Solution Of Problem Research Articles

Towards accuracy improvement in solution of inverse kinematic problem in redundant robot: A comparative analysis

AbstractThe redundant manipulators have more DOFs (degree of freedoms) than it requires to perform specified task. The inverse kinematic (IK) of such robots are complex and high nonlinear with multiple solutions and singularities. As such, modern Artificial Intelligence (AI) techniques have been used to address these problems. This study proposed two AI techniques based on Neural Network Genetic Algorithm (NNGA) and Particle Swarm Optimization (PSO) algorithm to solve the inverse kinematics (IK) problem of 3DOF redundant robot arm. Firstly, the forward kinematics for 3 DOF redundant manipulator has been established. Secondly, the proposed schemes based on NNGA and PSO algorithm have been presented and discussed for solving the inverse kinematics of the suggested robot. Thirdly, numerical simulations have been implemented to verify the effectiveness of the proposed methods. Three scenarios based on triangle, circular, and sine-wave trajectories have been used to evaluate the performances of the proposed techniques in terms of accuracy measure. A comparison study in performance has been conducted and the simulated results showed that the PSO algorithm gives 7% improvement compared to NNGA technique for triangle trajectory, while 2% improvement has been achieved by the PSO algorithm for circular and sine-wave trajectories.

A 3-D extension of the Multiscale Control Volume method for the simulation of the single-phase flow in anisotropic and heterogeneous porous media

The level of detail on modern geological models requires higher resolution grids that may render the simulation of multiphase flow in porous media intractable. Moreover, these models may comprise highly heterogeneous media with phenomena taking place in different scales. Scale transferring techniques allow for the solution of such problems in a lower resolution scale at reduced computational cost. Among these techniques, the Multiscale Finite Volume (MsFV) method constructs a set of numerical operators in order to map quantities from the fine-scale mesh to a coarser one and vice-versa while maintaining flux conservation on both scales. However, the MsFV formulation, as originally stated, is only consistent on k-orthogonal grids since it uses a linear Two-point Flux Approximation (TPFA) method and may struggle to generate consistent primal-dual coarse grids pairs on unstructured grids. The Multiscale Restriction Smoothed-Basis method (MsRSB) improves on the MsFV by introducing a new iterative procedure to find the multiscale operators and the concept of support regions which reduces the method's complexity when applied to unstructured fine and coarse grids. The original version was only consistent on k-orthogonal fine grids due to the TPFA discretization, but filtering methods have been developed to also enable consistent multipoint schemes on the fine scale. Meanwhile, the Multiscale Control Volume method (MsCV) replaces the TPFA by the Multipoint Flux Approximation with a Diamond stencil (MPFA-D) scheme on the fine-scale while further enhancing the generation of the geometric entities to allow unstructured grids on the fine and coarse scales for two-dimensional simulations. In this work we propose an extension to three-dimensional geometries of both the MsCV and the algorithm to obtain the multiscale geometric entities based on the concept of a background grid, a coarser grid used as a proxy for the primal coarse grid. We modify the original MPFA-D method to use the very robust Global Least Squares (GLS) interpolation technique to obtain the required auxiliary nodal unknowns. We also introduce an enhanced version of the 3-D MsCV with the incorporation of the enhanced MsRSB (E-MsRSB) to enforce M-matrix properties and improve convergence. Finally, we employ the MsCV operators in a two-stage smoother to show how it can be used as a good iterative procedure to recover the fine-scale solution. We show that the 3-D MsCV method produces good results employing unstructured grids on both scales to handle the simulation of the single-phase flow in anisotropic, and heterogeneous porous media and that the smoothing procedure is able to accurately retrieve the fine-scale solution within a few iterations.

The inverse problem for a class of implicit differential equations and the coisotropic embedding theorem

We carry on the approach used in [L. Schiavone, The inverse problem within free Electrodynamics and the coisotropic embedding theorem, Inter. J. Geom. Meth. Mod. Phys. 21(7) (2024) 2450131] to provide a solution for the inverse problem of the calculus of variations for Maxwell equations in vacuum and we provide an abstract theory including all implicit differential equations that can be formulated in terms of vector fields over pre-symplectic manifolds.

A fitted parameter convergent finite difference scheme for two-parameter singularly perturbed parabolic differential equation

The objective of this paper is to develop a numerical scheme that is uniform in its parameters for a specific type of time-dependent parabolic problem with two perturbation parameters. The existence of these two parameters in the terms with the highest-order derivatives results in the formation of boundary layer(s) in the solution of such problems. Solving these model problems using classical methods does not yield satisfactory results due to the layer behavior. Therefore, nonstandard finite difference schemes have been developed as a means to obtain numerical solutions for these problems. To develop the scheme, we employ the Crank-Nicolsondiscretization on a uniform time mesh and apply a fitted operator method with a uniform spatial mesh. We have established the stability and convergence of the proposed scheme. The proposed scheme exhibits uniform convergence of second order in the temporal direction and first order in the spatial direction. However, temporal mesh refinements is employed to enhance the order to two in both directions. Model examples are provided to validate the practicality of the proposed numerical scheme.

Eğitim Sistematiğinde Analitik Düşünme Öğretim Model ve Stratejilerinin İncelenmesi

21. in the developing world of the century, increasing global competition, access to technology, digital information and tools also affect the qualities that individuals should have. The adaptation of individuals to the advances in technology and the rapid developments in the production and transfer of information as a result requires them to use their thinking skills effectively. Therefore, 21. in the light of the century requirements, it is considered important to design educational policies and practices in order for students to achieve these skills. In addition, the curriculum, school, learning environments and teacher factors should also be included in this draft process. Undoubtedly, one of the most important issues that we face in this context is the development of analytical thinking teaching models and strategies in educational systematics. Analytical thinking The reasoning model is a teaching strategy that aims to involve students in the reasoning process or the solution of complex problems through peer or teacher-led group discussion in order to encourage them to think. The main point of the model is the criticisms against the traditional classroom discussion. It is criticized because the traditional classroom discussion is mostly dominated by the teacher and takes place in the form of a monologue with the teacher's questions to initiate the discussion-answer-evaluation. Educational thinkers suggest that students' conversations about their thinking processes and engaging in mutual dialogue develop analytical and independent thinking. Based on this view, they stated that this model, which includes collaborative reasoning discussion, is effective in analytical thinking education. At the first stage of the implementation of the model, students are taught the language, principles and skills of analytical thinking clearly and directly. Afterwards, students are supported to use these principles and skills in their learning. Students are being engaged in a series of thinking tasks that involve teacher- or peer-led collaborative reasoning discussions. Key Words: Educational Systematics, Analytical Thinking, Reasoning, Teaching Models and Strategies

Reliability on the Internet of Things with designing approach for exploratory analysis

The Internet of Things (IoT) proposes to transform human civilization so that it is smart, practical, and highly efficient, with enormous potential for commercial as well as social and environmental advantages. Reliability is one of the major problems that must be resolved to enable this revolutionary change. The reliability issues raised with specific supporting technologies for each tier according to the layered IoT reliability are initially described in this research. The research then offers a complete review and assessment of IoT reliability. In this paper, various types of reliability on the IoT have been analyzed with each layer of IoT to solve the issues of failure rates, latency, MTTF, and MTBF. Each parameter has a certain classification and perception as well as enhancement in efficiency, accuracy, precision, timeliness, and completeness. Reliability models provide efficient solutions for different IoT problems, which are mirrored in the proposed study and classified with four types of reliabilities. The field of IoT reliability exploration is still in its initial phases, despite a sizable research record. Furthermore, the recent case study of CHISS is elaborated with discovered behaviors including brand-new aspects such as the multifaceted nature of evolving IoT systems, research opportunities, and difficulties.

Exact and numerical solutions of a free boundary problem with a reciprocal growth law

Abstract A two-dimensional free boundary problem is formulated in which the normal velocity of the boundary is proportional to the inverse of the gradient of a harmonic function $T$. The field $T$ is defined in a simply connected region which includes the point at infinity where it has a logarithmic singularity. The growth problem in which the boundary expands outward is formulated both in terms of the Schwarz function of the boundary and a Polubarinova-Galin equation for the conformal map of the region from the exterior of the unit disk. An expanding free boundary is shown to be stable and explicit solutions for growing ellipses and a class of polynomial lemniscates are derived. Numerical solution of the Polubarinova-Galin equation is used to compute the evolution of the boundary having other initial shapes.

On dynamical system modeling of learned primal-dual with a linear operator K : stability and convergence properties

Learned Primal-Dual (LPD) is a deep learning based method for composite optimization problems that is based on unrolling/unfolding the primal-dual hybrid gradient algorithm. While achieving great successes in applications, the mathematical interpretation of LPD as a truncated iterative scheme is not necessarily sufficient to fully understand its properties. In this paper, we study the LPD with a general linear operator. We model the forward propagation of LPD as a system of difference equations and a system of differential equations in discrete- and continuous-time settings (for primal and dual variables/trajectories), which are named discrete-time LPD and continuous-time LPD, respectively. Forward analyses such as stabilities and the convergence of the state variables of the discrete-time LPD to the solution of continuous-time LPD are given. Moreover, we analyze the learning problems with/without regularization terms of both discrete-time and continuous-time LPD from the optimal control viewpoint. We prove convergence results of their optimal solutions with respect to the network state initialization and training data, showing in some sense the topological stability of the learning problems. We also establish convergence from the solution of the discrete-time LPD learning problem to that of the continuous-time LPD learning problem through a piecewise linear extension, under some appropriate assumptions on the space of learnable parameters. This study demonstrates theoretically the robustness of the LPD structure and the associated training process, and can induce some future research and applications.

Diastereo-Divergent Synthesis of Ring A-lactones Derived From Cholesterol and Diosgenin. A Convenient Solution for an Old Problem. NMR and X-Ray Characterization

A convenient protocol for the synthesis of A-ring lactones derived from cholesterol was developed. A lactone reduction-lactol separation-reoxidation sequence, applied to the inseparable mixture of diastereomeric lactones allows the production of multigram amounts of each lactone in pure form. The same sequence applied to A-ring lactones derived from diosgenin produced similar results. A detailed NMR characterization of all the obtained lactones is also provided. X-ray diffraction corroborated the structure of the obtained compounds.

Arbitrary High Order ADER-DG Method with Local DG Predictor for Solutions of Initial Value Problems for Systems of First-Order Ordinary Differential Equations

Arbitrary High Order ADER-DG Method with Local DG Predictor for Solutions of Initial Value Problems for Systems of First-Order Ordinary Differential Equations

The poroelastic layer with an axisymmetric cylindrical hole under different types of loading

The exact solution of the poroelastic axisymmetric problem for a layer with a cylinderical hole is constructed under assumptions of Biot's model. The calculations provided by derived explicit formulas for full stress and pore pressure allow to state some important dependencies between the poroelastic stress state of the layer and type of poroelastic materials, loading types and height of the layer.

Solution of a Scalar Two-Dimensional Nonlinear Problem of Diffraction on Objects of Arbitrary Shape

Solution of a Scalar Two-Dimensional Nonlinear Problem of Diffraction on Objects of Arbitrary Shape

Input‐output linearization and decoupling of mechanical control systems

AbstractIn this article, we present the problem of simultaneous input‐output feedback linearization and decoupling (noninteracting) for mechanical control systems with outputs. We show that the natural requirement of preserving mechanical structure of the system and of transformations imposes supplementary conditions when compared to the classical solution of the same problem for general control systems. These conditions can be expressed using objects on the configuration space only. We illustrate our results with several examples of mechanical control systems.

Stable difference scheme for the numerical solution of the source identification problem for hyperbolic equations

UDC 517.9 We present a stable difference scheme of the second order of accuracy for a one-dimensional hyperbolic equation. The well-posedness of the difference scheme is established. Numerical results are presented.

Риск-ориентированный анализ безопасности и защищенности промышленных объектов на основе характеристик прочности и ресурса

The concept of computation and experimental determination of safety and protectability of industrial facilities on parameters of risk of initiation of refusals, accidents and disasters taking into account possibility of regular and emergency situations is considered. The scientifically substantiated, normalized and controlled parameters of risks estimated by criteria of strength, life-time and survivability are its basis. Risks at the same time are estimated on probabilities of initiation of emergency situations and losses accompanying them at their interdependence. It is shown that generally safety is defined by ability of installations not to pass into emergency and catastrophic states with drawing significant damages to the person, a technosphere and environment; the risk is defined by probability of initiation on installation of adverse situations and possible losses from these situations; protectability is defined by ability of installation to resist to initiation and an evolution of adverse situations (refusals, accidents, disasters) in regular and emergency conditions. The new perspective direction for maintenance of conditions of safe service of industrial facilities is that which initially forms the level of their protectability, and this protectability is defined by the formed and acceptable risks. In this case the solution of basic problems of protectability, safety and risk has to be guided surely by the solution of problems of strength, a life-time, survivability in their direct interaction This circumstance is based on a quantitative estimation of conditions of service damages accumulation and on the analysis of conditions of transition from regular to the damaged and limit states of installation taking into account criteria of strength, fatigue life and survivability. The solution of practical problems of maintenance of strength, life-time and safety within of strength, life-time and risk-focused design assumes determination of nominal and local stresses from service loadings in the most loaded zones with use of characteristics of mechanical properties of constructional materials. In the paper it is put and solved the new scientific and almost important problem about risk-focused definition, maintenance, increase and a standartization of complex safety and protectability of technosphere installations by criteria of the acceptable and controlled risks.

DETERMINATION OF A KERNEL IN A NONLOCAL PROBLEM FOR THE TIME-FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION

In this work, we consider an inverse problem of determining the kernel of a fractional diffusion equation. The backward problem is the initial-boundary/value problem for this equation with non-local initial and homogeneous Dirichlet conditions. To determine the kernel, an overdetermination condition of the integral form is specified for the solution of the backward problem. Using the Fourier method and an ordinary fractional differential equation with a non-local boundary condition, the inverse problem is reduced to an equivalent problem. Further by using the fixed point argument in suitable Sobolev spaces, the global theorems of existence and uniqueness for the solution of the inverse problem are obtained.

Merging preferences into the best solution seeking for many-objective optimization problems

Finding out a best solution of the multi-objective optimization problem (MOP) or many-objective optimization problem (MaOP) in the user’s view, is a significant and practical problem. The multi-objective evolutionary algorithms (MOEAs) are applied to solve the MaOPs. Considering many conflicting objectives, they would generate numerous nondominated solutions. Merging the preferences from the user to objectives is an effective way to measure the nondominated solutions and find out the best one (a posterior approach). But the preference relations may be contradictory and highly sparse. In this paper, we propose a process of finding out a best solution with preference relations among attributes (BSPA). In which, we emphasize to test the contradiction and ease the high sparsity of preference relations, then an available preference degree matrix is obtained and merged into the selection of best solution. Based on the proposed process, three methods of NSGA-II-BSPA, P-NSGA-II and P-GA are proposed to solve the best solution of an MOP or MaOP. The experiments are conducted, and the metrics of contradiction probability, feasibility and availability are proposed to measure the BSPA and the vigorous results are obtained. At last, three case studies are adopted to verify the proposed methods’ effectiveness and efficiency. Meanwhile, the hypothesis tests are conducted and the results indicate that the obtained best solutions of proposed methods are satisfiable.

IDENTIFICATION OF POSITIONS OF SEPARATED RIGID INCLUSIONS BY BOUNDARY MEASUREMENTS FOR A SIGNORINI PROBLEM

A variational inequality describing an elastic body with a finite set of rigid inclusions is considered. The Signorini condition is imposed on a part of the boundary of the body. On the other part a homogeneous Dirichlet boundary condition is specified. The inclusions are arranged such that distance between any two inclusions is not less than a given positive number. All inclusions are located at a nonzero distance from the outer boundary. An inverse problem is investigated, which consists in identification of positions of the rigid inclusions from the measurement of displacements on an observation boundary. Continuous dependency of the solution of the forward problem on parameters of inclusions’ location and rotation is established. This provides existence of a solution for the inverse identification problem.

Iterated fractional Tikhonov method for recovering the source term and initial data simultaneously in a two-dimensional diffusion equation

In this paper, an inverse problem of a two-dimensional diffusion equation is considered. The purpose here includes recovering not only the source term but also the initial value from given observations at two fixed times t=T1 and t=T2. The uniqueness of the solutions for the inverse problem is given. Instead of the classical Tikhonov regularization strategy, we propose an iterated fractional Tikhonov regularization method to solve this problem, an a priori and an a posterior parameter selection rules and corresponding convergence rates are derived. For verification of the theoretical estimates, several numerical examples are constructed and compared with the standard iterated Tikhonov regularization method.

Predictive modeling of shallow tunnel behavior: Leveraging machine learning for maximum convergence displacement estimation

Accurate prediction of maximum convergence in unsupported, shallow tunnel construction is crucial for optimizing the lining and ensuring tunnel safety. Machine learning (ML) algorithms, especially through boosting techniques, enable effective solution of complex engineering problems and demonstrate their capabilities in problem solving and optimization. In this study, the FLAC 3D package was used to create a robust and validated database of 954 datasets. Five tree-based ML algorithms, including extreme gradient boosting (XGBoost), adaptive boosting (AdaBoost), gradient boosting machine (GBM), histogram-based gradient boosting (HGB) and categorical boosting (CatBoost), were used to predict the maximum convergence displacement for unsupported shallow tunnels. For the test dataset, XGBoost outperformed the other models with an excellent coefficient of determination of 0.9633, a minimum mean absolute error of 0.0021 and a low root mean squared error of 0.00725. HGB followed closely behind, and GBM and CatBoost showed strong performances, while Adaboost was less effective. The superior performance of XGBoost highlights its effectiveness in predicting maximum convergence in shallow tunnels. An in-depth sensitivity analysis within the XGBoost model showed the significant influence of soil elastic modulus on the maximum convergence displacement in unsupported tunnels. The remarkable results achieved by the XGBoost algorithm on our complex tunnel convergence predictions illustrate the profound ability of ML to tackle complicated geotechnical challenges. This interdisciplinary collaboration demonstrates the potential of advanced algorithms to improve safety and efficiency in construction, underlining the crucial role of technology in tackling complex problems and establishing a new paradigm for innovation in the field.