Search Results (509)

By taking the $L_{0/1}$-soft-margin loss and the working set selection strategy into account, we establish an enhanced projection twin SVM optimization model for general classification problems. The optimality properties of the presented model are analyzed via proximal stationary point theory. A working-set ADMM-type algorithm with quadratic correction terms is further developed for efficient model solution. Numerical experiments on synthetic samples, UCI benchmarks, and NDC datasets with different sample sizes illustrate the promising performance of the proposed method in comparison with existing alternatives. Full article

In this paper, we focus on one-dimensional vertical infiltration, assuming constant diffusivity and a quadratic relationship between hydraulic conductivity and water content. Under these assumptions, Richards’ equation reduces to Burgers’ equation, which we then linearize via the Hopf–Cole transformation. This turns the initial boundary value problem into a diffusion equation on a finite interval with mixed boundary conditions. To solve it, we use the Unified Transform Method (also known as the Fokas method). This approach gives an explicit integral representation of the solution, and when evaluated numerically, the results match classical Fourier series solutions exactly, but with better convergence and stability. Two examples from hydrological applications are examined. Full article

This work presents the kinematic analysis of a redundant planar parallel manipulator within the framework of screw theory. The main contribution of this work is the introduction and kinematic modeling of a novel redundant planar parallel manipulator topology composed exclusively of revolute joints. The proposed architecture is motivated by the search for structurally simple mechanisms with favorable analytical properties for screw-theoretic formulation and potential applications in robotic systems requiring compact and efficient planar motion. For completeness, the displacement analysis is included. Thanks to the simple topology of the otherwise complex mechanism, the inverse–forward displacement problem is resolved through straightforward quadratic equations. The velocity input–output relationship is derived without reliance on passive joint rate velocities, and the acceleration input–output equation is obtained independently of passive joint rate accelerations. These simplifications are achieved by exploiting reciprocal line properties. Numerical examples are provided to illustrate the robustness and effectiveness of the proposed kinematic analysis method across the main topics addressed in this contribution. Full article

Accurate representation of the pressure drop–flow rate (Δp–q) relationship of nozzle-type inflow control devices (ICDs) is critical for reliable reservoir–wellbore coupled simulation. Conventional ICD models in reservoir simulators rely primarily on empirical correlations or tabulated data, but commonly used formulations cannot consistently capture the linear behavior in the low-flow regime or the transition between flow regimes, which may reduce physical fidelity and numerical robustness. To overcome this limitation, this study proposes a unified characteristic-curve representation that integrates linear, transitional, and quadratic flow regimes into a single continuous and differentiable function through a physically constrained least-squares formulation, and further develops a physics-informed neural network (PINN) to learn the ICD pressure–flow relationship while enforcing physical consistency. The trained PINN model is embedded into a multi-segment well model within a reservoir–wellbore coupled simulation framework and evaluated using a mechanistic reservoir model containing permeability streaks with varying permeabilities. The results show that the proposed method improves numerical convergence and accurately reproduces ICD pressure–flow behavior across multiple flow regimes, providing a more physically consistent and robust representation of ICD performance for inflow control analysis and reservoir simulation. Full article

Liquid storage tanks are widely used in sectors such as water treatment, oil and gas, food processing, and chemical manufacturing. Knowing the exact amount of liquid in a tank is essential for ensuring safety, preventing spills, and optimizing process control; therefore, the liquid level in a tank must be maintained at a precise reference point. This is where liquid level control for tanks becomes crucial and constitutes a fundamental problem in the industrial sector due to nonlinearities, multivariable coupling, and stochastic disturbances. Given the drawbacks of available control methods, such as classical Model Predictive Control (MPC), which are highly dependent on model accuracy and struggle to reject complex stochastic noise, predicting random disturbances represents a major technological challenge. A new approach is proposed to specifically address the problem and challenge of the four-tank system, where water levels in two lower tanks must be controlled by two pumps, often with varying delays and significant parameter disturbances. To establish a relationship between expected performance and MPC parameters, this approach uses a novel hybrid nonlinear MPC, Extended State Observer, and Physics-Informed Neural State Estimation (NMPC-ESO-PINSE) architecture. A Physics-Informed Neural State Estimation (PINSE) layer, chosen for its learning capacity, is designed to filter sensor noise by applying Bernoulli’s physical laws, while an Extended State Observer (ESO) is integrated to capture and compensate for unmodeled uncertainties in the process. Finally, a proposed hybrid (NMPC-ESO-PINSE) strategy leverages these clean, physically consistent state estimations to solve a non-convex optimization problem via Sequential Quadratic Programming (SQP), computing optimal pump voltages. Extensive numerical simulations demonstrate the superior resilience of this decoupled framework against parametric drifts and continuous noise sequences, yielding a $+27.36\%$ reduction in global Root Mean Square Error (RMSE) compared to standard NMPC, accelerating the closed-loop settling time to $15.2 \mathrm{s}$, and restricting transient overshoot to just $0.18\%$. Full article

This study investigates the thermal optimization of unsteady nanofluid natural convection within a quarter-circular domain with an inner wavy boundary under inclined periodic magnetic forcing. A combined finite-element method (FEM) and central composite design-based response surface methodology (RSM) is employed for optimizing both the geometric configuration and the parametric setting. For the geometric optimization, we find that the wavy-wall amplitude is the key parameter to determine the optimal configuration, followed by the inner radius and undulation number. The parametric analysis shows that strong magnetic effects suppress convection, while increasing the Rayleigh number and the nanoparticle volume fraction significantly enhances heat transport. Additionally, rising magnetic field wavelength and/or inclination angle result in a reduction in heat transmission under strong magnetic intensity. A statistical quadratic correlation equation with the help of the RSM method between Rayleigh number, Hartmann number, and nanoparticle volume fraction, and the mean Nusselt number is formulated, which gives a good match with numerical FEM analysis results in which about 99% of the variation in the response variable is predicted (R² = 0.9975). The results obtained in this study offer valuable information along with computational efficiency in predicting the behavior of such advanced thermal systems. Full article

In this manuscript, the stability characteristics of nonlinear nonautonomous dynamical systems with the newly defined Caputo cotangent fractional derivative (CCFD) are discussed. Conditions that guarantee stability and asymptotic stability of the system are developed through comparison methods for CCFD systems using Lyapunov functions. A quadratic inequality for the CCFD and a sign lemma are established as key analytical tools. The additional parameter $r_2$ continuously recovers the classical Caputo derivative at $r_2=1$ and introduces an exponential attenuation mechanism when $0<r_2<1$. Analytical examples and a reproducible numerical trajectory study illustrate the influence of $r_2$ on the decay of solutions. The results extend classical Lyapunov stability theory to a broader class of nonlinear fractional systems and suggest modeling opportunities in systems where power-law memory and exponential attenuation coexist. Full article

In the design of structural wind resistance, it is necessary to consider the combination of load effect extremum caused by each wind component. The existing combination rules for Gaussian wind load effects are not applicable to the combination of non-Gaussian wind load effects. The Hermite polynomial transformation model is employed to transform the non-Gaussian wind effect process based on a potential standard Gaussian process in this paper. The probability distributions of the non-Gaussian wind effect process and the non-Gaussian peak factor are deduced. A simplified TR1 (Turkstra) combination equation for the two-component non-Gaussian wind effect process and a numerical integration expression for the TR2 combination rule are proposed. The improved simplified CQC (complete quadratic combination) equations for two-component non-zero-mean softening and hardening non-Gaussian wind effect processes are derived. The accuracy and validity of these simplified combination equations are verified using the Monte Carlo simulation method. Full article

This paper investigates joint deployment of unmanned aerial vehicle (UAV)-borne linear-array angle-of-arrival (AOA) sensors for localizing a target UAV in three-dimensional space. Since each sensing UAV carries a lightweight one-dimensional (1-D) AOA array, each measurement provides only one angular constraint, and its information contribution depends jointly on the UAV waypoint and array pointing direction. This leads to a coupled coordinate–orientation design problem that differs from conventional full-AOA deployment. We formulate a Cramér–Rao lower bound (CRLB)-based framework under A- and D-optimality criteria, covering both free-flight and constrained hovering regions. By exploiting the structure of the 1-D AOA Fisher information matrix, we show that, for fixed UAV coordinates, the orientation block can be exactly eliminated through a low-dimensional eigenproblem. The resulting reduced coordinate problem is then solved by a geometry-structured sequential quadratic programming (SQP) method, whose curvature model captures the radial and tangential sensitivities induced by line-of-sight geometry. Numerical simulations further validate the effectiveness of the proposed approach. Full article

This paper proves that existing implicit integration schemes for the modified cam-clay (MCC) cannot handle the dependency of critical state stress ratio on Lode angle, because the coaxiality between the deviatoric strain rate tensor and the deviatoric stress tensor, on which these algorithms are built, no longer holds when the Lode angle effect is considered. A more appropriate algorithm is proposed based on closet point return mapping, and a consistent tangent modulus is calculated. After detailed mathematical derivations, the proposed method is examined via four computational examples. The first example includes a series of numerical triaxial tests, for demonstrating the appropriateness of the employed constitutive equations. The second and third examples are convergence tests at the material (integration point) level and finite element (FE) level, respectively. The resulting quadratic converging rate proves that the Jacobian matrix for return mapping and the consistent tangent modulus for finite element implementation are correctly computed. The last example concerns drained penetration of a surface footing. The proposed method is demonstrated to be more efficient and robust in this case than the Abaqus built-in MCC model, which aborted halfway when simulating the same problem. Full article

With the emergence of global traffic problems, the development of safe, efficient, and reliable intelligent driving technologies has become a research hotspot. As a key component of intelligent driving technology, trajectory planning directly affects the safety, comfort, and operational efficiency of vehicles in complex traffic scenarios. Existing research typically relies on high-dimensional iterative numerical optimization or tightly coupled planning and control structures, leading to high computational complexity, insufficient real-time performance, and difficulty in ensuring trajectory smoothness. To address these issues, this paper proposes a decoupled and integrated trajectory planning and control method. Firstly, a method is proposed to construct the lateral trajectory based on a fifth-order polynomial and generate the longitudinal motion based on a quadratic acceleration model. Then, lane-change time is introduced as a single optimization variable to construct a cost function that balances comfort and efficiency, and continuous optimization is performed under longitudinal safety distance constraints. Finally, a horizontal and longitudinal hierarchical structure is constructed through model predictive control to solve the direction and speed adjustment problems and achieve high-precision tracking of the optimal trajectory. To verify the effectiveness of the proposed method, coupled simulation verification of trajectory generation and vehicle dynamic response is performed based on a joint simulation platform of MATLAB/Simulink and Carsim. The simulation results show that the proposed method can generate smooth, efficient, and controllable overtaking trajectories; significantly reduce computational complexity; and meet safety constraints, thus verifying the feasibility of the proposed method in complex lane-changing scenarios. Full article

The geometric characteristics of these fractures have a substantial influence on the mechanical and energy properties of heterogeneous rocks. This study calibrated the experimental results using the finite-discrete element method (FDEM). An orthogonal design was employed to investigate the effects of the homogeneity coefficient, fracture angle, fracture length, and fracture aperture on the mechanical and energy characteristics of fractured sandstone. The main factors influencing the mechanical properties and energy characteristics of rocks were explored through multi-factor correlation analysis. The effects of fracture geometric features and heterogeneity on the mechanical properties and energy characteristics of rocks were analyzed by single-factor analysis. A regression model between peak stress and fracture geometric features was established. The results show the following: The homogeneity coefficient and fracture length have a significant impact on the elastic modulus of fractured sandstone. The fracture angle and fracture length have a significant influence on the peak strain, elastic strain energy and total energy of fractured sandstone. The fracture angle, fracture length and homogeneity coefficient have a significant effect on the peak stress of fractured sandstone. The elastic modulus and peak stress show a logarithmic relationship with the homogeneity coefficient, while the elastic strain energy and total energy have a logarithmic relationship with the crack length. The peak strain and peak stress have a quadratic polynomial relationship with the crack angle, and the elastic strain energy and total energy also have a quadratic polynomial relationship with the crack angle. The elastic modulus, peak strain, and peak stress have a logarithmic relationship with the crack length. The predicted values of peak stress and numerical calculation errors of fractured rocks mainly range from 0.07% to 7.76%, with an average error of 2.58%. Both the peak stress prediction values and the numerical calculation results show a “U”-shaped change trend, first decreasing and then increasing with the increase in the fracture angle. This study investigates the influence of fracture geometric characteristics on the mechanical and energy characteristics of heterogeneous rocks, which is of great significance for the stability control of fractured rock masses and the optimization of underground engineering parameters. The core challenge for future research lies in revealing the intrinsic connection among fracture geometric features, rock mass heterogeneity, and multi-field coupling effects to meet the complex engineering demands of deep mining, thereby serving the safe production and disaster prevention of deep mines. Full article

A new class of modified minimum state error variance (MSEV) state-space based optimal linear quadratic Gaussian (LQG) regulators for closed-loop structures with estimated feedback has been proposed in this article. The negative feedback path is designed as the cascade of the digital LQG regulator and discrete Kalman state observer. The proposed design enables tracking of a time-varying reference input using the predictive control approach. Moreover, the proposed tracking method utilizes a multivariable continuous-time Cauchy state-space model of nonlinear, nonstationary dynamic systems. The resulting control strategy is approximately optimal, as the optimality of the LQG design holds locally for each linearized model around the respective operating point and does not extend to the global nonlinear system. In this sense, starting from the prespecified nominal state trajectory to be tracked, a numerical optimization procedure minimizing the squared tracking error at each step by using the Nelder–Mead direct search simplex algorithm under the required constraints on the input signal has been developed. The LQG regulator and Kalman state observer are designed by utilizing the linear discrete-time state variable models that properly approximate the nonlinear system dynamics across the nominal state trajectory. The performance of the proposed design is validated by simulating a six-degree-of-freedom nonlinear aircraft model across typical flight regimes. 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

This paper presents a surrogate-based uncertainty quantification (UQ) framework for coupled structural–acoustic systems subject to material and geometric variability. The proposed methodology integrates the Finite Element Method (FEM) with two metamodeling techniques—the Quadratic Response Surface (QRS) and Kriging—and Monte Carlo Simulations (MCS), to efficiently characterize the probabilistic behavior of the acoustic response. Two accuracy metrics (cross-validation error and prediction error) are used to validate the surrogate models. Numerical experiments demonstrate that the Kriging metamodel trained with 30 Latin Hypercube Sampling (LHS) points achieves superior predictive accuracy, with a Relative Maximum Error of 4.125 × 10⁻⁷. Monte Carlo Simulations conducted via the Kriging surrogate reduce the computational cost by more than six orders of magnitude compared to direct FEM-based MCS, while maintaining high accuracy. The proposed framework is validated on a rectangular cavity coupled with two flexible aluminum plates, and provides an efficient and accurate tool for vibro-acoustic UQ in complex engineering systems. Full article