singular terminal sliding surface is designed at the dynamic level, and a terminal reaching law is formulated to achieve finite-time convergence of velocity tracking errors. Furthermore, to compensate for external disturbances and unmodeled dynamics, a disturbance observer based on the super-twisting algorithm is developed, enabling finite-time high-precision estimation of lumped disturbances, with the estimation results incorporated into the control law for feedforward compensation. Finally, comparative simulations are conducted under two typical disturbance scenarios. The results demonstrate that the proposed method achieves instantaneous disturbance estimation (reducing convergence time from 3 s to near zero), significantly smoother control inputs, and superior tracking accuracy with RMSE as low as 0.6788 m and MAE as low as 0.1468 m, reducing errors by up to 30.6% compared to baseline methods. Full article

This study introduces an efficient and accurate two-stage explicit computational scheme for solving partial differential equations (PDEs) containing first-order time derivatives. The suggested method is a modification of the classical Runge–Kutta scheme that introduces a new first-stage formulation. This minimizes numerical error with moderate step sizes while preserving the stability region of the classical method. Spatial discretization is performed using a sixth-order compact finite-difference scheme to obtain high-resolution solutions. The analysis of stability and convergence is strictly determined for both scalar and system forms of convection–diffusion-type equations. To illustrate the suitability of the method, a dimensionless mathematical model of the unsteady, incompressible, laminar flow of a Prandtl-type non-Newtonian nanofluid over a Riga plate is considered, accounting for viscous dissipation, thermophoresis, Brownian motion, and a magnetic field. Here, the Prandtl ternary nanofluid is defined as a non-Newtonian nanofluid that follows the Prandtl rheological model, and it exhibits three critical transport phenomena: heat conduction, viscous dissipation, and nanoparticle diffusion. Representative values of the Prandtl number $P_r=3$ and Reynolds number $R_e=5$ are used to perform the simulation, and other parameters, including but not limited to the Hartmann number $H_a$, Williamson number $W_e$, thermophoresis $N_t$ and Brownian motion $N_b$, are varied to evaluate the flow behavior. Moreover, an artificial neural network (ANN)-developed surrogate model is used to calculate the skin friction coefficient and the local Sherwood number, using five input parameters: the Reynolds number, Prandtl number, Schmidt number, Brownian motion parameter, and thermophoresis parameter. The governing partial differential equations yield high-fidelity numerical data used to train the surrogate model. The data is split into 80% for training, 10% for validation, and 10% for testing. The ANN is tested using regression analysis and error histograms, which demonstrate high accuracy and generalization capacity. Numerical simulation combined with AI-based prediction is a cost-efficient method for real-time estimation of complex non-Newtonian nanofluid systems. Full article

In order to evade interception, advanced aircraft often adopt jump-gliding trajectories to efficiently utilize aerodynamics and achieve complex maneuvers. Precise guidance of UAVs for intercepting such targets is critically challenged due to their high speed and uncertain maneuvers. For terminal guidance scenarios, the extremely short engagement window necessitates strict convergence within the predefined finite time. While PPC offers a promising framework to ensure such convergence with guaranteed transient performance, it suffers from singularity when target uncertainties drive tracking errors beyond performance bounds. To address these challenges, this paper proposes an adaptive prescribed-performance guidance law with predefined-time convergence for UAVs. Built upon the analysis that jump-gliding targets exhibit predominantly longitudinal oscillatory maneuvers, we first establish a velocity model to characterize their motion uncertainties. Using the derived uncertainty bounds and estimated parameters, a predefined-time performance function (PPF) is then developed and robustly modified to eliminate the singularity risk. By integrating this modified PPC with an adaptive law, the proposed framework achieves robust predefined-time convergence of the line-of-sight angle while simultaneously compensating for unknown target maneuvers. Theoretical analysis verifies the framework’s stability, and simulation results demonstrate its effectiveness in intercepting highly maneuverable targets. Full article

This paper investigates the finite-time passivity and state estimation problem for quaternion-valued neural networks with two additive delays. By employing the Lyapunov method, several criteria are derived to ensure the finite-time passivity of the discussed system and the asymptotic stability of the error system. A novel controller is proposed to achieve finite-time passivity of the discussed system and a proportional–integral observer (PIO) strategy is adopted to tackle the state estimation problem. The direct approach is used to handle the quaternion-valued neural networks without decomposing them into real-valued or complex-valued systems, which substantially simplifies the analysis procedure. Moreover, various quaternion-valued inequalities are utilized in the analysis, contributing to reduced conservatism in the derived results. Finally, the theoretical results have been effectively demonstrated through two numerical simulation examples. Full article

This study presents a systematic comparative benchmark between two distinct paradigms for solving nonlinear partial differential equations (PDEs): the data-driven Physics-Informed Neural Networks (PINNs) and the analytical Homotopy Analysis Method (HAM). We apply both methods to a unified family of canonical PDEs, the Burgers, Huxley, Fisher, Burgers–Huxley, and Burgers–Fisher equations, under identical problem setups, domain discretization, and validation metrics. PINNs incorporate physical laws directly into neural network training by minimizing a loss function that enforces PDE residuals, yielding physically consistent solutions even for strongly nonlinear problems. HAM provides approximate analytical solutions using a unified framework, and the same initial guess, auxiliary linear operator, and auxiliary function across all equations despite their distinct nonlinearities. The controlled, consistent application of both methods enables a fair, reproducible comparison across this equation family. The results provide a quantitative performance map under identical conditions, delineating when PINNs (high accuracy, long-term stability, and generalization capability) are preferable, versus when HAM (computational speed, short-term analytic approximation, and lower memory footprint) offers advantages. While the finite radius of convergence of the truncated HAM series is theoretically expected, our controlled comparison quantifies for the first time how this degradation varies across equation types, revealing that the choice between methods depends on specific problem requirements including error tolerance, available computational resources, and temporal horizon. The novelty lies not in solving each equation individually, but in deriving a performance taxonomy that systematically connects equation features (shocks, stiffness, and reaction–diffusion coupling) to optimal solver choice—providing previously unavailable, evidence-based guidance for the scientific computing community. This study establishes the first rigorous, controlled comparative benchmark between analytic and data-driven PDE solvers across a spectrum of nonlinearities, providing a reproducible baseline for future hybrid scientific machine learning solvers. Full article

Crumb rubber concrete (CRC), as a heterogeneous multiphase composite material composed of coarse aggregate, rubber particles, cement mortar, pores, and other constituents, is frequently regarded as a homogeneous material in engineering applications. This study employs numerical homogenization to compute equivalent mechanical parameters for CRC. By establishing a two-dimensional parametric random aggregate model combined with Monte Carlo simulations and finite element computations, it systematically analyzes the influence of rubber content (0%, 5%, 10%, 15%) and specimen size (50–150 mm) on CRC’s macroscopic equivalent elastic modulus. The research reveals that stable homogenization results, usable as macroscopic equivalent material parameters, are attained when the Representative Volume Element (RVE) size of the CRC model is ≥5 times the maximum aggregate particle size (dₘₐₓ). The equivalent modulus E decreases rapidly initially with increasing size, followed by a decelerated decline toward stabilization. A predictive model based on the fitted formula ln Eᵣ = kᵣ ln L + bᵣ (where Eᵣ denotes reduced modulus) enables elastic modulus prediction for large-scale components up to 600 mm. This study elucidates the macro-mesoscopic linkage mechanism governing CRC’s equivalent elastic parameters, providing a theoretical foundation for engineering structural design. Full article

Interval-censored survival data arise frequently in biomedical and epidemiological studies where event times are observed only within observation intervals. Classical non-parametric estimators, such as the Kaplan–Meier (KM) estimator under imputation and the Turnbull estimator, often suffer from instability, irregular fluctuations, and overfitting when sample sizes are small or when the prevalence rate is low. Recent methodological developments, which include smoothed and penalized approaches, have been proposed to improve stability and reduce estimation error in such settings. This study evaluates and benchmarks the finite-sample performance of a nonparametric penalized likelihood KM estimator under interval-censored data. The method is compared with the classical KM estimator using four imputation strategies, that is, midpoint, regression, uniform, and multiple imputation. From a symmetry perspective, midpoint and uniform imputation preserve interval symmetry through deterministic and probabilistic mechanisms, respectively, whereas regression and multiple imputation intentionally introduce structural asymmetry to reflect data-driven risk heterogeneity and distributional uncertainty. To assess and benchmark the performance of the penalized KM estimator, an extensive Monte Carlo (MC) simulation study was conducted across varying sample sizes and prevalence rates using error-based metrics. The MC simulation results revealed that the nonparametric penalized KM estimator consistently outperforms the classical KM estimator in small samples across all prevalence rates. The gains are more pronounced under low prevalence rates where the penalized KM estimator is superior for small to relatively moderate samples of $n\approx$ 40–100. Among the imputation techniques, regression and multiple imputation generally exhibited superior performance. Real data application further confirms these findings, demonstrating that the nonparametric penalized KM estimator yields more stable and accurate survival curves than the classical KM estimator in small samples. Full article

Wheeled bipedal robots are promising for industrial mobility because they combine tight turning, agile balancing, and efficient rolling. Their inherently unstable and underactuated dynamics make reliable reference tracking challenging, particularly in the presence of sustained external disturbances and modeling errors. This paper presents a systematic modeling and control study using a three-degrees-of-freedom sagittal plane representation derived from the original six-degrees-of-freedom dynamics. Two linear tracking controllers are designed and compared: a full state feedback tracking controller and a linear quadratic servo controller with integral action. Practical performance is validated through real-time hardware in the loop simulation, where the controller runs on embedded hardware and the plant is executed on a real-time target including discrete time-sampling effects and analog input output communication noise associated with signal transmission. The results show that both controllers achieve stabilization, while the comparative HILS results reveal a trade-off rather than a uniformly superior controller. The full state feedback controller often yields lower finite-horizon position tracking errors, whereas the linear quadratic servo controller provides tighter body-pitch regulation and the more reliable removal of steady-state offset under sustained constant disturbances. These results demonstrate the feasibility of optimal servo control on cost-effective embedded platforms and indicate that controller selection should depend on the desired balance, considering tracking accuracy, disturbance rejection, convergence behavior, and actuator usage. Full article