Search Results (1,778)

This paper proposes a calibration method for redundant robot arms with highly elastic joints. The method uses the second-order Chebyshev polynomial to characterize the variation in the error with the poses of all joints. This error model is consistent with the variation in the gravitational torque on each joint and demonstrates good generalization. Based on this, the calibration model includes both kinematic errors and non-kinematic errors. For this high-dimensional model, an adaptive iterative identification algorithm is proposed for a large number of small error parameters of various types. The algorithm sets specific iteration rules for different types of error parameters and adjusts the convergence amplitude in each iteration, ensuring that the iterative algorithm converges to the global optimum. The simulation results show that for a redundant robot arm with 12 highly elastic joints, even with large linearization modeling errors, the new identification algorithm can gradually eliminate them during iteration, achieving an identification accuracy higher than 99.975% for all of the error parameters. The experimental results indicate that on a redundant robot arm with eight cable-driven elastic joints, the new model and identification algorithm reduce the 96.6% absolute positioning errors of the robot arm, enabling it to perform precise and flexible operations. It takes 40.534 s and 29.077 s to run the identification algorithm on MATLAB (R2023b, 2.10 GHz CPU) in the simulation and experiment, respectively. Full article

We develop a rigorous algebraic–analytic framework for multidual complex numbers ${\mathbb{DC}}_n$ within the setting of Clifford analysis and establish a comprehensive theory of hyperholomorphic multidual complex-valued functions. Our main contributions are (i) a fully coupled multidual Cauchy–Riemann system derived from the Dirac operator, yielding precise differentiability criteria; (ii) generalized conjugation laws and the associated norms that clarify metric and geometric structure; and (iii) explicit operator and kernel constructions—including generalized Cauchy kernels and Borel–Pompeiu-type formulas—that produce new representation theorems and regularity results. We further provide matrix–exponential and functional calculus representations tailored to ${\mathbb{DC}}_n$, which unify algebraic and analytic viewpoints and facilitate computation. The theory is illustrated through a portfolio of examples (polynomials, rational maps on invertible sets, exponentials, and compositions) and a solvable multidual boundary value problem. Connections to applications are made explicit via higher-order automatic differentiation (using nilpotent infinitesimals) and links to kinematics and screw theory, highlighting how multidual analysis expands classical holomorphic paradigms to richer, nilpotent-augmented coordinate systems. Our results refine and extend prior work on dual/multidual numbers and situate multidual hyperholomorphicity within modern Clifford analysis. We close with a concise summary of notation and a set of concrete open problems to guide further development. Full article

We study equations with real polynomials of arbitrary degree, such that each coefficient has a small, individual error; this may originate, for example, from imperfect measuring. In particular, we study the influence of the errors on the roots of the polynomials. The errors are modeled by imprecisions of Sorites type: they are supposed to be stable to small shifts. We argue that such imprecisions are appropriately reflected by (scalar) neutrices, which are convex subgroups of the nonstandard real line; examples are the set of infinitesimals, or the set of numbers of order $\epsilon$, where $\epsilon$ is a fixed infinitesimal. The Main Theorem states that the imprecisions of the roots are neutrices, and determines their shape. Full article

This paper investigates the stability of continued fractions with complex partial denominators and numerators equal to one. Such fractions are an important tool for function approximation and have wide application in physics, engineering, and mathematics. A formula is derived for the relative error of the approximant of a continued fraction, which depends on both the relative errors of the fraction’s elements and the elements themselves. Based on this formula, using the methodology of element sets and their corresponding value sets, conditions are established under which the approximants of continued fractions are stable to perturbations of their elements. Stability sets are constructed, which are sets of admissible values for the fraction’s elements that guarantee bounded errors in the approximants. For each of these sets, an estimate of the relative error that arises from the perturbation of the continued fraction’s elements is obtained. The results are illustrated with an example of a continued fraction that is an expansion of the ratio of Bessel functions of the first kind. A numerical experiment is conducted, comparing two methods for calculating the approximants of a continued fraction: the backward and forward algorithms. The computational stability of the backward algorithm is demonstrated, which corresponds to the theoretical research results. The errors in calculating approximants with this algorithm are close to the unit round-off, regardless of the order of approximation, which demonstrates the advantages of continued fractions in high-precision computation tasks. Another example is a comparative analysis of the accuracy and stability to perturbations of second-order polynomial model and so-called second-order continued fraction model in the problem of wood drying modeling. Experimental studies have shown that the continued fraction model shows better results both in terms of approximation accuracy and stability to perturbations, which makes it more suitable for modeling processes with pronounced asymptotic behavior. Full article

This study, inspired by the impact resistance of the pistol shrimp’s predatory claw, investigates the design and optimization of bionic energy absorption structures. Four types of bionic hierarchical porous metamaterial lattice structures with a negative Poisson’s ratio were developed based on the microstructure of the pistol shrimp’s fixed claw. These structures were validated through finite element models and quasi-static compression tests. Results showed that each structure exhibited distinct advantages and shortcomings in specific evaluation indices. To address these limitations, four new bionic structures were designed by coupling the characteristics of the original structures. The coupled structures demonstrated a superior balance across various performance indicators, with the EOS (Eight pillars Orthogonal with Side connectors on square frame) structure showing the most promising results. To further enhance the EOS structure, a parametric study was conducted on the distance d from the edge line to the curve vertex and the length-to-width ratio y of the negative Poisson’s ratio structure beam. A fifth-order polynomial surrogate model was constructed to predict the Specific Energy Absorption (SEA), Crush Force Efficiency (CFE), and Undulation of Load-Carrying fluctuation (ULC) of the EOS structure. A multi-objective genetic algorithm was employed to optimize these three key performance indicators, achieving improvements of 1.98% in SEA, 2.42% in CFE, and 2.05% in ULC. This study provides a theoretical basis for the development of high-performance biomimetic energy absorption structures and demonstrates the effectiveness of coupling design with optimization algorithms to enhance structural performance. Full article

During the cooling phase of injection molding, the conformal cooling channel system optimizes the uniformity of mold temperature, diminishes warping deformation, and contributes substantially to heightened product precision. The injection molding process involves complex process parameters that may result in uneven cooling between components, leading to prolonged cycle times, increased shrinkage depth, and warping deformation of the plastic parts. These manifestations negatively impact the surface quality and structural strength of the final product. This article combined theoretical algorithms with finite element simulation (CAE) methods to optimize complex injection molding processes. Firstly, the characteristics of six different types of materials were examined. Melt temperature, mold opening time, injection time, holding time, holding pressure, and mold temperature were chosen as optimization variables. Meanwhile, the warpage deformation and shrinkage depth of the formed sample were selected as optimization objectives. Secondly, an L27 orthogonal experimental design (OED) was established, and the signal-to-noise ratio was processed. The entropy weight method (EWE) was used to calculate the weights of the total warpage deformation and shrinkage depth, thereby obtaining the grey correlation degree. The influence of process parameters on quality indicators was analyzed using grey relational analysis (GRA) to calculate the range. A second-order polynomial regression model was established using response surface methodology (RSM) to investigate the effects of six factors on the warpage deformation and shrinkage depth of injection molded parts. Finally, a comprehensive comparison was made on the impact of various optimization methods and models on the forming parameters. Analyze according to different optimization principles to obtain the corresponding optimal process parameters. The research results indicate that under the principle of prioritizing warpage deformation, the effectiveness ranking of the three optimization analyses is RSM > OED > GRA. The minimum deformation rate is 0.1592 mm, which is 27.37% lower than before optimization. Under the principle of prioritizing indentation depth, the effectiveness ranking of the three optimization analyses is OED > GRA > RSM. The minimum depth of shrinkage is 0.0312 mm, which is 47.21% lower than before optimization. This discovery provides strong support for the optimal combination of process parameters suitable for production and processing. Full article

Accurate spatial interpolation of environmental data requires utilizing flexible models that can capture complex spatial patterns. In this paper, we present two improved dual kriging (DK) models comprising a nonlinear trend function that combines Gaussian radial basis functions with a first-order polynomial. The proposed model, DK–RBFP, and its extension, DK–RBFPGA, which includes k-means clustering and a genetic algorithm for parameter optimization, respectively, exhibit enhanced performance in capturing spatial variation. The complete monotonicity of the covariance function and the strict positive definiteness of the coefficient matrix provide theoretical support for the uniqueness of the DK solution. When applied to datasets of PM_2.5 concentrations for northern Thailand, both models perform better than the conventional DK model using a second-order polynomial trend (DK–POLY), as evidenced by accuracy metrics including the mean absolute percentage error (MAPE), the mean squared error (MSE), and the root mean square error (RMSE). The outcomes indicate that integrating nonlinear trend components with data-driven optimization significantly enhances accuracy and flexibility in environmental spatial predictions. Full article

The present study examines the application of interactive software models for training on the topic of “Cyclic Codes” in order to increase the success rate and engagement of students in technical disciplines. Two models have been developed—based on the polynomial method and the LFSR approach—through an established methodology adapted to the specifics of the content. A pedagogical experiment with a control and experimental group was conducted, and ANCOVA analysis was applied to eliminate the influence of initial grades. The results show a statistically significant advantage of the experimental group in terms of final grades, which confirms the positive effect of using interactive models. The analysis of engagement and solved tasks reveals that the polynomial model is used more widely and contributes to the systematic application of algorithmic steps, while the LFSR model has an illustrative nature and supports intuitive understanding through visualization of processes. The feedback received from students shows high satisfaction and points to improvements in the interface and functionality. In conclusion, interactive models prove their effectiveness as complementary tools for learning complex technical concepts, and prospects for future development through the integration of artificial intelligence and enhanced gamification are also discussed. Full article

In the development of artificial intelligence (AI) technology, utilizing datasets for model instruction to achieve higher predictive and reasoning efficacy has become a common technical approach. However, primordial datasets often contain a significant number of redundant features (RF), which can compromise the prediction accuracy and generalization ability of models. To effectively reduce RF in datasets, this work advances a new version of the Pufferfish Optimization Algorithm (POA), termed AMFPOA. Firstly, by considering the knowledge disparities among different groups of members and incorporating the concept of adaptive learning, an adaptive exploration strategy is introduced to enhance the algorithm’s Global Exploration (GE) capability. Secondly, by dividing the entire swarm into multiple subswarms, a three-swarm search strategy is advanced. This allows for targeted optimization schemes for different subswarms, effectively achieving a good balance across various metrics for the algorithm. Lastly, leveraging the historical memory property of Fractional-Order theory and the member weighting of Bernstein polynomials, a Fractional-Order Bernstein exploitation strategy is advanced, which significantly augments the algorithm’s local exploitation (LE) capability. Subsequent experimental results on 23 real-world Feature Selection (FS) problems demonstrate that AMFPOA achieves an average success rate exceeding 87.5% in fitness function value (FFV), along with ideal efficacy rates of 86.5% in Classification Accuracy (CA) and 60.1% in feature subset size reduction. These results highlight its strong capability for RF elimination, establishing AMFPOA as a promising FS method. Full article

To address the issues of low efficiency, high cost of manual harvesting, and the lack of mechanized harvesting technology and equipment for high-stem Chrysanthemum coronarium, a self-propelled orderly harvester was designed to perform key harvesting operations such as row alignment, clamping and cutting, orderly conveying, and collection. Based on the analysis of agronomic requirements for cultivation and mechanized harvesting needs, the overall structure and working principle of the machine were described. Meanwhile, the key components such as the reciprocating cutting mechanism and orderly conveying mechanism were structurally designed and theoretically analyzed. The main structural and operating parameters of the harvester were determined based on the geometric and kinematic conditions of high-stem Chrysanthemum coronarium during its movement along the conveying path, as well as the mechanical model of the conveying process. In addition, a three-factor, three-level Box-Behnken field experiment was also conducted with the experimental factors including the machine’s forward, cutting, and conveying speed, and evaluation indicators like harvesting loss rate and orderliness. A second-order polynomial regression model was established to analyze the relationship between the evaluation indicators and the factors using the Design-Expert 13 software, which revealed the influence patterns of the machine’s forward speed, reciprocating cutter cutting speed, conveying device speed, and their interaction influence on the evaluation indicators. Moreover, the optimal parameter combination, obtained by solving the optimization model for harvesting loss rate and orderliness, was forward speed of 260 mm/s, cutting speed of 250 mm/s, and conveying speed of 300 mm/s. Field test results showed that the average harvesting loss rate of the prototype was 4.45% and the orderliness was 92.57%, with a relative error of less than 5% compared to the predicted values. The key components of the harvester operated stably, and the machine was capable of performing cutting, orderly conveying, and collection in a single pass. All performance indicators met the mechanized orderly harvesting requirements of high-stem Chrysanthemum coronarium. Full article

The implementation of efficient free-space channels is fundamental for both classical and quantum free-space optical (FSO) communication. This can be challenging for fiber-coupled receivers, due to the time variant inhomogeneity of the refractive index that can cause strong fluctuations in the power coupled into the single-mode fiber (SMF), and requires the use of adaptive optics (AO) systems to correct the atmospheric-induced aberrations. In this work, we present two adaptive optic systems, one using a fast-steering prism (FSP) for the correction of tip-tilt and a second one based on a multi-actuator deformable lens (MAL), capable of correcting up to the third order of Zernike’s polynomials. We test both systems at telecom wavelength both with artificial turbulence in the laboratory and on a free-space channel, demonstrating their effectiveness in increasing the fiber coupling efficiency. Full article

Dynamic compaction has been widely applied to reinforce soft soils in port areas due to its high efficiency and cost-effectiveness. However, a comprehensive understanding of the deformation mechanisms and stiffness evolution of treated soils under static and dynamic loading remains limited. This study integrated one-dimensional consolidation tests, resonant column tests, and bender element tests to systematically investigate the mechanical behavior of soft clay before and after dynamic compaction under varying stress levels and loading frequencies. The results show that dynamic compaction significantly enhances the compression modulus and consolidation stability of soft clay while reducing the settlement rate during primary consolidation. The shear modulus exhibits nonlinear degradation with increasing strain, whereas the damping ratio increases rapidly before reaching a plateau, indicating typical strain-dependent behavior. A three-parameter model and a second-order polynomial model effectively characterize the degradation of the shear modulus and the evolution of the damping behavior, respectively. Moreover, the strong consistency between the resonant column and bender element test results enables continuous characterization of the shear stiffness across small- to intermediate-strain ranges. These findings provide theoretical insight and practical guidance for modeling the dynamic response of soft clay and evaluating the effectiveness of dynamic compaction as a ground improvement technique. Full article

Xanthones from mangosteen pericarp (MP) are bioactive compounds with promising pharmaceutical and nutraceutical applications. However, their efficient and selective extraction using environmentally friendly solvents remains a challenge. This study aimed to evaluate tricaprylin (C8) and tricaprin (C10) as novel green co-extractants in supercritical carbon dioxide (scCO₂) extraction for the recovery of xanthones from MP, using a mass ratio of C8:C10 = 0.64:0.36, hereafter referred to as C8/C10, and to model extraction kinetics for process design and scale-up. Extraction performance was investigated using different C8/C10–MP mass ratios and scCO₂ conditions at temperatures of 60 °C and 70 °C and pressures of 250 bar, 350 bar, and 450 bar. A pseudo-first-order kinetic model was applied to describe the extraction profile, and the kinetic parameters were generalized using second-order polynomial functions of temperature and pressure. The highest xanthone yield (39.93 ± 0.37%) and total xanthone content (51.44 ± 2.22 mg/g) were obtained at a 40% C8/C10–MP ratio under 70 °C and 350 bar, where the C8/C10 mixture outperformed other tested co-extractants in both efficiency and selectivity, particularly for α-mangostin. The extraction profiles were well described by the pseudo-first-order kinetic model, and the generalized model predicted the extraction yield with an uncertainty of 2.3%. C8/C10 is a highly effective and scalable co-extractant for scCO₂ extraction of xanthones, offering a foundation for industrial applications in food, nutraceutical, and pharmaceutical sectors. Full article

To model the response of neural networks to electromagnetic radiation in real-world environments, this study proposes a memristive dual-wing fractional-order Hopfield neural network (MDW-FOMHNN) model, utilizing a fractional-order memristor to simulate neuronal responses to electromagnetic radiation, thereby achieving complex chaotic dynamics. Analysis reveals that within specific ranges of the coupling strength, the MDW-FOMHNN lacks equilibrium points and exhibits hidden chaotic attractors. Numerical solutions are obtained using the Adomian Decomposition Method (ADM), and the system’s chaotic behavior is confirmed through Lyapunov exponent spectra, bifurcation diagrams, phase portraits, and time series. The study further demonstrates that the coupling strength and fractional order significantly modulate attractor morphologies, revealing diverse attractor structures and their coexistence. The complexity of the MDW-FOMHNN output sequence is quantified using spectral entropy, highlighting the system’s potential for applications in cryptography and related fields. Based on the polynomial form derived from ADM, a field programmable gate array (FPGA) implementation scheme is developed, and the expected chaotic attractors are successfully generated on an oscilloscope, thereby validating the consistency between theoretical analysis and numerical simulations. Finally, to link theory with practice, a simple and efficient MDW-FOMHNN-based encryption/decryption scheme is presented. Full article

During the processes of excavation, restoration, and conservation of archaeological sites, it is common practice to perform physical and chemical characterization of the site materials. This is carried out to determine the best methods and materials for conserving and preserving the site. For this reason, techniques such as infrared spectroscopy and elemental analysis by X-ray fluorescence (XRF) are primarily used for chemical characterization, while mechanical tests such as the uniaxial compression test and hardness tests are used for physical and mechanical characterization. However, a common limitation is obtaining samples for destructive physical tests, such as compression tests, due to their invaluable cultural value. To address this problem, this work proposes the mechanical characterization of the material through nanoindentation. This technique requires a smaller sample size and can be performed in a timely manner by observing the resistance of each mineralogical phase present in the material. Thus, a preliminary predictive model of mechanical resistance is proposed based on the composition observed in the samples from the archaeological site of Cerro de los Remedios, located in the municipality of Comonfort, Guanajuato, Mexico. The samples were characterized using infrared spectroscopy, XRF, XRD, and SEM-EDS. The results indicate that the stone (caliche) is formed from 95.6–93% micrite calcite; 2.51–0.42% aluminosilicate; 3.14–1.89% high-calcium aluminosilicate; and 3.43–2.39 quartz or amorphous SiO₂. The proposed correlation models were adjusted to a linear function, a second-order polynomial, and a logarithmic function. In the M2–linear model, the non-linear effects generated by variables such as texture, porosity, phase adhesion, cement type, and cracks or discontinuities were not considered. In this model the best prediction of the experimental data was obtained within a variation of ±15%. Full article