Search Results (123)

Millimeter-wave (MMW) fuze signals experience significant degradation in rainy environments due to combined raindrop-induced attenuation and scattering effects, substantially reducing echo signal-to-noise ratio (SNR) and critically impacting ranging accuracy. To address these limitations while satisfying real-time processing requirements, this study proposes (1) a novel segmented low-order bistable stochastic resonance (SLOBSR) system based on piecewise polynomial potential functions and (2) a corresponding fixed-distance target detection algorithm incorporating signal pre-processing, particle swarm optimization (PSO)-based parameter optimization, and kurtosis threshold detection. Experimental results demonstrate the system’s effectiveness in achieving a 9.94 dB SNR enhancement for MMW fuze echoes under rainy conditions, enabling reliable target detection at SNRs as low as −15 dB. Comparative analysis confirms the SLOBSR method’s superior performance over conventional approaches in terms of both SNR enhancement and computational efficiency. The proposed method significantly enhances the anti-rainfall interference capability of the MMW fuze. Full article

Half-cell potential (HCP) is widely acknowledged as a nondestructive method for assessing the durability of concrete, although the variability in environmental and material conditions compromises its accuracy. The reliability of traditional prediction models, which are often derived from limited data, is questionable under various conditions. This study employed a Bayesian-enhanced probabilistic model to predict corrosion reinforcement using HCP, addressing both known and unknown uncertainties. Constructed as a piecewise function, the model integrates insights from the literature with the results of an accelerated corrosion experiment conducted by the research team, thereby validating the effectiveness of the probabilistic approach. This study also examines the influence of prior knowledge on the accuracy of predictions. The findings revealed a biphasic relationship between HCP and the corroded mass reduction ratio. HCP decreased exponentially with a corroded mass reduction ratio below 15%, whereas beyond this threshold, the decline became more pronounced, modeled by a combination of exponential and cubic polynomial functions. These results underscore the critical role of employing a piecewise function to accurately define the relationship between HCP and corrosion in reinforced concrete, thereby providing a solid foundation for future durability assessments. Full article

Compared with planar layering, the morphology of spatial GMA deposition beads formed by curved layering is influenced by gravity, resulting in asymmetric and complex cross-sections. To quantitatively describe the bead orientation and cross-sectional shape, this study introduces the path inclination angle and path direction angle, along with five characteristic parameters—height, width, eccentricity, upper plumpness, and lower plumpness—using piecewise polynomial fitting for profile modeling. A full-factorial experiment was conducted to establish the relationship between deposition speed, bead spatial orientation, and cross-sectional features. The obtained fitting equation had a mean relative error of less than 2.5%, and an overlapping strategy was proposed to achieve flat, curved GMA layers. The proposed bead characterization method, parameter planning model, and overlap strategy were validated through deposition experiments on cylindrical surfaces without a positioner, providing a foundation for high-precision curved GMA additive manufacturing. Full article

This paper presents an improved methodology for optimizing the fed-batch fermentation process of xylitol production, aiming to maximize the final concentration in a bioreactor co-fed with xylose and glucose. Xylitol is a valuable sugar alcohol widely used in the food and pharmaceutical industries, and its microbial production requires precise control over substrate feeding strategies. The proposed technique employs Legendre polynomials to parameterize two control actions (the feeding rates of glucose and xylose), and it uses a hybrid optimization algorithm combining Monte Carlo sampling with genetic algorithms for coefficient selection. Unlike traditional optimization approaches based on piecewise parameterization, which produce discontinuous control profiles and require post-processing, this method generates smooth profiles directly applicable to real systems. Additionally, it significantly reduces mathematical complexity compared to strategies that combine Fourier series with orthonormal polynomials while maintaining similar optimization results. The methodology achieves good results in xylitol production using only eight parameters, compared to at least twenty in other approaches. This dimensionality reduction improves the robustness of the optimization by decreasing the likelihood of convergence to local optima while also reducing the computational cost and enhancing feasibility for implementation. The results highlight the potential of this strategy as a practical and efficient tool for optimizing nonlinear multivariable bioprocesses. Full article

The higher integration of photovoltaic (PV) units is an inevitable component of smart city development. Thanks to smart meter devices that can record the exchange of power between the grid and customers, it is expected that homeowners and businesses will tend to install PV arrays on their rooftops and parking lots to benefit from selling power back to the grid. However, the overvoltage issue resulting from high PV penetration is a major challenge that necessitates the active power curtailment of PV units to ensure power grid stability. Fairness-oriented methods aim to minimize the active power of PV units as much as possible, adopting a fairer approach, and then address the PV owner’s satisfaction with fair profit and loss. Maintaining voltage within a limited standard range under very low load conditions while prioritizing PV inverters’ participation in reactive power contribution and attempting to ensure fairer curtailment of active power presents challenges to existing control design approaches. This paper presents twelve new volt–watt curve design methods to achieve these goals and address the challenges. The methods yield polynomial curves, piecewise linear curves, and single linear curves. A unique voltage sensitivity value for each PV inverter is used to determine the control region area and the slope of the curve at the starting point in certain instances. The effectiveness of the proposed methods is discussed by evaluating their capabilities on the 37-bus IEEE system. Full article

In this paper, we study asymptotic bounds on the m-th derivatives of general algebraic polynomials in weighted Bergman spaces. We consider regions in the complex plane defined by bounded, piecewise, asymptotically conformal curves with strictly positive interior angles. We first establish asymptotic bounds on the growth in the exterior of a given unbounded region. We then extend our analysis to the closures of the region and derive the corresponding growth bounds. Combining these bounds with those for the corresponding exterior, we obtain comprehensive bounds on the growth of the m-th derivatives of arbitrary algebraic polynomials in the whole complex plane. Full article

Although fractional calculus has evolved significantly since its origin in the 1695 correspondence between Leibniz and L’Hôpital, the numerical treatment of multi-order fractional differential equations remains a challenge. Existing methods are often either computationally expensive or reliant on complex operational frameworks that hinder their broader applicability. In the present study, a novel numerical algorithm is proposed based on orthogonal hybrid functions (HFs), which were constructed as linear combinations of piecewise constant sample-and-hold functions and piecewise linear triangular functions. These functions, belonging to the class of degree-1 orthogonal polynomials, were employed to obtain the numerical solution of multi-order fractional differential equations defined in the Caputo sense. A generalized one-shot operational matrix was derived to explicitly express the Riemann–Liouville fractional integral of HFs in terms of the HFs themselves. This allowed the original multi-order fractional differential equation to be transformed directly into a system of algebraic equations, thereby simplifying the solution process. The developed algorithm was then applied to a range of benchmark problems, including both linear and nonlinear multi-order FDEs with constant and variable coefficients. Numerical comparisons with well-established methods in the literature revealed that the proposed approach not only achieved higher accuracy but also significantly reduced computational effort, demonstrating its potential as a reliable and efficient numerical tool for fractional-order modeling. Full article

High-quality data are foundational to reliable environmental monitoring and urban planning in smart cities, yet challenges like missing values and outliers in air pollution and meteorological time series data are critical barriers. This study developed and validated a dual-phase framework to improve data quality using a 60-month gas and weather dataset from Jubail Industrial City, Saudi Arabia, an industrial region. First, outliers were identified via statistical methods like Interquartile Range and Z-Score. Machine learning algorithms like Isolation Forest and Local Outlier Factor were also used, chosen for their robustness to non-normal data distributions, significantly improving subsequent imputation accuracy. Second, missing values in both single and sequential gaps were imputed using linear interpolation, Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), and Akima interpolation. Linear interpolation excelled for short gaps (R² up to 0.97), and PCHIP and Akima minimized errors in sequential gaps (R² up to 0.95, lowest MSE). By aligning methods with gap characteristics, the framework handles real-world data complexities, significantly improving time series consistency and reliability. This work demonstrates a significant improvement in data reliability, offering a replicable model for smart cities worldwide. Full article

With the increasing integration of large-scale renewable energy sources, the coordinated participation of hydropower and energy storage in frequency regulation has become a critical means of ensuring the safe and economical operation of power grids. This paper proposes an optimization method for the allocation of frequency regulation reserves between hydropower and energy storage based on marginal substitution rate (MRS) analysis. First, a frequency response model that captures the synergistic interaction between hydropower and energy storage is established, with the root mean square error (RMSE) of the area control error (ACE) serving as the performance metric for frequency regulation. To reduce simulation computational burdens, key simulation data are obtained via Gaussian process regression (GPR), and a piecewise polynomial fitting method is employed to generate the marginal substitution curve. Experimental results indicate that under the condition of achieving equivalent frequency regulation performance (ACE_RMSE), 51.60 MW of energy storage reserve can replace 68.38 MW of hydropower reserve, thereby reducing the total regulation capacity reduction of 13.42%. Furthermore, by incorporating the differing cost characteristics of hydropower and energy storage, the optimal configuration is determined, resulting in an overall cost reduction of 17.58%. This method not only ensures system frequency stability but also fully leverages the potential of the available frequency regulation resources. Full article

Continuous data associated with many real-world events often exhibit non-normal characteristics, which contribute to the difficulty of accurately modeling such data with statistical procedures that rely on normality assumptions. Traditional statistical procedures often fail to accurately model non-normal distributions that are often observed in real-world data. This paper introduces a novel modeling approach using mixed third-order polynomials, which significantly enhances accuracy and flexibility in statistical modeling. The main objective of this study is divided into three parts: The first part is to introduce two new non-normal probability distributions by mixing standard normal and logistic variables using a piecewise function of third-order polynomials. The second part is to demonstrate a methodology that can characterize these two distributions through the method of L-moments (MoLMs) and method of moments (MoMs). The third part is to compare the MoLMs- and MoMs-based characterizations of these two distributions in the context of parameter estimation and modeling non-normal real-world data. The simulation results indicate that the MoLMs-based estimates of L-skewness and L-kurtosis are superior to their MoMs-based counterparts of skewness and kurtosis, especially for distributions with large departures from normality. The modeling (or data fitting) results also indicate that the MoLMs-based fits of these distributions to real-world data are superior to their corresponding MoMs-based counterparts. Full article

This paper extends the well-known transfinite interpolation formula, which was developed in the late 1960s by the applied mathematician William Gordon at the premises of General Motors as an extension of the pre-existing Coons interpolation formula. Here, a conjecture is formulated, which claims that the meaning of the involved blending functions can be enhanced, such that it includes any linear independent and complete set of functions, including piecewise-linear, trigonometric functions, Bernstein polynomials, B-splines, and NURBS, among others. In this sense, NURBS-based isogeometric analysis and aspects of T-splines may be considered as special cases. Applications are provided to illustrate the accuracy in the interpolation through the L₂ error norm of closed-formed functions prescribed at the nodal points of the transfinite patch, which represent the solution of partial differential equations under boundary conditions of the Dirichlet type. Full article

Motion planning is critical for ensuring precise and efficient operations of unmanned aerial vehicles (UAVs). While polynomial parameterization has been the prevailing approach, its limitations in handling complex trajectory requirements have motivated the exploration of alternative methods. This paper introduces a finite Fourier series (FFS)-based trajectory parameterization for UAV motion planning, highlighting its unique capability to produce piecewise infinitely differentiable trajectories. The proposed approach addresses the challenges of fixed-time minimum-snap trajectory optimization by formulating the problem as a quadratic programming (QP) problem, with an analytical solution derived for unconstrained cases. Additionally, we compare the FFS-based parameterization with the polynomial-based minimum-snap algorithm, demonstrating comparable performance across several representative trajectories while uncovering key differences in higher-order derivatives. Experimental validation of the FFS-based parameterization using an in-house quadrotor confirms the practical applicability of the FFS-based minimum-snap trajectories. The results indicate that the proposed FFS-based parameterization offers new possibilities for motion planning, especially for scenarios requiring smooth and higher-order derivative continuity at the expense of minor increase in computational cost. Full article

The leaf area index (LAI) serves as a key metric for tracking crop growth and can be integrated into crop models for yield estimation. Although the remote sensing LAI data provide a critical foundation for monitoring crop growth and estimating yields, the existing datasets often exhibit notable errors due to the pixel-level heterogeneity. To improve the applicability and inversion accuracy of MODIS LAI products in the Northeast China (NEC) region, this study upscaled the 500-m resolution MODIS LAI product to a 5-km resolution by initially calculating the mean value. Then, the scale factors were estimated based on the observed LAI data of spring maize. To further refine the accuracy of the remotely sensed LAI, 1-km resolution land use data were resampled to 500-m resolution, and the pixel purity of spring maize was calculated for each 5-km grid cell. The scale factor time series was fitted with and without consideration of pixel purity, and the accuracy of the adjusted LAI using these two methods was compared. Our findings demonstrate that the optimal method for fitting scale factors for spring maize LAI data is piecewise function method which combines Gaussian and quadratic polynomial functions. The time series of scale factors derived from high- and low-purity pixels, differentiated by a 50% purity threshold, resulted in improved performance in adjusting the spring maize LAI compared to traditional remote sensing LAI data. The adjusted LAI performed better in reflecting the growth characteristics of spring maize in the NEC region, with the relative mean square errors between observed and adjusted LAI of spring maize during 2016 and 2020 below 1 m²/m². This study provides crucial support for monitoring the growth process and estimating the yield of spring maize in the NEC region and also offers valuable scientific references for the optimization and application of remote sensing data. Full article

The manipulator has been widely used in the wood processing industry; the main problem currently faced is optimizing the motion trajectory to enhance the processing efficiency and operational stability of the woodworking manipulator and worktable. A 5-7-5 piecewise polynomial interpolation method is proposed to construct the spatial trajectories of each joint. An improved non-dominated sorting genetic algorithm (INSGA-II) is proposed to achieve a time–jerk multi-objective trajectory planning that can meet the dual requirements of minimal processing time and reduced motion impact. In order to address the limitations of the standard NSGA-II algorithm, which is prone to local optima and exhibits slow convergence, we propose a good point set method for multi-objective optimization population initialization and a linear ranking selection method to refine the parent selection process within the genetic algorithm. The improved NSGA-II algorithm markedly enhanced both the uniformity of the population distribution and convergence speed. In practical applications, selecting suitable weightings to construct a normalized weight function can identify the optimal solution from the Pareto frontier curve. A high-order continuous and smooth optimal trajectory without abrupt changes can be obtained. The simulation results demonstrated that the 5-7-5 piecewise polynomial interpolation curve effectively constructed a high-order smooth processing trajectory with continuous and smooth velocity, acceleration, and jerk, free from discontinuities. Moreover, the INSGA-II algorithm outperforms the original algorithm in terms of convergence and distribution, enabling the optimal time–jerk multi-objective trajectory planning that adheres to constraint conditions. Optimized by the improved NSGA-II algorithm, the optimal total running time is 4.5400 s, and the optimal jerk is 17.934 $\mathrm{m}\left(\mathrm{r}\mathrm{a}\mathrm{d}\right)/{\mathrm{s}}^3$. This provides a novel approach to solving the inefficiencies and operational instability prevalent in traditional woodworking equipment. Full article

This paper presents direct and inverse theorems concerning the approximation of functions of several variables with bounded p-fluctuation using Walsh polynomials. These theorems provide estimates for the best approximation of such functions by polynomials in the norm of the space under consideration. The paper investigates the properties of the Walsh system, which includes piecewise constant functions, and builds on earlier work on trigonometric and multiplicative systems. The results are theoretical and have potential applications in such areas as coding theory, digital signal processing, pattern recognition, and probability theory. Full article