Non-orthogonal System Research Articles

Accurate extrinsic calibration method of a line structured-light sensor based on a standard ball

In order to implement 3D measurement in different measurement systems with line structured-light sensor, the extrinsic matrix for transforming the position between the structured-light sensor and the measurement platform must be calibrated. An extrinsic calibration method, achieved by measuring the fixed point (the centre of a standard ball) of the measuring system with the sensor in different positions, was proposed. In order to calculate the coordinate of the ball centre in the laser plane frame more accurately, the images containing fewer pixels were filtered and the noise around the slice was removed. Experimental study was carried out on a four-axis coordinate measuring machine (CMM) with a ball supplied by CIMCORE and showed that the method is simple; it can also be used in a non-orthogonal measurement system.

Expression of Joint Moment in the Joint Coordinate System

The question of using the nonorthogonal joint coordinate system (JCS) to report joint moments has risen in the literature. However, the expression of joint moments in a nonorthogonal system is still confusing. The purpose of this paper is to present a method to express any 3D vector in a nonorthogonal coordinate system. The interpretation of these expressions in the JCS is clarified and an example for the 3D joint moment vector at the shoulder and the knee is given. A nonorthogonal projection method is proposed based on the mixed product. These nonorthogonal projections represent, for a 3D joint moment vector, the net mechanical action on the JCS axes. Considering the net mechanical action on each axis seems important in order to assess joint resistance in the JCS. The orthogonal projections of the same 3D joint moment vector on the JCS axes can be characterized as "motor torque." However, this interpretation is dependent on the chosen kinematic model. The nonorthogonal and orthogonal projections of shoulder joint moment during wheelchair propulsion and knee joint moment during walking were compared using root mean squares (rmss). rmss showed differences ranging from 6 N m to 22.3 N m between both projections at the shoulder, while differences ranged from 0.8 N m to 3.0 N m at the knee. Generally, orthogonal projections were of lower amplitudes than nonorthogonal projections at both joints. The orthogonal projection on the proximal or distal coordinates systems represents the net mechanical actions on each axis, which is not the case for the orthogonal projection (i.e., motor torque) on JCS axes. In order to represent the net action at the joint in a JCS, the nonorthogonal projection should be used.

Performance Study of a Network Coded Non-orthogonal User Cooperation System over Nakagami-m Channels

Performance Study of a Network Coded Non-orthogonal User Cooperation System over Nakagami-m Channels

Wavelets in Littlewood–Paley space, and Mexican hat completeness

We resolve a long-standing question on completeness of the non-orthogonal Mexican hat wavelet system, in L p for 1 < p < 2 and in the Hardy space H p for 2 / 3 < p ⩽ 1 . Tools include the discrete Calderón condition, a generalization of the Daubechies frame criterion to a weighted L 2 space, and imbeddings of that weighted space into L p and Hardy spaces.

Simulation of triaxial induction measurements in dipping, invaded, and anisotropic formations using a Fourier series expansion in a nonorthogonal system of coordinates and a self-adaptive hp finite-element method

Borehole triaxial induction instruments were designed to diagnose and measure rock electrical conductivity parallel and perpendicular to the bedding plane. Experience has shown that the interpretation of triaxial induction measurements often requires numerical modeling for a proper diagnosis of rock electrical conductivity anisotropy in the presence of geometric effects such as dipping wells, layer boundaries, and invasion. We introduce a new algorithm to simulate triaxial induction measurements that combines a Fourier series expansion in a nonorthogonal system of coordinates with a 2D goal-oriented, self-adaptive, high-order [Formula: see text] finite-element method. This procedure enables the accurate and reliable simulation of triaxial induction measurements across reservoir rock formations with extreme contrasts of electrical conductivity while reducing the 3D computational complexity associated with deviated wells. Numerical results indicate that borehole dip effects on triaxial induction measurements are larger than on standard coaxial induction measurements. The sensitivity of triaxial induction measurements to transversely isotropic rock formations decreases with increasing dip angle.

Non-Orthogonal View Iris Recognition System

This paper proposes a non-orthogonal view iris recognition system comprising a new iris imaging module, an iris segmentation module, an iris feature extraction module and a classification module. A dual-charge-coupled device camera was developed to capture four-spectral (red, green, blue, and near-infrared) iris images which contain useful information for simplifying the iris segmentation task. An intelligent random sample consensus iris segmentation method is proposed to robustly detect iris boundaries in a four-spectral iris image. In order to match iris images acquired at different off-axis angles, we propose a circle rectification method to reduce the off-axis iris distortion. The rectification parameters are estimated using the detected elliptical pupillary boundary. Furthermore, we propose a novel iris descriptor which characterizes an iris pattern with multiscale step/ridge edge-type maps. The edge-type maps are extracted with the derivative of Gaussian and the Laplacian of Gaussian filters. The iris pattern classification is accomplished by edge-type matching which can be understood intuitively with the concept of classifier ensembles. Experimental results show that the equal error rate of our approach is only 0.04% when recognizing iris images acquired at different off-axis angles within ±30°.

Development of a Theoretical Process Map for Laser Cladding Using a Three-Dimensional Conduction Heat Transfer Model

In this article, a three-dimensional conduction heat transfer model is developed to predict the clad geometry (e.g., height, width, and dilution) and microstructure (scale and morphology) of the solidified layer for a laser cladding process. The effect of controllable input process parameters like absorbed laser power, powder deposition rate, and processing speed on the clad characteristics is critically assessed with the help of dimensionless parameters. A process map is developed which enables operators to pick up the proper process parameters for a feasible laser cladding process with desirable characteristics. The present conduction model is solved using the finite-volume method in a multiblock, nonorthogonal grid system. The effect of melt pool convection is taken care of by introducing an enhanced thermal conductivity factor for the molten pool.

PHY Abstraction Methods for OFDM and NOFDM Systems

In the paper various PHY abstraction methods for both orthogonal and non-orthogonal systems are presented, which allow to predict the coded block error rate (BLER) across the subcarriers transmitting this FEC-coded block for any given channel realization. First the efficiency of the selected methods is investigated and proved by the means of computer simulations carried out in orthogonal muticarrier scenario. Presented results are followed by the generalization and theoretical extension of these methods for non-orthogonal systems.

Comparison of waterjet performance in tracked vehicles by impeller diameter

A waterjet propulsion system has many advantages over a conventional screw propeller system in amphibious military vehicles. These advantages include good maneuverability at low speeds, operability in shallow waters, high thrust at low speeds to aid maneuverability and water exit. A flush type waterjet propulsion unit (duct, impeller, stator, and nozzle) was designed for an amphibious tracked vehicle that can cross rivers or lakes using a twin waterjet propulsion system. Due to its compactness and weight, primary considerations in military tracked vehicles, axial flow waterjets are usually used in spite of their relatively low speed. Impeller diameter is a specific parameter for determining the size of a waterjet, and it is related to weight. The weight and compactness of propulsion system are important factors in amphibious military vehicles because of their effect on buoyancy. In terms of buoyancy, a smaller diameter is expected to be better, while in terms of performance, a large diameter is expected to be better. In the present study, the performance of waterjet systems using different impeller diameters was investigated in order to determine the optimum waterjet for a 250 hp amphibious tracked vehicle. The RANS equations were solved using a moving, non-orthogonal multiblocked grid system. The momentum flux approach and the ITTC 96 standard method, which have been used worldwide for the analysis of waterjet performance analysis, were used in the experiments. This paper emphasizes the performance of waterjets by diameter size.

Experiment and simulation on interface shapes of an yttrium aluminium garnet miniature molten zone formed using the laser-heated pedestal growth method for single-crystal fibers

A two-dimensional simulation was employed to study the melt/air and melt/solid interface shapes of the miniature molten zone formed in a laser-heated pedestal growth (LHPG) system. Using a non-orthogonal body-fitting grid system with the control-volume finite-difference method, the interface shape can be determined both efficiently and accurately. During stable growth, the dependence of the molten-zone length and shape on the heating CO2laser is examined in detail under both the maximum and the minimum allowed powers with various growth speeds. The effect of gravity on the miniature molten zone is also simulated and the possibility of horizontally oriented LHPG is revealed. Such a horizontal system is good for the growth of long crystal fibers.

Numerical modelling of EHD effects on heat transfer and bubble shapes of nucleate boiling

In this article, mathematical and numerical models are developed to study pure electrohydrodynamic (EHD) effects on heat transfer and bubble shapes when an initial bubble attached to a superheated horizontal wall in nucleate boiling. In the modelling of EHD effects on heat transfer, an undeformed bubble is considered; the electric body force and Joule heat are added to the momentum and energy equations; governing equations for heat, fluid flow and electric fields are coupled numerically and solved using a non-orthogonal body-fitted mesh system with necessary interfacial treatments at the gas–liquid boundary. While, to study the pure effect of EHD on the deformation of the bubble, the evaluation of a deformable bubble without heat transfer is simulated by volume of fluid (VOF) method based on an axial symmetric Cartesian coordinate system. The simulations indicate that EHD can effectively enhance heat transfer rate of nucleate boiling by influencing the motion of the ring vortex around the bubble and that bubble can be elongated due to the pull in axial direction and push in the negative radial direction by the electric field force.

냉각탑 주위 장애물에 의한 재순환 현상에 관한 3차원 수치해석

The present study has been preformed to investigate the effect of obstacles around a cooling tower with air-guide to prevent recirculation. The external region as well as the cooling tower are included in the computational domain to analyze the flow phenomena around a cooling tower accurately. Three-dimensional analysis is performed using the finite volume method with non-orthogonal and unstructured grid system. The standard turbulence model is used to consider the turbulence effect. In order to investigate the recirculation phenomena, flow and temperature fields are calculated with the distance between cooling tower and obstacle, the allocated geometrical type and the air-guide. The moisture fraction rates decrease with increment of the distance between cooling tower and obstacle. The effect of air-guide to reduce the mean recirculation rate is obviously observed.

Simulation of DC dual-laterolog measurements in complex formations: A Fourier-series approach with nonorthogonal coordinates and self-adapting finite elements

Dual laterolog (DLL) makes use of a galvanic conduction principle to focus electrical currents into rock formations, thereby minimizing shoulder and borehole effects in the measurement of formation resistivity. The tool includes two separate focusing systems: deep-sensing (LLd) and shallow-sensing modes (LLs). Laterolog current-focusing systems were designed for operation primarily in vertical boreholes penetrating horizontal layers; only recently their design has been revised for operation in deviated wells in the presence of electrical anisotropy. We simulated three-dimensional (3D) DLL measurements in dipping, invaded, and electrically anisotropic formations and appraised the corresponding effects on apparent resistivity logs. Simulations were performed by combining the use of a Fourier-series expansion in a nonorthogonal system of coordinates with an existing 2D goal-oriented, higher-order, and self-adaptive finite-element method. This numerical algorithm yields accurate solutions in limited CPU time because only a few Fourier modes are needed to simulate practical applications. For the calculation of focused currents, we introduced an embedded postprocessing method that incorporates a synthetic focusing principle to compute current intensities at each iterative step of optimal mesh refinements. Our numerical method accurately simulates 3D DLL measurements in rock formations that exhibit extreme contrasts of electrical resistivity. Simulations indicate that LLs resistivity logs are more sensitive to both invaded and anisotropic layers than LLd resistivity logs. In deviated wells, shoulder-bed effects on apparent resistivity logs increase with an increase of dip angle, and are emphasized across thin conductive layers. Electrical anisotropy effects on apparent resistivity logs increase substantially with dip angle.

Computation of a quasi-static field induced by two long straight parallel wires in a conductor with a rough surface

This paper deals with the computation of the quasi-static electromagnetic field due to an eddy current probe scanning a conductive half-space. Two homogeneous media are separated by a cylindrical metallic surface characterized by an arbitrary aperiodic profile. The eddy current induction problem with a rough surface is rigorously tackled by a semi-analytical approach based on Maxwell's equations written in a non-orthogonal coordinates system adapted to the geometry of the profile. The choice of a two-dimensional eddy current probe (a long coil carrying an alternating current) is carried out in order to simplify the presentation, for the first time, of a specific semi-analytical approach which will be in fine dedicated to the simulation of EC testing of conducting magnetic test pieces of complex shapes without resorting to pure numerical methods.

Numerical Investigation of Turbidity Currents Flowing Through Minibasins on the Continental Slope

Abstract Numerical investigation of the dynamics of turbidity currents flowing through a series of minibasins is conducted. A two-dimensional vertical-structure-resolving finite-volume model is developed to solve the Reynolds-averaged Navier-Stokes equations along with the sediment mass conservation equation in a non-orthogonal grid system. In addition, the Exner equation of bed sediment conservation is solved to study changes in the bed level. The model is verified against three laboratory experiments conducted by Lamb et al. (2004) and Lamb et al. (2006) to study the dynamics of continuous-feed turbidity currents and the depositional characteristics in a minibasin. Simulation results show that the sediment deposition pattern predicted by the model is in reasonably close agreement with the measurements. The model successfully captures draping of sediment over the initial bed irregularities. Vertical distributions of concentration profiles are also found to be in good agreement with the measured data. Field-scale investigation is carried out by considering two minibasins in a series. It is observed that the inflow condition of a continuous-feed turbidity current can strongly influence the bed morphology of the minibasin. For the same inflow velocity and suspended-sediment concentration, larger sediment particles in the inflow cause overall deposition while smaller sediment particles lead to erosion.

Fourier series expansion in a non-orthogonal system of coordinates for the simulation of 3D alternating current borehole resistivity measurements

We describe a method to simulate 3D resistivity borehole measurements acquired with alternating current (AC) logging instruments. It combines the use of a Fourier series expansion in a non-orthogonal system of coordinates with an existing 2D goal-oriented higher-order self-adaptive hp-finite element (FE) algorithm. The method is used to simulate measurements acquired with both wireline and logging-while-drilling (LWD) borehole logging instruments in deviated wells. It enables a considerable reduction of the computational complexity with respect to available 3D simulators, since the number of Fourier modes (basis functions) needed to solve practical applications is limited (typically, below 13). The fast convergence of the method is studied via numerical experimentation by simulating two wireline and one LWD instruments in a deviated well across a possibly invaded formation. Numerical results confirm the efficiency and reliability of the method for simulating challenging 3D AC resistivity borehole problems in deviated wells, while avoiding the expensive construction of optimal 3D grids. We accurately simulate challenging electrodynamic problems within a few seconds (or minutes) of CPU time per logging position. The method is especially well-suited for inversion of triaxial electromagnetic (EM) measurements, since we demonstrate that the number of Fourier modes needed for the exact representation of the material function is limited to only one (the central mode) for the case of borehole measurements acquired in deviated wells.

Three-Dimensional Conduction Heat Transfer Model for Laser Cladding Process

Cladding is the process of depositing a superior built-up layer on a substrate by fusion. In the present study a three-dimensional conduction heat transfer model is developed and solved using the finite-volume method in a nonorthogonal grid system for a blown-powder laser cladding process. Comparisons with experimental data for deposition of copper powder on SS316 stainless steel show that the developed model can predict the geometry of the buildup layer above the substrate within an acceptable range of tolerance. The overall absorption of the CO2 laser radiation is in the range of 14–17%.

A Parallel, Fourier Finite-Element Formulation with an Iterative Solver for the Simulation of 3D LWD Measurements Acquired in Deviated Wells

We describe a new method to simulate resistivity measurements acquired with induction logging instruments in deviated wells. The method combines: (1) a highly e-cient iterative solver, (2) a parallel implementation, (3) a Fourier Finite-Element (FFE) formulation in a non-orthogonal system of coordinates, and (4) a 2D hp-Finite Element (FE) goal-oriented self-adaptive grid-reflnement strategy. We apply the new method to simulate measurements acquired with a logging-while-drilling (LWD) instrument operating at 1.75MHz in a 55-degree deviated well. Numerical results conflrm the high-accuracy and e-ciency of the method. An error level below 1% is achieved in reservoirs with high-contrast in electrical resistivity using an average CPU time of 1{3 minutes per logging position.

Fourier series expansion in a non-orthogonal system of coordinates for the simulation of 3D-DC borehole resistivity measurements

We describe a new method to simulate 3D borehole resistivity measurements at zero frequency (DC). The method combines the use of a Fourier series expansion in a non-orthogonal system of coordinates with an existing 2D goal-oriented higher-order self-adaptive hp-finite element algorithm. The new method is suitable for simulating measurements acquired with borehole logging instruments in deviated wells. It delivers high-accuracy simulations and it enables a considerable reduction of the computational complexity with respect to available 3D simulators, since the number of Fourier modes (basis functions) needed to solve practical applications is limited (typically, below 10). Furthermore, numerical results indicate that the optimal 2D grid based on the 0th Fourier mode (also called central Fourier mode) can be employed to efficiently solve the final 3D problem, thereby, avoiding the expensive construction of optimal 3D grids. Specifically, for a challenging through-casing resistivity application, we reduce the computational time from several days (using a 3D simulator) to just 2 h (with the new method), while gaining accuracy. The new simulation method can be easily extended to different physical phenomena with similar geometries, as those arising in the simulation of 3D borehole electrodynamics and sonic (acoustics coupled with elasticity) measurements. In addition, the method is especially suited for inversion, since we demonstrate that the number of Fourier modes needed for the exact representation of the materials is limited to only one (the central mode) for the case of borehole measurements acquired in deviated wells.

COMPARATIVE STUDY OF WAVELET BASED NEURAL NETWORK AND NEURO-FUZZY SYSTEMS

Based on the wavelet transform theory and its well emerging properties of universal approximation and multiresolution analysis, the new notion of the wavelet network is proposed as an alternative to feed forward neural networks and neuro-fuzzy for approximating arbitrary nonlinear functions. Earlier, two types of neuron models, namely, Wavelet Synapse (WS) neuron and Wavelet Activation (WA) functions neuron have been introduced. Derived from these two neuron models with different non-orthogonal wavelet functions, neural network and neuro-fuzzy systems are presented. Comparative study of wavelets with NN and NF are also presented in this paper.