Radial Basis Functions Interpolation Technique Research Articles

Multi-body mesh deformation using a multi-level localized dual-restricted radial basis function interpolation

Multi-body dynamic problems with moving boundaries are prevalent in the computational fluid dynamics. In these problems, the original mesh is unsuitable for subsequent solution steps and is needed to be deformed. The radial basis function (RBF) interpolation is a common algorithm for the mesh deformation task. However, the multi-body mesh may contain numerous individuals and volume nodes, which will harm the computational efficiency. In order to optimize this process, we propose a new method for the mesh deformation of the multi-body configuration. In this new approach, each individual is deformed separately. Thus the global problem is decomposed into a series of local mesh deformation problems. As the computational cost to construct the interpolation system in RBF algorithm is proportional to the cube of the number of support points on the surface, converting it into multiple local mesh deformation problems can effectively reduce the CPU cost. To treat each local problem, we employ a dual-restricted RBF interpolation technique which could avoid the influence of moving individual on the other individuals. This new localized approach effectively improves the computational efficiency to construct the interpolation system but sometimes will increase the CPU cost of the mesh updating procedure. To avoid this drawback, the existed multi-level restricted RBF strategy is coupled with the new localized method to further reduce the CPU cost to update the mesh. The combination of the two techniques could enhance their advantages and avoid their drawbacks. Some numerical examples have demonstrated the abilities of the new algorithm. For instance, in the case of the three-dimensional birds flock, the CPU time to construct the interpolation system and deform the volume mesh was respectively reduced by three and two orders of magnitude compared to the global single-level method.

Enhancing CFD predictions in shape design problems by model and parameter space reduction

In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

Smooth point-to-point trajectory planning for robot manipulators by using radial basis functions

SUMMARYThe paper introduces the use of radial basis functions (RBFs) to generate smooth point-to-point joint trajectories for robot manipulators. First, Gaussian RBF interpolation is introduced taking into account boundary conditions. Then, the proposed approach is compared with classical planning techniques based on polynomial and trigonometric models. Also, the trajectory planning problem involving via-points is solved using the proposed RBF interpolation technique. The obtained trajectories are then compared with those synthesized using algebraic and trigonometric splines. Finally, the proposed method is tested for the six-joint PUMA 560 robot in two cases (minimum time and minimum time-jerk) and results are compared with those of other planning techniques. Numerical results demonstrate the advantage of the proposed technique, offering an effective solution to generate trajectories with short execution time and smooth profile.

Medical Image Inpainting with RBF Interpolation Technique

Inpainting is a method for repairing damaged images or to remove unwanted parts of an image. While this process has been performed by professional artists in the past, today, the use of this technology is emerging in the medical area – especially in the medical imaging realm. In this study, the proposed inpainting method uses a radial basis function (RBF) interpolation technique. We first explain radial basis functions and then, the RBF interpolation system. This technique generally depends on matrix processes. Thus, matrix operations are executed after the interpolation and form a main part of the process. This interpolation matrix has a known value used for interpolating n values and we need to find M – 1 for the n + 1 values of the original and inserted data. Implementation of an inpainting operation is carried out in an object-oriented programming (OOP) language. This is where the process is completed. The algorithm used in this study has a graphical user interface. Further, several skin images are used for testing this system. The obtained output represents a high level of accuracy that can support the validity of the proposed method.

Thin-plate-Spline Curvilinear Meshing on a Calculus-of-Variations Framework

High-order, curvilinear meshes have recently become popular due to their ability to conform to the geometry of the domain. Curvi- linear meshes are generated by first constructing a straight-sided mesh and then curving the boundary elements (and, consequently, some of the interior edges and faces) to respect the geometry of the domain. The locations of the interior vertices can be viewed as an interpolation of a mapping function whose values at the boundary vertices (of the straight-sided mesh) are equal to the vertex locations on the curved domain. We solve this interpolation problem using radial basis functions (RBFs) by extending earlier algo- rithms that were developed for linear mesh deformation. An RBF interpolation technique using a biharmonic kernel is also called a thin plate spline. We analyze the resulting mapping function (the RBF interpolation) in a framework based on calculus of variations and provide a detailed explanation of the reasons the thin plate kernel RBF-based techniques have always yielded higher-quality meshes than other techniques. It is known that the thin plate kernel RBF interpolation minimizes the “bending energy” associated with a function, which depends on its second-order partial derivatives. We show that the minimization of the bending energy attempts to preserve the shape of an element after the transformation. Other techniques minimize either a functional (that depends on the first-order partial derivatives) that attempts to preserve the size of an element, or the bending energy in a smaller subspace of functions. Thus, our experimental results show that our algorithm generates higher-quality meshes than prior algorithms.