Simulation modelling of mechanical systems for intra-row weeding in a precision farming approach

Aim of study: To test new approaches to perform mechanical weeding inside the row in horticulture and tree fruit fields. The idea is to weed the row by skipping the crop by means of a rotating system instead of a traditional crosswise one. Area of study: North of Italy. Material and methods: Numerical models have been developed to simulate mechanical weeding over time by generating numerical maps to quantify the different kind of worked areas. Main results: Considering the efficiency of weed control on the row, the rotating plant-skipping system with vertical axis (RPSS-VA model) with two working tools gives the best performance index (1.1.RWA% = 95.9%). A similar performance can be obtained by the crosswise displacement plant-skipping system (CDSS model, 1.1.RWA% = 95.9 %), but with very high crosswise translation velocity (with va/vr ratio = 1/5, 1.1.RWA% = 94.5%). With regard to the outwards worked area the RPSS-VA models give the best performances (2.2.%OWAR index from 127.2% up to 282.3%). To reduce the worked area outside the row, the FBTS models give lower index (2.1.OWAR%), while the RPSS-HA works only on the row, but with the lower 1.1.RWA% index among all tested models (55.8%). Research highlights: Rotating systems resulted more efficient than traditional ones, and provide considerations on the use of electric drive power instead of hydraulic one. This study highlights also the need of new approaches in designing lighter working tools. Lastly, the proposed classification of the worked areas could be used as reference standard.

Design and analysis of a faster King-Werner-type derivative free method

We introduce a new faster King-Werner-type derivative-free method for solving nonlinear equations. The local as well as semi-local convergence analysis is presented under weak center Lipschitz and Lipschitz conditions. The convergence order as well as the convergence radii are also provided. The radii are compared to the corresponding ones from similar methods. Numerical examples further validate the theoretical results.

Extended local convergence for Newton-type solver under weak conditions

We present the local convergence of a Newton-type solver for equations involving Banach space valued operators. The eighth order of convergence was shown earlier in the special case of the k-dimensional Euclidean space, using hypotheses up to the eighth derivative although these derivatives do not appear in the method. We show convergence using only the rst derivative. This way we extend the applicability of the methods. Numerical examples are used to show the convergence conditions. Finally, the basins of attraction of the method, on some test problems are presented.

Composite plate analysis made in an unsymmetric configuartion

The work presents a thin-walled plate element with the central rectangular cut-out which can be use as an elastic or load-bearing element. Plates were made of carbon epoxy laminate and subjected to uniform compression. Plates were simply supported on shorter edges, and loaded axial load. The study included analysis of the critical and weakly post-critical behavior using experimental and numerical methods. Numerical analysis was performed with using linear analysis of eigenvalue problem to determination critical loads. The second step connected nonlinear analysis of structure with initiated geometrically imperfection corresponding to the flexural-torsional buckling mode of the plate. To the numerical calculations the commercial ABAQUS program was used.

Multi-Scroll Attractors with Hyperchaotic Behavior Using Fractional-Order Systems

In this paper, a systematic design is proposed to generate multi-scroll attractors with hyperchaotic behavior using fractional-order systems, in which switched SC-CNN is triggered with error function. Sprott Systems Case H is reconstructed with fractional-order switched SC-CNN system. Herein, the goal is to increase the complexity of chaotic signals, hence providing safer and reliable communication by generating multi-scroll attractors with hyperchaotic behavior using fractional-order systems. Theoretical analysis of the proposed system’s dynamical behaviors is scrutinized, while numerical investigations are carried out with equilibrium points, Lyapunov exponent, bifurcation diagrams, Poincaré mapping and 0/1 test methods. Numerical results are validated through simulations and on an FPAA platform.

Extended Kung–Traub Methods for Solving Equations with Applications

Kung and Traub (1974) proposed an iterative method for solving equations defined on the real line. The convergence order four was shown using Taylor expansions, requiring the existence of the fifth derivative not in this method. However, these hypotheses limit the utilization of it to functions that are at least five times differentiable, although the methods may converge. As far as we know, no semi-local convergence has been given in this setting. Our goal is to extend the applicability of this method in both the local and semi-local convergence case and in the more general setting of Banach space valued operators. Moreover, we use our idea of recurrent functions and conditions only on the first derivative and divided difference, which appear in the method. This idea can be used to extend other high convergence multipoint and multistep methods. Numerical experiments testing the convergence criteria complement this study.

Optimization of a Class of n-Sub-Step Time Integration Methods for Structural Dynamics

This paper develops a family of optimized [Formula: see text]-sub-step time integration methods for structural dynamics, in which the generalized trapezoidal rule is used in the first [Formula: see text] sub-steps, and the last sub-step employs [Formula: see text]-point backward difference formula. The proposed methods can achieve second-order accuracy and unconditional stability, and their degree of numerical dissipation can range from zero to one. Also, the proposed methods can achieve the identical effective stiffness matrices for all sub-steps, reducing computational costs in the analysis of linear systems. Using the spectral analysis, optimized algorithmic parameters are presented, ensuring that the proposed methods can accurately calculate different types of dynamic problems such as wave propagation, stiff and nonlinear systems. Besides, with the increase in the number of sub-steps, the accuracy of the proposed methods can be enhanced without extra workload compared with single-step methods. Numerical experiments show that the proposed methods perform better in different dynamic systems.

Local convergence for a family of sixth order methods with parameters

Local convergence of a family of sixth order methods for solving Banach space valued equations is considered in this article. The local convergence analysis is provided using only the first derivative in contrast to earlier works on the real line using the seventh derivative. This way the applicability is expanded for these methods. Numerical examples complete the article.

Unified Convergence Analysis of Two-Step Iterative Methods for Solving Equations

In this paper we consider unified convergence analysis of two-step iterative methods for solving equations in the Banach space setting. The convergence order four was shown using Taylor expansions requiring the existence of the fifth derivative not on this method. But these hypotheses limit the utilization of it to functions which are at least five times differentiable although the method may converge. As far as we know no semi-local convergence has been given in this setting. Our goal is to extend the applicability of this method in both the local and semi-local convergence case and in the more general setting of Banach space valued operators. Moreover, we use our idea of recurrent functions and conditions only on the first derivative and divided differences which appear on the method. This idea can be used to extend other high convergence multipoint and multistep methods. Numerical experiments testing the convergence criteria complement this study.