Cartesian System Research Articles

Deep Reinforcement Learning-Assisted Teaching Strategy for Industrial Robot Manipulator

This paper introduces an innovative algorithm aimed at enhancing robot learning using dynamic trajectory modeling and time-dependent state analysis. By integrating reinforcement learning (RL) and trajectory planning, the proposed approach enhances the robot’s adaptability in diverse environments and tasks. The framework begins with a comprehensive analysis of the robot’s operational space, focusing on Cartesian coordinates and configuration systems. By modeling trajectories and states within these systems, the robot achieves sequential tracking of arbitrary states, facilitating efficient task execution in various scenarios. Experimental results demonstrate the algorithm’s efficacy in manipulation tasks and path planning in dynamic environments. By integrating dynamic trajectory modeling and time-dependent state analysis, the robot’s adaptability and performance improve significantly, enabling precise task execution in complex environments. This research contributes to advancing robot learning methodologies, particularly in human–robot interaction scenarios, promising applications in manufacturing, healthcare, and logistics.

Circular-ESG Model for Regenerative Transition

This paper presents a novel circular-ESG framework integrating circular economy (CE) principles with environmental, social, and governance (ESG) criteria to address the lack of uniform sustainability measures. We introduce normalized sustainability coordinates (NSCs) as a comprehensive metric for sustainability performance, reconciling economic development with environmental balance. The circular-ESG model employs a four-quadrant Cartesian system to map business model impacts on natural and socio-economic systems, ranging from linear open-loop to circular closed-loop ESG models. This framework enables empirical analysis through data-driven NSCs (−1 to 1) and establishes temporal key performance indicators. By incorporating the Human Development Index within ecological limits, the model promotes regenerative development aligned with planetary boundaries. The circular-ESG approach offers a practical tool for businesses, households, organizations, and policymakers to navigate sustainable development complexities. This integrated framework fosters innovation and supports a just transition towards regenerative practices, providing a roadmap for high human development within ecological limits. The circular-ESG model advances sustainability science and management, contributing to the discourse on measuring and implementing sustainable practices across sectors and scales. The model is currently conceptual; we encourage empirical validation and further research to explore its practical applications and effectiveness in real-world scenarios. While the provided examples of use cases serve as conceptual demonstrations, future research could empirically apply the model to real-world data.

Modeling the optimal deceleration for asymmetric rigid body motion under the influence of a gyrostatic moments and viscous friction

This study focuses on determining the required minimum-time (MT) for the spatial motion of a free rigid body (RB) experiencing gyrostatic moments (GMs) and viscous friction. The study assumes that the body’s center of mass coincides with the original point of two Cartesian systems of coordinates. An optimal control law for slow motion is established, and the corresponding time and phase pathways are analyzed. The innovative results are presented for two new cases through various graphs highlighting the positive effects of the GMs. A comparison is achieved between the obtained results and previous outcomes that did not consider gyrostatic moments, showing remarkable consistency with slight deviations that are discussed. The practical applications of this study, which limits itself to using gyroscopic theory to maintain the stability and balance of vehicles in which gyroscopes are used, as well as figuring out the trajectory of aircraft and marine vehicles, are what make it noteworthy.

Dynamic responses of transversely isotropic and layered elastic media with imperfect interfaces under moving loads

Flexible pavement is widely used in engineering practice but is often subjected to the moving traffic loads, with imperfect contact behavior at the interfaces between adjacent layers. This study investigates transversely isotropic and layered elastic media with imperfect interfaces under moving vertical and horizontal loads using a semi-analytical method. The governing equation for moving loads is established within a Cartesian coordinate system and by virtue of the Galilean transformation, which is further decoupled into two ordinary differential equations in terms of the powerful Cartesian system of vector functions. General solutions for any layer are obtained, and the dual-variable position method is applied to derive the semi-analytical solutions for the layered pavement in the vector function domain. The lately introduced refined conversion algorithm, originally from the discrete convolution-fast Fourier transform (DC-FFT) algorithm, is applied to obtain the solution in the physical domain, which can efficiently remove the Gibbs effect near the source. The solutions are validated by comparison with existing solutions and numerical examples are presented to study the effect of interface modulus, moving load velocity, Young’s modulus of asphalt concrete and horizontal/vertical loading ratio on the surface dynamic response of the flexible pavement. Finally, the fatigue and rutting life of the pavement structures corresponding to different imperfect interface moduli are analyzed. The present solution provides practical guidance for the design of flexible pavement.

Формування вихідних даних для вирішення задач маршового розрахунку надзвукового обтікання ракет різного компонування

This paper gives a general overview of components and layouts used in supersonic rockets of different purposes. The rocket layout is specified as a structure and a set of components (a wing, a rudder, a stabilizer, a destabilizer, and a superstructure) arranged along the rocket structure. The goal of this work is to develop a unified approach to specifying the shape parameters of rocket layouts regardless of the rocket type. For complex-shape rocket layouts, the paper proposes an approach in which the shapes of the rocket structure and the additional components installed thereon are specified independently. The additional components of the rocket layout are bound to the rocket structure using operation parameters. The use of the operation parameters binds each additional component of the rocket layout to the rocket structure, thus offering a unified method for specifying the geometrical parameters of variously shaped rocket layouts. This approach is developed towards more complex shapes of rocket layout elements arbitrarily placed on rocket structures. The outside shape of each rocket component is specified in a Cartesian system of coordinates rigidly bound thereto. A unified approach to specifying the outside shape of various rocket components is presented. According to the general scheme of specifying the geometrical parameters of rocket layout components, they are specified by three methods: analytically, by plan shape, and by plan shape with board and end chord profiles. To describe the outside shape of a component, the specification method and the number and the values of its key parameters are specified. To specify rocket layout input data, one has to fix the number of additional components to be installed on the rocket structure. For each layout component, the parameters that define its shape, location on the rocket structure, and deflection angle are specified. To each layout component there corresponds an input data set of its own. The set consists of parameters that define the shape of the component and parameters of its operation as a part of the layout. A standard input data file for specifying rocket layout shapes is configured.

Разработка и применение программы для автоматического нахождения невязки при пространственном контроле режимной метеорологической информации

Objective: to develop and apply software for automatic finding of discrepancies in automated meteorological stations in order to identify dubious and unreliable data without direct manual control in Fortran using PostgreSQL programming language queries. Write a program block for processing data from the archive of the database of meteorological stations of the unified network. Having provided a connection, with the help of requests, to ensure the receipt of data of the averaged values of ten-minute meteorological reports according to a special processing technique. Create a subroutine for solving the equation by the least squares matrix method, compare it to check the results with the linear regression method in a third-party application. Ensure proper recording of data before sending them to the database, prepare the necessary table for correct demonstration of data and user convenience in their use. Formulate correct queries to send the results of finding the discrepancy to the database. Formulate queries to create the necessary table, formulate queries and identify conditions for the implementation of the program for its more “flexible”functioning, that is, the ability to process data and find a discrepancy in the case of non-daily operation of the program. Methods: the methodology is similar to the principles of recommendations for the analysis of the results of spatial monitoring of regime meteorological information of the Main Geophysical Observatory named after Voeikova A. I. Methods include the translation of coordinates into a Cartesian system and the implementation of the solution of equation systems by the least squares method. Results: a program has been created that can work without the participation of an operator, performing automatic startup, data processing and data recording for further storage. Practical importance: the program allows you to receive data quickly due to the fast processing speed without errors caused by the human factor.

Adjoint-based shape optimization for radiative transfer in porous structure for volumetric solar receiver

Due to their large surface areas, porous structures are often used for volumetric solar receivers for efficient utilization of the solar energy. However, the precise simulation and optimization of radiative heat transfer inside porous structures are still challenging due to their complex geometries. In the present study, an adjoint-based shape optimization framework for radiative transfer in porous structures is first proposed. Specifically, an arbitrary complex geometry of a porous structure is represented by a level-set function embedded in a Cartesian grid system. The volume penalization method combined with the discrete ordinate method is employed to simulate a forward radiative transfer problem in a porous structure. Then, a cost functional for an adjoint analysis is defined by the volume average of the divergence of the radiative heat flux, which corresponds to the total heat absorbed by the porous structure with a negative sign. The adjoint equations for minimizing the cost functional, and the corresponding shape update formula are derived and implemented in an open-source software, OpenFOAM. The developed adjoint-based shape optimization framework is applied to three types of initial porous structures, i.e., SC Kelvin, BCC Kelvin, and square honeycomb models. For all the initial porous models, the front surface commonly extends towards the direction of the incident radiation, and consequently notable improvements of the absorption efficiency can be achieved through the optimization. In addition, a systematic parametric survey for the initial shape of the SC Kelvin model is conducted to reveal the impacts of the number of unit cells, the solid emissivity, and the solid temperature on the optimal shapes and the resulting absorption efficiencies.

Defects and waves in anisotropic and layered media: Stroh formalism in terms of the Cartesian system of vector functions

ABSTRACT When waves propagate through anisotropic elastic media, P- and SV-type waves (Rayleigh waves) are generally coupled with SH-type waves (Love waves). In contrast, in isotropic elastic media, SH/Love waves are decoupled and separate from other body/surface waves. However, the conditions under which these waves in anisotropic media may be decoupled remain unclear. In this paper, we introduce a Cartesian vector function system, named as the Cartesian LMN vector system, and derive solutions using this system within the Stroh formalism. This approach inherently accounts for both coupling and decoupling cases. Various source functions based on the Cartesian LMN vector system are derived. The Cartesian LMN system further enables a straightforward reduction to two-dimensional wave problems, including simplified source functions for line forces and lattice dislocations.

Design and construction of a fraction collector for liquid chromatography

The aim of this work is to design and implement a fraction collector for liquid chromatography, a chemical method to separate the components of a mixture. A fraction collector is a piece of equipment that automatically collects each of the recovered fractions. The collector´s CAD model (Computer Assisted Design), based on a Cartesian-type system, is developed in Autodesk's FUSION360 software, in which a stress and strain study is also carried out using finite element analysis to rule out any possible structural failure. Subsequently, for its implementation, the different components of the designed CAD model were built using 3D printing. The developed system takes as input variables the number of samples to collect and the time that must elapse before changing the head to the next tube to collect the next sample. For this, a control system is implemented using the Arduino uno development board, which controls the movement in the X and Y axes of the Cartesian system through two stepper motors, as well as the user interface that consists of an LCD screen and a group of buttons that allow you to set the operating parameters and visualize the status of the equipment. The equipment designed has shown functionality like that of commercial equipment with basic characteristics, which allows obtaining precise samples efficiently and at a lower cost.

Implementation of a level-set-based volume penalization method for solving fluid flows around bluff bodies

A volume penalization-based immersed boundary technique is developed and thoroughly validated for fluid flow problems, specifically flow over bluff bodies. The proposed algorithm has been implemented in an open source field operation and manipulation (OpenFOAM), a computational fluid dynamics solver. The immersed boundary method offers the advantage of inserting a complex solid object inside a Cartesian grid system, and therefore, the governing equations can be applied to such a simpler grid arrangement. For capturing the fluid–solid interface more accurately, the grid is refined near the solid surface using topoSetDict and refineMeshDict utilities in OpenFOAM. In order to avoid any numerical oscillation and to compute the gradients accurately near the interface, the present volume penalization method (VPM) is integrated with a signed distance function, which is also referred to as a level-set function. Benchmark problems, such as flows around a cylinder and a sphere, are considered and thoroughly validated with the results available in the literature. For the flow over a stationary cylinder, the Reynolds number is varied so that it covers from a steady two-dimensional flow to an unsteady three-dimensional flow. The capability of the present solver has been further verified by considering the flow past a vibrating cylinder in the cross-stream direction. In addition, a flow over a sphere, which is inherently three-dimensional due to its geometrical shape, is validated in both steady and unsteady regimes. The results obtained by the present VPM show good agreement with those obtained by a body-fitted grid using the same numerical scheme as that of the VPM, and also with those reported in the literature. The present results indicate that the VPM-based immersed boundary technique can be widely applicable to scientific and engineering problems involving flow past stationary and moving bluff bodies of arbitrary geometry.

Entropy generation in free convective micropolar couple stress regime in vertical channel

The study reports an application of homotopy perturbation method to investigate entropy generation in the steady micropolar couple stress fluidics inside a vertical porous medium channel. The channel is composed of two isothermal parallel walls maintained at different temperatures. The governing equations are framed in the Cartesian system. The boundary value problem depicting the thermofluidic configuration is treated by the homotopy perturbation method (HPM) and for its validation, the 4th-order Runge-Kutta scheme is also invoked. The quantities of interest, viz. skin friction, wall couple stress, Nusselt number computed by HPM, and 4th order R-K method are found to be in good agreement. After getting the velocity, temperature, and microrotation regime, the entropy involved with the thermodynamic process was modeled to facilitate future thermodynamic optimizations.

Analysis of Lightweight Structure Mesh Topology of Geodesic Domes

This paper presents two methods of shaping the mesh topology of lightweight structures as spherical domes. The two given methods of dividing the initial face of the polyhedra determine the obtained structures, which differ in the way of connecting the nodal points. These points were obtained by applying the algorithm for calculating spherical coordinates presented in the paper, which were then converted to the Cartesian system using transformation formulas. Two models of dome structures are presented, based on a 4608-hedron according to the first division method, and on a 4704-hedron, using the second proposed method with numerical analysis. Thus, the novelty of this paper is an implementation of the formulas and algorithms from geodesic domes based on the regular dodecahedron to the regular octahedron, which has not been presented so far. The choice of the shape of the structure has impacts on sustainable development, dictated by structural and visual considerations, leading to the design of a light structure with low consumption of construction material (steel), which can undoubtedly be helpful when making the final structure shape. In addition, according to this research, it can be concluded that using the first method to create a geodesic dome mesh is more straightforward, safer, and requires less design experience.

Influence of orientation of fibres on surface wave in fibre‐induced anisotropic elastic medium

AbstractAn isotropic elastic solid reinforced with a family of parallel fibres behaves anisotropic to any deformation. With orientation of all fibres along a coordinate axis in rectangular Cartesian system, this anisotropy reduces to transverse isotropy. Else with arbitrary orientation of fibre‐family, induced anisotropy lacks any symmetry. In this composite medium with arbitrary anisotropy, three‐dimensional wave motion decaying with depth propagates as a surface wave along all directions on plane boundary. Real phase velocity for this surface wave lies implicit in a system of three equations with complex coefficients. An appropriate transformation of this system yields a real characteristic equation, which is solved to get the anisotropic phase velocity of generalised surface wave. This phase velocity defines a complex slowness vector, which is used to calculate the particle motion at any point in the medium. Effects of fibre‐orientation are analysed, numerically, on the phase velocity and polarisation of surface wave. For example, in the reinforced fibres alters the contours of particle motion through increased ellipticity. However, in the presence of fibres, the decay of particle motion with depth slows down.

Design and analysis of a 4-axis cartesian robot for unloading plastic injection machines in industrial applications

In both industrial and educational settings, efficient handling of products from Plastic Injection Machines is crucial for precise and stable system operation. Enhancements in the design and production processes, achieved through the implementation of a Four Axis (4D) BOM type Cartesian System, lead to significant improvements in cost-effectiveness and product quality. In this study focuses on optimizing system operations, including rotational movements and the operation of the vertical cylinder through forward-backward movements. Finite element analysis is employed to investigate potential issues arising from shape changes in the mechanical structure due to dynamic loads on the plate joint connections. By addressing these concerns during the design phase through simulation, mechanical structure errors are eliminated, resulting in improved system performance.

Use of 2D FFT and DTW in Protein Sequence Comparison.

Protein sequence comparison remains a challenging work for the researchers owing to the computational complexity due to the presence of 20 amino acids compared with only four nucleotides in Genome sequences. Further, protein sequences of different species are of different lengths; it throws additional changes to the researchers to develop methods, specially alignment-free methods, to compare protein sequences. In this work, an efficient technique to compare protein sequences is developed by a graphical representation. First, the classified grouping of 20 amino acids with a cardinality of 4 based on polar class is considered to narrow down the representational range from 20 to 4. Then a unit vector technique based on a two-quadrant Cartesian system is proposed to provide a new two-dimensional graphical representation of the protein sequence. Now, two approaches are proposed to cope with the varying lengths of protein sequences from various species: one uses Dynamic Time Warping (DTW), while the other one uses a two-dimensional Fast Fourier Transform (2D FFT). Next, the effectiveness of these two techniques is analyzed using two evaluation criteria-quantitative measures based on symmetric distance (SD) and computational speed. An analysis is performed on five data sets of 9 ND4, 9 ND5, 9 ND6, 12 Baculovirus, and 24 TF proteins under the two methods. It is found that the FFT-based method produces the same results as DTW but in less computational time. It is found that the result of the proposed method agrees with the known biological reference. Further, the present method produces better clustering than the existing ones.

Numerical simulations of underwater explosions using a compressible multi-fluid model

We present a novel solver for simulating compressible multi-fluid multiphase flow in underwater explosions (UNDEXs). The developed solver uses a modified version of Saurel's six-equation model, which includes an additional total mixture energy equation to resolve discrepancies in the thermodynamic states predicted under shock conditions. Additionally, we integrate a more precise stiffened gas equation of state (SG-EOS) that is determined using a novel method to enhance the accuracy of predicting experimental data based on a shock Hugoniot curve. We also propose a solution procedure using the modified Saurel's six-equation model on a three-dimensional (3D) structured Cartesian grid system. This involves discretizing the equation system using a Godunov scheme with a two-fluid Harten-Lax-van Leer-Contact approximate Riemann solver and a MUSCL-Hancock primitive scheme with total-variation-diminishing limiters, achieving a second-order extension. Both the dimensional splitting and fractional-step methods are utilized to model one-dimensional (1D) operators, splitting them into sequential operators. The modified model is validated for 1D and 3D problems, including the water–air shock tube, cavitation, shock–bubble interaction, and UNDEX problems in a free field, near a free surface, and near a rigid dam. Our simulations accurately predict the shockwave propagation, shock and free-surface interactions, cavitation evolution, and water jetting impact characteristics, exhibiting satisfactory agreement with those of previous studies. The proposed solver provides insight into the effects of UNDEXs on rigid structures, with potential applications in engineering and defense. The proposed method for determining the SG-EOS parameters can be applied to other areas of research involving high-pressure multi-phase flows.

3D NUMERICAL STUDY OF HYDROYNAMICS AROUND A MONOPILE FOUNDATION UNDER COMBINED WAVE CURRENT EFFECT

A numerical investigation of hydrodynamics around a monopile foundation is presented in the paper. An open-source CFD program REEF3D is used for the present study. The REEF3D model solves the Reynolds-averaged Naiver-Stokes equation with k-w turbulence closure to obtain the flow hydrodynamics. The code utilizes a staggered cartesian grid system. Also, Message Passing Interface (MPI) based parallelization is used for domain decomposition. In order to ensure the precision of the flow field, the model is first validated for four different combined wave-current scenarios, where the currents and waves are following each other. The results obtained from the validation studies exhibit good agreement with the already reported experimental results. Initially, a grid convergence study has been performed to ensure that the Numerical wave tank is independent of the mesh size. Finally, numerical experiments corresponding to four different combined wave-current cases for different wave steepness are simulated using the code.

On the Use of Metal Sinter Powder in Laser Powder Bed Fusion Processing (PBF-LB/M).

Metal Laser Powder Bed Fusion (PBF-LB/M Powder Bed Fusion, Laser-Based/Metal) offers decisive advantages over conventional manufacturing processes. Complex geometries can be produced that cannot, or only to a limited extent, be manufactured with conventional manufacturing processes. One of the main disadvantages of the process are high investment and operating costs. In order to make the PBF-LB/M process accessible to new research areas, the costs need to be reduced. Therefore, this work investigates whether laser beam sources and motion systems in currently established PBF-LB/M systems can be replaced by more cost-effective components. To reduce the operating costs for PBF-LB/M, the studies are carried out based on previous work with water-atomized, process-foreign sinter powder instead of gas-atomized, spherical PBF-LB/M powders. A cost-efficient, low-alloyed powder is selected (Höganäs HP1) and processed on two different PBF-LB/M machines with a restricted process window using process parameter values that current low-cost machines can achieve. The results show that a multimode fiber laser leads to a more stable process and wider melt pools compared to a single mode fiber laser. In addition, a lower sensitivity of the process with respect to modified process parameters is observed for the multimode laser, resulting in a wider range of stable process windows. A Cartesian motion system (gantry) is suitable for use in PBF-LB/M despite lower scan speeds compared to galvanometer scanners. Beam guidance in the XY-plane offers new possibilities for machine and process design that are not possible with usual scanner systems.

Dynamic loading in a transversely isotropic and layered elastic half-space

By introducing the Cartesian system of vector functions, we investigate the responses of a layered transversely isotropic elastic half-space induced by a dynamic load. The load is vertically applied in the layered half-space. It can be either time-harmonic or horizontally moving with a given velocity. It is demonstrated that, in each layer, in terms of the Cartesian vector functions, we need only a 4 × 4 system of equations for the expansion coefficients of the displacement and traction components, instead of a 6 × 6 system as usually presented. Furthermore, utilizing the vector functions, both the time-harmonic and moving-load cases can be solved in the same way. For the layered case, the previously introduced dual-variable and position method is further used to propagate the solutions from one layer to the other, with unconditional stability. The fast Fourier transform (FFT) is applied to obtain accurate results in the space/time domain efficiently by the numerical inverse Fourier transform, properly developed within the framework of the discrete convolution-FFT (DC-FFT) algorithm. The unique formulation and its corresponding sophisticated algorithm are first validated against existing solutions, and then applied to calculate the displacements and stresses in a layered transversely isotropic half-space. Finally, a typical three-layer flexible pavement structure under a moving circular load is analyzed in detail. Numerical results clearly show the significant effects of both material anisotropy and layering. The present formulation is concise and efficient for the calculation of all the displacements and stresses, which can be applied to the involved engineering practice. The results can also serve as benchmarks for future research in this direction.

Study and application of geometric concepts in the movement of a vehicle using cartesian coordinates

Autonomous vehicles are already a reality in many contexts. Most of them need sensors to move around their environment, which increases the complexity and cost of the project. This study uses the coordinates of the Cartesian plane to orient a prototype vehicle in relation to its geographic space, allowing it to move to predefined coordinates without the use of any sensors. For the steering system of the prototype, concepts of point, line, and vectors were used. The initial position of the vehicle is represented by a vector, which informs its direction in the plane, having as final destination any point in the Cartesian system. From this information, a displacement vector is created, which leads the prototype to the reference point, and indicates the angle it must rotate. Regarding the direction of rotation, the concept of parallel lines between the prototype's vector and the destination point was used, where the analysis of their y-intercept determines if the vehicle rotates to the left or right. So, with the use of vectors and the Cartesian plane, it was possible to determine fundamental information for the locomotion of the prototype, such as angle and direction of rotation, although there was some difficulty in determining the graphic location of the vector.