Search Results (83)

In the current study, we used Chebyshev’s Pseudospectral Method (CPM), a novel numerical technique, to solve nonlinear third-order Emden–Fowler delay differential (EF-DD) equations numerically. Fractional derivatives are defined by the Caputo operator. These kinds of equations are transformed to the linear or nonlinear algebraic equations by the proposed approach. The numerical outcomes demonstrate the precision and efficiency of the suggested approach. The error analysis shows that the current method is more accurate than any other numerical method currently available. The computational analysis fully confirms the compatibility of the suggested strategy, as demonstrated by a few numerical examples. We present the outcome of the offered method in tables form, which confirms the appropriateness at each point. Additionally, the outcomes of the offered method at various non-integer orders are investigated, demonstrating that the result approaches closer to the accurate solution as a value approaches from non-integer order to an integer order. Additionally, the current study proves some helpful theorems about the convergence and error analysis related to the aforementioned technique. A suggested algorithm can effectively be used to solve other physical issues. Full article

In this paper, a new class of fifth-order Chebyshev–Halley-type methods with a single parameter is proposed by using the polynomial interpolation method. The convergence order of the new method is proved. The dynamic behavior of the new method on quadratic polynomials $P\left(x\right)=(x-a)(x-b)$ is analyzed, the strange fixed points and the critical points of the operator are obtained, the corresponding parameter planes and dynamic planes are drawn, the stability and convergence of the iterative method are visualized, and some parameter values with good properties are selected. The fractal results of the new method corresponding to different parameters about polynomial $G\left(x\right)$ are plotted. Numerical results show that the new method has less computing and higher computational accuracy than the existing Chebyshev–Halley-type methods. The fractal results show the new method has good stability and convergence. The numerical results of different iteration methods are compared and agree with the results of dynamic analysis. Full article

This paper compares different point measurement strategies for spherical surfaces using a coordinate measuring machine. A total of 77 points were measured using the Sphere, Touch Point, Space Point, and Mid Point strategies, and approximately 2200 points were measured by scanning the surface with eight circles. Three probe configurations with different probe tip diameters were used for the measurements. The acquired data were processed with Calypso software, and the results for sphere diameters and centers were verified using the LSQ algorithms with the Kåsa and Newton methods, as well as Chebyshev fitting. Spherical shell half-widths and Root Mean Square Errors were used to evaluate accuracy. The results show that the sensor with $r_{\mathrm{probe}}=2.500557$ mm provides the smallest deviation from the certified value for both diameter and center position. The deviations remain smaller than the maximum permissible error of length measurement ${\mathrm{E}}_{0,\mathrm{MPE}}$. The scanning strategy does not consistently provide better results for either the diameter or the sphere center compared to point measurement. The results of the LSQ method in Calypso correspond to those obtained by the Kåsa/Newton methods (with results identical at the $\mathsf{\mu }$m scales), while the Calypso Minimum Feature evaluation method corresponds to the Chebyshev fit. Full article

The high cost of wind turbine maintenance has intensified the need for reliable fault detection and condition monitoring methods. While Supervisory Control and Data Acquisition (SCADA) systems provide valuable operational data, the raw signals often contain noise, outliers, and missing or redundant entries, which can compromise analysis accuracy. This study presents a novel cluster-based outlier removal approach for SCADA data preprocessing, featuring a unique flexibility to include or exclude negative power values—a factor rarely investigated but potentially critical for fault detection performance. The method applies the K-Means++ unsupervised clustering algorithm to group data points along the wind speed–power curve. The number of clusters is determined heuristically using the elbow method, while outliers are identified through Mahalanobis distance with thresholds derived from Chebyshev’s inequality theorem. The approach was validated using SCADA data from a wind farm in Portugal and further assessed with a CUSUM test-based structural change detection method to study how preprocessing choices—outlier thresholds (5% vs. 1%) and inclusion/exclusion of negative power values—affect early fault identification. Results demonstrate reliable fault detection up to 14 days before failure, retaining over 99% of the original dataset. This work provides key insights into preprocessing impacts on model reliability and offers an open-source Python implementation for reproducibility. Full article

The aim of this study was to examine the effect of a change of the beam support point within the same support cross section and that of a change in the location of load application points on critical load values. In the literature on the stability of structures, the problem of a change of a rod system’s support point (within the same cross section) is neglected. Solely the effect of a change in load application points on the critical load value is considered. In this study, displacement differential equations describing the general stability loss problem for any nonprismatic thin-walled beam were derived. To solve the equations an approximation method (described in earlier papers by the authors), using the Chebyshev series of the first kind to approximate the sought functions, was employed. In the provided numerical examples the buckling problem was solved for nonprismatic I-beams with a bisymmetric cross section and a monosymmetric cross section. The determined critical load values were compared with the results obtained using the finite element method and the commercial Sofistik software. The results obtained in this study show the significant effect of beam support point location (within the same cross section), as well as the effect of load application point location, on critical load values. Full article

In this paper, a full-domain stochastic response analysis is performed based on the meshless method to reveal the time–frequency dynamic characteristics, including the power spectral density (PSD) responses in the frequency domain and the evolving PSD distribution in the time domain for a sandwich trapezoidal plate–shell coupled system. The general governing equations are derived based on the first-order shear deformation theory (FSDT), linear piston theory and Hamilton’s principle, and the stochastic excitation is integrated into the meshless framework based on the pseudo-excitation method (PEM). By constructing the meshless shape function covering the entire structural domain from Chebyshev polynomials and discretizing the continuous domain into a series of nodes within a square definition domain, the points are assembled according to the sequence number and the equilibrium relationship on the coupling edge to obtain the overall vibration equations. The validity is demonstrated by matching the mode shapes, PSD responses, time history displacement and critical flutter boundaries with FEM simulation and reported data. Finally, the time–frequency characteristics of each substructure under global and single stochastic excitation, and the effect of aerodynamic pressure on full-domain stochastic vibration, are revealed. Full article

The A* algorithm is broadly identified for its application in diverse fields, such as agriculture, robotics and GPS technology, due to its effectiveness in route planning. Despite its broad utility, the algorithm faces inherent limitations regarding operational efficiency and the length of the paths it generates. Addressing these constraints, this paper proposes an enhancement to the traditional A* algorithm that significantly improves its performance. Our innovative approach integrates Euclidean and Chebyshev distances into a single heuristic function, thereby enhancing pathfinding accuracy and flexibility. This combined heuristic leverages the strengths of both distance measures: the Euclidean distance provides an accurate straight-line measure between points, while the Chebyshev distance effectively handles scenarios allowing diagonal movement. Furthermore, we incorporate Bezier curves into the algorithm to smooth the generated paths. This addition is particularly advantageous in agricultural environments, where machinery must navigate complex terrains without causing damage to crops. The smooth paths produced by Bezier curves ensure more efficient and safer navigation in such settings. Comprehensive experiments conducted in various agricultural scenarios demonstrate the superior performance of the enhanced algorithm. These results reveal that the improved algorithm not only reduces the computation time needed for route planning but also generates shorter and smoother paths compared to the standard A* algorithm. The proposed approach significantly enhances the operational efficiency and route optimization capabilities of the A* algorithm, making it more suitable for complex and dynamic applications in agriculture. This advancement also holds promise for improving navigation systems in various other domains. Full article

The cislunar space navigation satellite system is essential infrastructure for lunar exploration in the next phase. It relies on high-precision orbit determination to provide the reference of time and space. This paper focuses on constructing a navigation constellation using special orbital locations such as Earth–Moon libration points and distant retrograde orbits (DRO), and it discusses the simplification of planetary perturbation models for their autonomous orbit determination on board. The gravitational perturbations exerted by major solar system bodies on spacecraft are first analyzed. The minimum perturbation required to maintain a precision of 10 m during a 30-day orbit extrapolation is calculated, followed by a simulation analysis. The results indicate that considering only gravitational perturbations from the Moon, Sun, Venus, Saturn, and Jupiter is sufficient to maintain orbital prediction accuracy within 10 m over 30 days. Based on these findings, a method for simplifying the ephemeris is proposed, which employs Hermite interpolation for the positions of the Sun and Moon at fixed time intervals, replacing the traditional Chebyshev polynomial fitting used in the JPL DE ephemeris. Several simplified schemes with varying time intervals and orders are designed. The simulation results of the inter-satellite links show that, with a 6-day orbit arc length, a 1-day lunar interpolation interval, and a 5-day solar interpolation interval, the accuracy loss for cislunar space navigation satellites remains within the meter level, while memory usage is reduced by approximately 60%. Full article

Background: Traditional neonatal assessments rely on anthropometric measures such as weight, body size, and head circumference. However, recent studies suggest that objective movement quantification may serve as a complementary clinical indicator of development in preterm infants. Methods: This study evaluates non-invasive computer vision-based quantification of neonatal movement using contactless pose tracking based on computer vision. We analyzed approximately 800,000 postural data points from ten preterm infants to identify reliable algorithms, optimal recording duration, and whether whole-body or regional tracking is sufficient. Results: Our findings show that 30 s video segments are adequate for consistent motion quantification. Optical flow methods produced inconsistent results, while distance-based algorithms—particularly Chebyshev and Minkowski—offered greater stability, with coefficients of variation of 5.46% and 6.40% in whole-body analysis. Additionally, Minkowski and Mahalanobis metrics applied to the lower body yielded results similar to full-body tracking, with minimal differences of 0.89% and 1%. Conclusions: The results demonstrate that neonatal movement can be quantified objectively and without physical contact using computer vision techniques and reliable computational methods. This approach may serve as a complementary clinical indicator of neonatal progression, alongside conventional measures such as weight and size, with applications in continuous monitoring and early clinical decision-making for preterm infants. Full article

Diffusiophoresis of a weakly charged dielectric droplet in a cylindrical pore is investigated theoretically in this study. The governing fundamental electrokinetic equations are solved with a patched pseudo-spectral method based on Chebyshev polynomials, coupled with a geometric mapping scheme to take care of the irregular solution domain. The impact of the boundary confinement effect upon the droplet motion is explored in detail, which is most profound in narrow channels. We found, among other things, that the droplet moving direction may reverse with varying channel widths. Enhanced motion-inducing double-layer polarization due to the presence of a nearby channel wall is found to be responsible for it. In particular, an interesting and seemingly peculiar phenomenon referred to as the “solidification phenomenon” is observed here at some specific critical droplet sizes or electrolyte strengths in narrow channels, under which all the droplets move at identical speeds regardless of their viscosities. They move like a rigid particle without the surface spinning motions and the induced interior recirculating vortex flows. As the corresponding shear rate is zero at this point, the droplet is resilient to undesirable exterior shear stresses tending to damage the droplet in motion. This provides a helpful guideline in the fabrication of liposomes in drug delivery in terms of the optimal liposome size, as well as in the microfluidic and nanofluidic manipulations of cells, among other potential practical applications. The effects of other parameters of electrokinetic interest are also examined. Full article

This paper concerns accurate spectral collocation solutions, more precisely Chebyshev collocation (ChC), to some third-order nonlinear and singular boundary value problems on unbounded domains. The problems model some draining or coating fluid flows. We use exclusively ChC, in the form of Chebfun, avoid any obsolete shooting-type method, and provide reliable information about the convergence and accuracy of the method, including the order of Newton’s method involved in solving the nonlinear algebraic systems. As a complete novelty, we combine a graphical representation of the convergence of the Newton method with a numerical estimate of its order of convergence for a more realistic value. We treat five challenging examples, some of which have only been solved by approximate methods. The found numerical results are judged in the context of existing ones; at least from a qualitative point of view, they look reasonable. Full article

The segmentation of jujube tree branches and the estimation of primary branch inclination angles (IAs) are crucial for achieving intelligent pruning. This study presents a primary branch IA estimation algorithm for jujube trees based on an improved PointNet++ network. Firstly, terrestrial laser scanners (TLSs) are used to acquire jujube tree point clouds, followed by preprocessing to construct a point cloud dataset containing open center shape (OCS) and main trunk shape (MTS) jujube trees. Subsequently, the Chebyshev graph convolution module (CGCM) is integrated into PointNet++ to enhance its feature extraction capability, and the DBSCAN algorithm is optimized to perform instance segmentation of primary branch point clouds. Finally, the generalized rotational symmetry axis (ROSA) algorithm is used to extract the primary branch skeleton, from which the IAs are estimated using weighted principal component analysis (PCA) with dynamic window adjustment. The experimental results show that compared to PointNet++, the improved network achieved increases of 1.3, 1.47, and 3.33% in accuracy (Acc), class average accuracy (CAA), and mean intersection over union (mIoU), respectively. The correlation coefficients between the primary branch IAs and their estimated values for OCS and MTS jujube trees were 0.958 and 0.935, with root mean square errors of 2.38° and 4.94°, respectively. In summary, the proposed method achieves accurate jujube tree primary branch segmentation and IA measurement, providing a foundation for intelligent pruning. Full article

This paper introduces a novel Shifted Gegenbauer Pseudospectral (SGPS) method for approximating Caputo fractional derivatives (FDs) of an arbitrary positive order. The method employs a strategic variable transformation to express the Caputo FD as a scaled integral of the mth-derivative of the Lagrange interpolating polynomial, thereby mitigating singularities and improving numerical stability. Key innovations include the use of shifted Gegenbauer (SG) polynomials to link mth-derivatives with lower-degree polynomials for precise integration via SG quadratures. The developed fractional SG integration matrix (FSGIM) enables efficient, pre-computable Caputo FD computations through matrix–vector multiplications. Unlike Chebyshev or wavelet-based approaches, the SGPS method offers tunable clustering and employs SG quadratures in barycentric forms for optimal accuracy. It also demonstrates exponential convergence, achieving superior accuracy in solving Caputo fractional two-point boundary value problems (TPBVPs) of the Bagley–Torvik type. The method unifies interpolation and integration within a single SG polynomial framework and is extensible to multidimensional fractional problems. Full article

Trajectory planning and tracking control strategies have a significant impact on the fast and stable operation of high-precision position servo permanent magnet synchronous motors (PMSMs). Therefore, this paper proposes an active disturbance rejection control (ADRC) strategy for high-precision position servo PMSMs based on jerk- and time-optimal trajectory planning. Firstly, in order to meet the requirement of continuous jerk in the positioning process of precision loads, the seventh-degree Chebyshev polynomial is adopted to establish the point-to-point trajectory planning function. Based on the dynamic boundary conditions under the short-term overload of PMSMs, and with the positioning time as the optimization objective, the optimal coefficient of the polynomial is solved through the fast particle swarm optimization (FPSO) algorithm to obtain the trajectory planning function that takes into account both jerk and time performance. Then, the trajectory plan is used as the position loop reference signal to construct a non-cascade second-order ADRC strategy, leading to a position servo PMSM control strategy that combines a second-order disturbance observer and feedback control law. Finally, the experimental platform is set up to verify the proposed method. The results show that, compared with the traditional control methods, the steady-state positioning time of the control strategy proposed under typical working conditions is reduced by 12.5%, and the jerk continuity during the positioning process has also been significantly improved. Full article

The efficiency and smoothness of path planning algorithms are critical factors influencing their practical applications. A traditional A* algorithm suffers from limitations in search efficiency, path smoothness, and obstacle avoidance. To address these challenges, this paper introduces an improved A* algorithm that integrates the Salp Swarm Algorithm (SSA) for heuristic function optimization and proposes a refined B-spline interpolation method for path smoothing. The first major improvement involves enhancing the A* algorithm by optimizing its heuristic function through the SSA. The heuristic function combines Chebyshev distance, Euclidean distance, and obstacle density, with the SSA adjusting the weight parameters to maximize efficiency. The simulation experimental results demonstrate that this modification reduces the number of searched nodes by more than 78.2% and decreases planning time by over 48.1% compared to traditional A* algorithms. The second key contribution is an improved B-spline interpolation method incorporating a two-stage optimization strategy for smoother and safer paths. A corner avoidance strategy first adjusts control points near sharp turns to prevent collisions, followed by a path obstacle avoidance strategy that fine-tunes control point positions to ensure safe distances from obstacles. The simulation experimental results show that the optimized path increases the minimum obstacle distance by 0.2–0.5 units, improves the average distance by over 43.0%, and reduces path curvature by approximately 61.8%. Comparative evaluations across diverse environments confirm the superiority of the proposed method in computational efficiency, path smoothness, and safety. This study presents an effective and robust solution for path planning in complex scenarios. Full article