Efficient and Stable Voxel-Based Algorithm for Computing 3D Zernike Moments and Shape Reconstruction

3D Zernike moments based on 3D Zernike polynomials have been successfully applied to the field of voxelized 3D shape retrieval and have attracted more attention in biomedical image processing. As the order of 3D Zernike moments increases, both computational efficiency and numerical accuracy decrease. Due to this phenomenon, a more efficient and stable method for computing high-order 3D Zernike moments was proposed in this study. The proposed recursive formula for computing 3D Zernike radial polynomials combines the recursive calculation of spherical harmonics to develop a voxel-based algorithm for the calculation of 3D Zernike moments. The algorithm was applied to the 3D shape Michelangelo's David with a size of 150×150×150 voxels. As compared to the method without additional acceleration, the proposed method uses a group action of order sixteen orthogonal group and saving unnecessary iterations, the factor of speed-up is 56.783±3.999 when the order of Zernike moments is between 10 and 450. The proposed method also obtained an accurate reconstructed shape with the error rate (normalized mean square error) of 0.00 (4.17×10^-3) when the reconstruction was computed for all moments up to order 450.

Lattice star and acyclic branched polymer vertex exponents in 3d

Numerical values of lattice star entropic exponents $\gamma_f$, and star vertex exponents $\sigma_f$, are estimated using parallel implementations of the PERM and Wang-Landau algorithms. Our results show that the numerical estimates of the vertex exponents deviate from predictions of the $\eps$-expansion and confirms and improves on estimates in the literature. We also estimate the entropic exponents $\gamma_\mathcal{G}$ of a few acyclic branched lattice networks with comb and brush connectivities. In particular, we confirm within numerical accuracy the scaling relation $$ \gamma_{\mathcal{G}}-1 = \sum_{f\geq 1} m_f \, \sigma_f $$ for a comb and two brushes (where $m_f$ is the number of nodes of degree $f$ in the network) using our independent estimates of $\sigma_f$.

Preliminary Validation of a Low-Cost Motion Analysis System Based on RGB Cameras to Support the Evaluation of Postural Risk Assessment

This paper introduces a low-cost and low computational marker-less motion capture system based on the acquisition of frame images through standard RGB cameras. It exploits the open-source deep learning model CMU, from the tf-pose-estimation project. Its numerical accuracy and its usefulness for ergonomic assessment are evaluated by a proper experiment, designed and performed to: (1) compare the data provided by it with those collected from a motion capture golden standard system; (2) compare the RULA scores obtained with data provided by it with those obtained with data provided by the Vicon Nexus system and those estimated through video analysis, by a team of three expert ergonomists. Tests have been conducted in standardized laboratory conditions and involved a total of six subjects. Results suggest that the proposed system can predict angles with good consistency and give evidence about the tool’s usefulness for ergonomist.

Analysis of chosen numerical methods for the application in high order interior ballistics simulations

Considering constant development of the interior ballistics, along with new gun and ammunition designs, the necessity of in-depth analysis of the shot event is continuously increasing. Numerical simulations of interior ballistics problems are useful for optimising new designs or explaining complex issues, regarding performance instabilities and catastrophic failures. With the rise of the computing power, there is a significant urge to drive the numerical errors towards machine zero. This goal demands using methods of high order of accuracy in both space and time. Current methods allow to achieve an arbitrary order of numerical accuracy, thus allowing to shift the focus towards sophistication of the mathematical model of the studied phenomenon. Therefore, in this work, some numerical schemes, in context of finite volume method, are reviewed and studied using well established test problems. The results of the presented analysis are meant to become the basis for future development of a high order numerical scheme for simulation of interior ballistics problems.

Research on the Influence of Shear Turbulence on the Aerodynamic Loads Characteristics of Wind Turbine

In order to accurately analysis the aerodynamic loads characteristics of the wind turbine under different turbulent wind conditions, the horizontal homogeneity in the flow field without a wind turbine and the numerical accuracy of the homogeneous flow field with a wind turbine were validated against the experimental results. The aerodynamic loads of the wind turbine were studied under the conditions of the uniform wind with a uniform turbulence intensity, the uniform wind with a shear turbulence intensity, the shear wind with a uniform turbulence intensity and the shear wind with a shear turbulence intensity. The results show that the increasing turbulence intensity leads to a small reduction in the torque of the wind turbine. Compared with uniform wind, shear inflow leads to a sine or cosine variation in the aerodynamic performance of the wind turbine and a reduction in the wind turbine’s thrust and torque. Compared with uniform turbulence intensity, shear turbulence intensity leads to a reduction in the wind turbine’s thrust and torque, and a more obvious phase lag effect, but it has little influence on the yawing moment and pitching moment.

A Contribution to Analytical Solutions for Buckling Analysis of Axially Compressed Rectangular Stiffened Panels

Analytical solution to the buckling problems of stiffened panels subjected to in-plane compressive loads is presented. The total potential energy functional of stiffened panel is obtained by the summation of that of a line continuum and stiffened panel derived from elastic principles of mechanics. Minimizing the resulting equation with respect to deflection coefficient and rearranging gives the expression for obtaining the buckling load of stiffened panel. Exact deflection functions were substituted directly in the new solution and various edge conditions were considered in this analysis. Obtained results were compared with analytical results of previous works. The method is computationally efficient for complex edge conditions and gives high numerical accuracy.

Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines

We address a new numerical method based on a class of machine learning methods, the so-called Extreme Learning Machines (ELM) with both sigmoidal and radial-basis functions, for the computation of steady-state solutions and the construction of (one-dimensional) bifurcation diagrams of nonlinear partial differential equations (PDEs). For our illustrations, we considered two benchmark problems, namely (a) the one-dimensional viscous Burgers with both homogeneous (Dirichlet) and non-homogeneous boundary conditions, and, (b) the one- and two-dimensional Liouville–Bratu–Gelfand PDEs with homogeneous Dirichlet boundary conditions. For the one-dimensional Burgers and Bratu PDEs, exact analytical solutions are available and used for comparison purposes against the numerical derived solutions. Furthermore, the numerical efficiency (in terms of numerical accuracy, size of the grid and execution times) of the proposed numerical machine-learning method is compared against central finite differences (FD) and Galerkin weighted-residuals finite-element (FEM) methods. We show that the proposed numerical machine learning method outperforms in terms of numerical accuracy both FD and FEM methods for medium to large sized grids, while provides equivalent results with the FEM for low to medium sized grids; both methods (ELM and FEM) outperform the FD scheme. Furthermore, the computational times required with the proposed machine learning scheme were comparable and in particular slightly smaller than the ones required with FEM.

A SPH-GFDM Coupled Method for Elasticity Analysis

SPH (smoothed particle hydrodynamics) is one of the oldest meshless methods used to simulate mechanics of continuum media. Despite its great advantage over the traditional grid-based method, implementing boundary conditions in SPH is not easy and the accuracy near the boundary is low. When SPH is applied to problems for elasticity, the displacement or stress boundary conditions should be suitably handled in order to achieve fast convergence and acceptable numerical accuracy. The GFDM (generalized finite difference method) can derive explicit formulae for required partial derivatives of field variables. Hence, a SPH–GFDM coupled method is developed to overcome the disadvantage in SPH. This coupled method is applied to 2-D elastic analysis in both symmetric and asymmetric computational domains. The accuracy of this method is demonstrated by the excellent agreement with the results obtained from FEM (finite element method) regardless of the symmetry of the computational domain. When the computational domain is multiply connected, this method needs to be further improved.