Search Results (133)

In this paper, we present an algorithmic modeling approach based on Disjunctive Programming using Boolean logic “OR” to solve the Optimal Phasor Measurement Unit Placement (OPP). We propose a framework for modeling the optimal PMU placement subject to disjunctive constraints. A convex objective function is minimized subject to a bilinear equality constraint with a piecewise linear structure. The polynomial constraint constitutes a union of linear segments conceptually analyzed in the two-dimensional continuous space, separating the infeasible from the feasible region. This work investigates the trajectory of iterates from infeasible initial points to stationary solutions and analyzes the convergence behavior using Interior-Point Method (IPM) and Sequential Quadratic Programming (SQP). Our algorithmic model addresses the progress of infeasible and feasible iterates, step computation using line-search and trust-region mechanisms. Combined with second-order correction (SOC) and filter methods, these mechanisms enable the algorithm to maintain a unit primal step, even when starting from an infeasible initial point. Network observability constraints are transformed from a Conjunctive Normal Form (CNF) into a Disjunctive Normal Form (DNF) via Balas’s theory. This geometry transformation reformulates the feasible set into a union of convex affine pieces, effectively eliminating constraint curvature issues. This affine reformulation ensures that gradient-based algorithms maintain a smooth optimization trajectory along a convex local manifold. This trajectory enables the algorithm to preserve the full Newton step, maintaining a superlinear convergence rate. Its underlying piecewise linear convexity inherently enables the gradient-based algorithm to avoid the Maratos effect. Numerical results on IEEE power systems validate the optimization problem. Our framework uses the IEEE-14 bus system to address the high-degree non-convexities. Monte Carlo simulations further enhance the argument that piecewise convexity enables IPM and SQP to converge to binary local minima. Depending on multiple-run initialization, these methods reach the same objective function value. These local minima can be characterized as non-strict optimum points that are structurally symmetric but exhibit unequal basins of attraction. Hence, this geometry-driven formulation enables gradient-based methods to reliably identify binary-valued optimal solutions for the OPP. Full article

This paper presents a comparative study of two approaches for solving second-order ordinary differential equations arising from the membrane theory of shells of revolution. The considered equations originate from the rotational symmetry of shell structures, which enables the reduction of the governing partial differential equations to a sequence of ordinary differential equations corresponding to individual circumferential harmonics. The study compares the classical Differential Transform Method (DTM) with Physics-Informed Neural Networks (PINNs). Both initial value and boundary value problems are investigated, including benchmark examples with known analytical solutions and a systematic analysis of the influence of PINN architecture on the solution accuracy. For the PINN approach, the effects of the number of collocation points, hidden layers, and neurons per layer on the approximation error and training time are examined. The results demonstrate that DTM provides an efficient framework for constructing analytical solutions of initial value problems with minimal computational cost. However, its application to boundary value problems requires the introduction of additional auxiliary parameters and the solution of supplementary nonlinear equations, considerably increasing the analytical complexity of the procedure. In contrast, PINNs achieve high accuracy for both initial and boundary value problems while naturally incorporating boundary conditions through the loss function. The presented results demonstrate how the exploitation of geometric symmetry, combined with modern scientific machine learning techniques, provides an effective computational framework for solving differential equations arising in shell mechanics. Full article

Information-flow waste refers to activities within organizational information flows that consume resources without creating value, yet standardized instruments for systematically measuring this construct remain lacking. This study aims to clarify the construct structure of information-flow waste and develop a corresponding scale. Candidate items were generated through literature analysis, expert interviews, and cognitive interviews. The scale was then purified and validated using two independent manufacturing samples (n = 266 and n = 287) through exploratory factor analysis, confirmatory factor analysis, measurement invariance testing, and nomological validity testing. The results support a second-order structure comprising information acquisition, information transmission, information storage, and information processing, yielding a final 23-item Information-Flow Waste Scale. The scale demonstrates good reliability, convergent validity, and discriminant validity and achieves strict measurement invariance across production and operations, professional and technical, and supervisory and managerial job groups. Information-flow waste is significantly and positively associated with information overload, providing initial support for the scale’s nomological validity. This study provides a standardized measurement instrument for subsequent empirical research on information-flow waste and, in manufacturing contexts, a measurement basis for identifying manifestations of waste across stages of information flow and conducting subsequent problem analysis. Full article

A large collection of real-world classification and regression problems can be addressed using machine learning tools such as, for example, radial basis function networks (RBF networks). However, the techniques used for training RBF networks often exhibit various problems, such as getting trapped in the local minima of the error function, or even encountering numerical issues when solving systems of linear equations in order to estimate the parameters of the RBF network. This paper presents a multi-stage evolutionary technique based on genetic algorithms for the effective training of RBF networks. In the first stage, the value ranges of the RBF network parameters are estimated using the K-Means algorithm. In the second stage, the chromosomes of the genetic algorithm are initialized within the parameter ranges determined in the first stage, followed by the execution of the genetic algorithm. Each chromosome of the genetic algorithm is considered a candidate parameter vector for the machine learning model. The centers and variances of the RBF network are estimated by the genetic algorithm, while the network weights are determined by solving a system of linear equations. This method was applied to a large set of classification and data-fitting problems, yielding excellent results. Full article

Wastewater from textile industries that contain methylene blue poses a serious environmental problem due to its stability and toxicity. In the current study, calf starter feed (CSF), goat feed (GF), and lamb grower feed (LGF) were investigated as potential adsorbents for methylene blue removal from aqueous solutions. For structure and surface analyses of the adsorbents, EDX analysis was performed with FTIR and SEM, respectively. Parameters such as pH, adsorbent dosage, dye concentration, and time were varied, and optimum pH values of 6.0 and 7.0 were obtained for CSF and both GF and LGF, respectively. It was noted that adsorption increased with adsorbent concentration; conversely, it decreased with an increase in initial dye concentration. Among all the isotherms examined, the Langmuir isotherm yielded the best correlation, with R² > 0.98. The maximum adsorption capacity was found to be 12.4, 11.5, and 11.01 mg g⁻¹ for CSF, GF, and LGF, respectively. Kinetic analysis showed that the pseudo-second-order model provided the best fit to the experimental data, suggesting that adsorption may involve surface interaction processes. The findings demonstrate that commercial animal feeds can serve as alternative adsorbents for methylene blue removal and provide the first evidence of their potential application in wastewater treatment. Full article

A novel distributed-order Cattaneo–Christov model is proposed to effectively characterize non-classical heat conduction processes with memory effect and time–space relaxation behaviors originating from distributed-order fractional derivatives. A fractional physics-informed neural networks (fPINN) algorithm is employed to address both the forward and inverse problems of the distributed-order heat conduction model. For the forward problem, we propose an SfPINN algorithm that incorporates a squared loss term and employs an adaptive updating strategy for the loss-term weights. First, the boundary conditions are embedded into the network output such that they are automatically satisfied. In addition, we design a two-stage training strategy to enhance computational efficiency: in the first stage, the squared loss term associated with the initial condition is incorporated into the loss function; in the second stage, the squared residual term of the governing equation is introduced into the loss function. Numerical results show that the proposed algorithm outperforms the standard fPINN method in both solution accuracy and training iteration speed. For the inverse problem, the numerical results demonstrate that as the iteration number increases, the estimated parameter values progressively converge to their true values and finally stabilize. Full article

Accurate estimation of the State of Charge (SOC) of lithium-ion batteries is one of the core functions of a battery management system and is of great significance for ensuring the safe operation of electric vehicles and optimizing energy utilization. However, due to the strong nonlinearity, time-varying characteristics, and interference from complex operating conditions within the battery, high-precision SOC estimation faces severe challenges. To address the problems that a single data-driven method lacks physical constraints and a single model-driven method struggles to characterize complex nonlinearities, this paper proposes a series-connected LSTM-UKF fusion estimation method. This method first utilizes a Long Short-Term Memory network to learn the dynamic characteristics of the battery from historical voltage and current data, capturing the long-term dependencies of SOC changes to achieve an initial prediction. Subsequently, using this predicted value as the observation input, an Unscented Kalman Filter based on a second-order RC equivalent circuit model is introduced for optimal state correction, effectively suppressing model uncertainty and measurement noise. Simulation validation under various dynamic conditions, such as constant current discharge and FUDS, shows that compared to single LSTM or UKF algorithms, the proposed fusion method has significant advantages in estimation accuracy, convergence speed, and robustness. Its root mean square error is reduced to 0.0031, and it maintains stable estimation performance under different operating conditions. This study provides an effective data-model fusion solution for high-precision SOC estimation of lithium-ion batteries under complex operating conditions. Full article

Mathematical modeling of heat and mass transfer processes in porous media using fractional derivative equations is of great practical importance. Within the framework of such models, obtaining analytical solutions to the corresponding initial–boundary value problems is generally difficult. In this work, we numerically investigate quasilinear parabolic problems involving Caputo time-fractional derivatives. First, the well-posedness and existence of weak solutions are discussed. Then, we construct and implement a finite-difference scheme that is fourth-order accurate in space and second-order accurate in time. Convergence in the maximum norm is proven. Numerical experiments confirm the accuracy and efficiency of the proposed approach. Full article

This article proposes single-layer neural network algorithms for solving second-order ordinary differential equations, based on the principles of functional connection. According to this principle, the hidden layer of the neural network is replaced by a functional expansion unit to improve input patterns using orthogonal Chebyshev, Legendre, and Laguerre polynomials. The polynomial neural network algorithms were implemented in the Python programming language using the PyCharm environment. The performance of the polynomial neural network algorithms was tested by solving initial-boundary value problems for the nonlinear Lane–Emden equation. The solution results are compared with the exact solution of the problems under consideration, as well as with the solution obtained using a multilayer perceptron. It is shown that polynomial neural networks can perform more efficiently than multilayer neural networks. Furthermore, a neural network based on Laguerre polynomials can, in some cases, perform more accurately and faster than neural networks based on Legendre and Chebyshev polynomials. The issues of overtraining of polynomial neural networks and scenarios for overcoming it are also considered. Full article

In this paper, we take the longitudinal two-stage and two-yard EMU (Electric Multiple Unit) depot as an example and discusses the optimization challenges of the first-level maintenance shunting operation plan under the background of limited maintenance capacity. A multi-objective programming is constructed, which adopts the lexicographic ordering method and aims to minimize the occupancy time of key line areas and the number of train storage times. In order to enhance the flexibility and solution efficiency of the shunting operation plan, we design an efficient three-stage strategy algorithm. Specifically, in the first stage, the genetic and mutation rules are integrated, and the fast iterative advantage of the genetic algorithm is utilized to solve the time decision variables in the optimization problem. In the second stage, the allocation of track occupancy variables is further solved. The third stage focuses on the optimized allocation of maintenance team variables to ensure the scientific scheduling of maintenance resources. Finally, a validation experiment was conducted using the maintenance tasks of 19 EMU sets as the test scenario. The results indicate that when the number of maintenance teams is set to 4, an optimal balance between maintenance efficiency and operational cost is achieved, the occupancy duration of key line zones reaches 3034 min (the theoretical optimum), the number of maintenance teams is reduced by 33.33% compared to the initial 6 teams, and the number of storage operations is optimized to 27 times. Additionally, the algorithm’s solution time remains under 50 s, demonstrating significantly improved computational efficiency. Comparative experiments with baseline algorithms show that the proposed method reduces the occupancy duration of key line zones by up to 0.49%, decreases the number of storage operations by 14 times, and advances the maximum completion time by 20 min. In summary, the proposed method provides solid theoretical support for the formulation of maintenance plans and shunting schedules in EMU depots. Particularly in complex scenarios with limited maintenance capacity, it offers innovative and robust decision-making foundations, demonstrating significant practical guidance value. Full article

Guided by principles of symmetry to achieve a proper balance among model consistency, accuracy, and complexity, this paper proposes a new approach for identifying the unknown parameters of nonlinear one-degree-of-freedom mechanical systems using nonlinear regression methods. To this end, the steps followed in this study can be summarized as follows. Firstly, given a proper set of input time histories and a virtual model with all parameters known, the dynamic response of the mechanical system of interest, used as output data, is evaluated using a numerical integration scheme, such as the classical explicit fixed-step fourth-order Runge–Kutta method. Secondly, the numerical values of the unknown parameters are estimated using the Levenberg–Marquardt nonlinear regression algorithm based on these inputs and outputs. To demonstrate the effectiveness of the proposed approach through numerical experiments, two benchmark problems are considered, namely a mass-spring-damper system and a simple pendulum-damper system. In both mechanical systems, viscous damping is included at the kinematic joints, whereas dry friction between the bodies and the ground is accounted for and modeled using the Coulomb friction force model. While the source of nonlinearity is the frictional interaction alone in the first benchmark problem, the finite rotation of the pendulum introduces geometric nonlinearity, in addition to the frictional interaction, in the second benchmark problem. To ensure symmetry in explaining model behavior and the interpretability of numerical results, the analysis presented in this paper utilizes five different input functions to validate the proposed method, representing the initial phase of ongoing research aimed at applying this identification procedure to more complex mechanical systems, such as multibody and robotic systems. The numerical results from this research demonstrate that the proposed approach effectively identifies the unknown parameters in both benchmark problems, even in the presence of nonlinear, time-varying external input actions. Full article

This paper presents the development and analysis of novel explicit special two-derivative Runge–Kutta (STDRK) pairs for the numerical integration of ordinary differential equations (ODEs), with a focus on achieving seventh-order accuracy and embedded fifth-order error estimation. The proposed schemes utilize both the first and second derivatives of the solution, leveraging the identity $y^{\prime \prime }=f^{\prime }\left(y\right)f\left(y\right)$, to attain high-order accuracy while minimizing the number of evaluations of the primary function f. A notable feature of the constructed methods is that they require only a single evaluation of f per step, along with five evaluations of $g=f^{\prime }f$, resulting in a significant reduction in computational cost compared to classical Runge–Kutta methods. The necessary order conditions are derived via an algebraic framework based on compositions with parts not exceeding 2. A supporting Mathematica package facilitates the construction of methods of arbitrary order. A new STDRK pair of orders seven and five is derived. Numerical experiments on standard benchmark problems, including the Prothero–Robinson, Kaps, and Kepler systems, highlight the efficiency and competitive performance of the proposed schemes relative to established Runge–Kutta pairs. Full article

In this study, we consider and analyze an inhomogeneous Whittaker-type differential equation of the form ${\displaystyle \frac{d^{2}y\left(x\right)}{d{x}^2}}+{\displaystyle \frac{1}{x}}{\displaystyle \frac{dy\left(x\right)}{dx}}-{\alpha }^2\left(x^2-{\beta }^2\right)y\left(x\right)=g\left(x\right)$, where $\alpha$ and $\beta$ are given parameters. We investigate the analytical structure of its solution through the application of the Whittaker integral representation. The analysis encompasses both initial value problems (IVPs) and boundary value problems (BVPs), wherein appropriate conditions are imposed within a unified analytical framework. Furthermore, a systematic methodology is developed for constructing explicit solutions within the framework of Whittaker function theory. This approach not only elucidates the functional behaviour of the solutions but also provides a foundation for extending the analysis to more general classes of second-order linear differential equations. Full article

A variety of methods that provide approximate piecewise- analytical solutions to initial-value problems governed by scalar, nonlinear, first-order, ordinary differential equations is presented. The methods are based on fixing the independent variable in the right-hand side of these equations and approximating the resulting term by either its first- or second-order Taylor series expansion. It is shown that the second-order Taylor series approximation results in Riccati equations with constant coefficients, whereas the first-order one results in first-order, linear, ordinary differential equations. Both approximations are shown to result in explicit finite difference equations that are unconditionally linearly stable, and their local truncation errors are determined. It is shown that, for three of the nonlinear, first-order, ordinary differential equations studied in this paper that are characterized by growing or decaying solutions, as well as by solutions that first grow and then decrease, a second-order Taylor series expansion of the right-hand side of the differential equation evaluated at each interval’s midpoint results in the most accurate method; however, the accuracy of this method degrades substantially for problems that exhibit either blowup in finite time or quadratic approximations characterized by a negative radicand. It is also shown that methods based on either first- or second-order Taylor series expansion of the right-hand side of the differential equation evaluated at either the left or the right points of each interval have similar accuracy, except for one of the examples that exhibits blowup in finite time. It is also shown that both the linear and the quadratic approximation methods that use the midpoint for the independent variable in each interval exhibits the same trends as and have errors comparable to the second-order trapezoidal technique. Full article

In this article, we present an efficient and highly accurate numerical scheme that achieves exponential convergence for solving nonlinear Riesz distributed-order fractional differential equations (RDFDEs) in one- and two-dimensional initial–boundary value problems. The proposed method is based on a two-stage collocation framework. In the first stage, spatial discretization is performed using the shifted Legendre–Gauss–Lobatto (SL-G-L) collocation method, where the approximate solutions and spatial derivatives are expressed in terms of shifted Legendre polynomial expansions. This reduces the original problem to a system of fractional differential equations (FDEs) for the expansion coefficients. Then, the temporal discretization is achieved in the second stage via Romanovski–Gauss–Radau collocation approach, which converts the system into a system of algebraic equations that can be solved efficiently. The method is applied to one- and two-dimensional nonlinear RDFDEs, and numerical experiments confirm its spectral accuracy, computational efficiency, and reliability. Existing numerical approaches to distributed-order fractional models often suffer from poor accuracy, instability in nonlinear settings, and high computational costs. By combining the efficiency of Legendre polynomials for bounded spatial domains with the stability of Romanovski polynomials for temporal discretization, the proposed two-stage framework effectively overcomes these limitations and achieves superior accuracy and stability. Full article