First-order Interpolation Research Articles

A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder

AbstractA boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work. The present approach is an improvement to the conventional IB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximately satisfied. As a result, there is flow penetration to the solid boundary. Another drawback of conventional IB-LBM is the use of Dirac delta function interpolation, which only has the first order of accuracy. In this work, the no-slip boundary condition is directly implemented, and used to correct the velocity at two adjacent mesh points from both sides of the boundary point. The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation. Obviously, the two drawbacks of conventional IB-LBM are removed in the present study. Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newton’s second law. To validate the proposed method, the two-dimensional vortex decaying problem and incompressible flow over a circular cylinder are simulated. As shown in the present results, the flow penetration problem is eliminated, and the obtained results compare very well with available data in the literature.

The Research of NURBS Curve Interpolation Algorithm Based on Parabolic and the First-Order Taylor Expansion Interpolation Algorithm

The NURBS curve interpolation algorithm based on parabolic interpolation error and the first-order Taylor expansion interpolation algorithm is proposed to improve part surface quality and chord error of NURBS curve interpolation algorithm. The part surface quality is improved effectively by the parabolic interpolation algorithm in the conduction that the previous point, the current point and the next point which was computed by the first order Taylor expansion interpolation algorithm were known. The effectiveness of this algorithm is proved by the NURBS curve interpolation simulation.

Generating accurate dipole moment surfaces using modified Shepard interpolation.

We outline an approach for building molecular dipole moment surfaces using modified Shepard interpolation. Our approach is highly automated, requires minimal parameterization, and is iteratively improvable. Using the water molecule as a test case, we investigate how different aspects of the interpolation scheme affect the rate of convergence of calculated IR spectral line intensities. It is found that the interpolation scheme is sensitive to coordinate singularities present at linear geometries. Due to the generally monotonic nature of the dipole moment surface, the one-part weight function is found to be more effective than the more complicated two-part variant, with first-order interpolation also giving better-than-expected results. Almost all sensible schemes for choosing interpolation reference data points are found to exhibit acceptable convergence behavior.

Data Parallel Implementation of Geometric Operations

The data parallel implementation scheme of zero-order interpolation and first-order interpolation of backward mapping is proved and discussed. It is shown that the complexity of data parallel implementation scheme presented in this paper is Ο(M+N) instead of Ο(MN) in sequential processing, thereby it can easily meet the real time requirements of the digital image processing.

Signal‐to‐noise ratio estimation on SEM images using cubic spline interpolation with Savitzky–Golay smoothing

A new technique based on cubic spline interpolation with Savitzky-Golay noise reduction filtering is designed to estimate signal-to-noise ratio of scanning electron microscopy (SEM) images. This approach is found to present better result when compared with two existing techniques: nearest neighbourhood and first-order interpolation. When applied to evaluate the quality of SEM images, noise can be eliminated efficiently with optimal choice of scan rate from real-time SEM images, without generating corruption or increasing scanning time.

Gross Error Denoising Method for Slope Monitoring Data at Hydropower Station

There are mainly two types of errors existed in monitoring displacement of a rock slope: gross errors and random errors. Monitoring data is very important for the safety construction and operation of the Hydropower Station. The use of slope monitoring data for safety evaluation is influenced by the gross errors during the monitoring process. This paper presents a gross error denosing method for a nonlinear time series based on the three-standard-deviation rule (3-σ rule), and then reconstructing the time series by a first-order Lagrange interpolation method. The present method is applied to the gross error analysis of the slope displacement monitoring data collected at the Jinping I Hydropower Station. Computed results show that the first-order difference values of the gross errors can be above or below the upper or lower three-standard-deviation boundary, and the gross errors can be removed effectively. DOI: http://dx.doi.org/10.11591/telkomnika.v11i10.3337

GEOMETRICAL RAY-BUNDLE REVERBERATION MODELING

The classical ray approach for monostatic ocean boundary reverberation has been re-examined based on a geometrical ray-bundle concept. In this new formulation, the impulse response for the averaged scattering intensity is expressed by a simple function consisting of continuous ray-bundle quantities with respect to the time, and which can be regarded as a generalized function for ray-based reverberation in a boundary cell. To numerically evaluate this impulse response, a zeroth- and a first-order polynomial interpolation method are respectively applied to approximate the ray-bundle quantities. Then, the impulse function is reduced to the forms of the delta function and the rectangular function either with or without linear amplitude modulation linear in time. These basic functions are used to develop an explicit numerical scheme for the monostatic reverberation, which originates in the split-step marching algorithm for the range. This numerical scheme provides a considerable accuracy even with larger range steps and gives reasonable results for numerical examples of ocean waveguides with isovelocity, summer, and winter sound-speed profiles.

Selecting a sampling period for a sampled-data submarine motion control system

The paper investigates how sampling period affects the modal controllability and stabilizability of a sampled-data submarine motion control system. Systems with a computation delay using generalized DAC as a digital-to-analog converter are considered. A set of pathological periods, when the system may turn unstabilizable, is constructed. Selection of a sampling period for a system with first-order extrapolator and interpolator is shown by a numerical example.

Large Deformation Geometric Nonlinear Beam Element Based on U.L. Format

Based on the geometric deformation of the Euler-Bernoulli beam element, the geometric nonlinear Euler-Bernoulli beam element based on U.L. formulation is derived. The element’s transverse first-order displacement field is constructed using the cubic Hermite interpolation polynomial, and the first-order Lagrange interpolation polynomial is used for the axial displacement field. Then the additional displacements induced from the rotation of the elemental are included into the transverse and longitudinal displacement fields, so those displacement fields are expressed as the quadratic function of nodal displacement. Afterwards the nonlinear finite element formulas of Euler-Bernoulli beam element under the form of U.L. formulation are derived using Cauchy strain tensor and the principle of virtual displacements. The total equilibrium equation and tangent stiffness for large displacement geometric nonlinear analysis of frame are obtained in the total coordinate system. The correctness of this element is proved by typical example.

Large Deformation Geometric Nonlinear Beam Element Based on U.L. Format

Based on the geometric deformation of the Euler-Bernoulli beam element, the geometric nonlinear Euler-Bernoulli beam element based on U.L. formulation is derived. The element’s transverse first-order displacement field is constructed using the cubic Hermite interpolation polynomial, and the first-order Lagrange interpolation polynomial is used for the axial displacement field. Then the additional displacements induced from the rotation of the elemental are included into the transverse and longitudinal displacement fields, so those displacement fields are expressed as the quadratic function of nodal displacement. Afterwards the nonlinear finite element formulas of Euler-Bernoulli beam element under the form of U.L. formulation are derived using Cauchy strain tensor and the principle of virtual displacements. The total equilibrium equation and tangent stiffness for large displacement geometric nonlinear analysis of frame are obtained in the total coordinate system. The correctness of this element is proved by typical example.

Image noise cross‐correlation for signal‐to‐noise ratio estimation in scanning electron microscope images

A new and robust parameter estimation technique, named image noise cross-correlation, is proposed to predict the signal-to-noise ratio (SNR) of scanning electron microscope images. The results of SNR and variance estimation values are tested and compared with nearest neighborhood and first-order interpolation. Overall, the proposed method is best as its estimations for the noise-free peak and SNR are most consistent and accurate to within a certain acceptable degree, compared with the others.

Real-Time Solution of Velocity-Based First-Order Continuum Traffic Model with Finite Element Method

Two approximate solution methods are investigated for the velocity-based version of a first-order continuum traffic flow model commonly known as the Lighthill–Whitham–Richards model. The finite difference and finite element methods are commonly used to numerically solve partial differential equations. The finite difference method adopted uses a standard Godunov scheme to solve the continuum model. The finite element method uses one-dimensional simplex elements with first-order interpolation function along with a Galerkin scheme to derive the element characteristic matrices and vectors. A high-resolution, real-world data set from the Next Generation Simulation program is used to evaluate the two solution methods. Results show that both methods provide accurate approximations to the observed speeds. The accuracy and quality of solutions and future directions of work in this area are discussed.

A Parametric Curve Interpolation Algorithm for High Speed Machining

This paper proposed a new and effective parametric curve interpolation algorithm with error compensation capability for high speed machining. The proposed algorithm is developed from the first-order Taylor expansion interpolation algorithm and the speed-controlled interpolation algorithm. It is also incorporated the geometry features of the machined curves, the dynamic characteristics of machine tools and the adaptive error control. The proposed algorithm achieves high surface accuracy and avoids feedrate fluctuations. Simulation results have demonstrated the effectiveness and satisfactory performance of the proposed algorithm.

Fast First-Order Polynomials Convolution Interpolation for Real-Time Digital Image Reconstruction

This letter presents a high-performance architecture of a novel first-order polynomial convolution interpolation for digital image scaling. A better quality of interpolation is achieved by using higher order model that requires complex computations. The kernel of the proposed method is built up of first-order polynomials and approximates the ideal sinc-function in the interval [-2, 2]. The proposed architecture reduces the computational complexity of generating weighting coefficients and provides a simple hardware architecture design and low computation cost, and easily meets real-time requirements. The architecture is implemented on the Virtex-II FPGA, and the high-performance very-large-scale integration architecture has been successfully designed and implemented with the TSMC 0.13 μm standard cell library. The simulation results indicate that the interpolation quality of the proposed architecture is mostly better than cubic convolution interpolations, and is able to process varying-ratio image scaling for high-definition television in real-time.

Topological criterion for selection of quintic Pythagorean-hodograph Hermite interpolants

A topological approach to identifying the “good” interpolant among the four distinct solutions to the first-order Hermite interpolation problem for planar quintic Pythagorean-hodograph curves is presented. An existence theorem is proved, together with a complete analysis of uniqueness/non-uniqueness properties. A simple formula for finding the “good” solution, without appealing to curve fairness or energy integrals, is also presented.

Regranulation: A granular algorithm enabling communication between granular worlds

In this paper, we describe a granular algorithm for translating information between two granular worlds, represented as fuzzy rulebases. These granular worlds are defined on the same universe of discourse, but employ different granulations of this universe. In order to translate information from one granular world to the other, we must regranulate the information so that it matches the information granularity of the target world. This is accomplished through the use of a first-order interpolation algorithm, implemented using linguistic arithmetic, a set of elementary granular computing operations. We first demonstrate this algorithm by studying the common “fuzzy-PD” rulebase at several different granularities, and conclude that the “3 × 3” granulation may be too coarse for this objective. We then examine the question of what the “natural” granularity of a system might be; this is studied through a 10-fold cross-validation experiment involving three different granulations of the same underlying mapping. For the problem under consideration, we find that a 7 × 7 granulation appears to be the minimum necessary precision.

Kinetic energy conservation issues associated with the collocated mesh scheme for incompressible flow

The collocated-mesh scheme is often favored over the staggered-mesh scheme for turbulence simulation in complex geometries due to its simpler form in curvilinear coordinates. The collocated mesh scheme does not conserve kinetic energy however, and few careful checks of the impact of these errors have been made. In this work, analysis is used to identify two sources of kinetic energy conservation error in the collocated-mesh scheme: (1) errors arising from the interpolations used to estimate the velocity on the cell faces, and (2) errors associated with the slightly inconsistent pressure field used to ensure mass conservation for the cell face volume fluxes. It is shown that the interpolation error can be eliminated through the use of first-order accurate centered interpolation operators with mesh-independent weights. The pressure error appears to be intrinsic to the scheme and it is shown to scale as O(Δ t 2Δ x 2). The effects of the conservation errors are investigated numerically through simulations of inviscid flow over an airfoil and in large eddy simulations of turbulent channel flow. Neither the interpolation error nor the pressure error appear to lead to significant problems in the channel flow simulations where viscous dissipation is present and where the Cartesian mesh is stretched in only one direction. The inviscid airfoil simulations performed on a curvilinear mesh show a much greater sensitivity to the interpolation error. The standard second-order centered interpolation is shown to lead to severe numerical oscillations, while the kinetic energy-conserving first-order centered interpolation produces solutions that are almost as smooth as those obtained with a third-order upwind interpolation. When compared in channel flow simulations, however, the first-order centered interpolation is shown to be far superior to the third-order upwind interpolation, the latter being adversely affected by numerical dissipation. Only slight differences were noted when comparing channel flow simulations using first-order and second-order centered interpolations. These results suggest that numerical oscillations can be controlled in curvilinear coordinates through the use of properly-constructed non-dissipative centered interpolations.

From Basic Research to Applications

Forty years have passed since Prof. Lotfi A. Zadeh introduced fuzzy set theory in his known article “Fuzzy Sets” in Information and Control, 8, 1965, sparking new development in information technology and automation. This article also formed the roots of the Fuzzy Systems Research Group, an active part of the Laboratory of Applied Mathematics, Lappeenranta University of Technology. Rough set theory, evolutionary computing, and neural computing followed, together with their combinations. This Special Issue presents 10 papers representing these areas. Many of the contributors of this Special Issue belong to the Fuzzy Systems Research Group and others work in close co-operations with this group. The first paper considers the use of linguistically expressed objectives in multicriteria decision-making in selection processes based on topological similarity M-relations between L-sets. The second presents basic ideas and fundamental concepts of rough set theory and considers properties of rough approximations. The third combines Lukasiewicz logics and modifier algebras based on Zadeh algebras, i.e., quasi-Boolean algebras of membership functions. The fourth applies Mö{o}bius transformations, known in complex analysis, to fuzzy subgroups in a topological point of view. The fifth discusses the stability of a classifier based on the Lukasiewicz structure and tests Schweizer and Sklar's implications with an extension to generalized mean to a classification task. The sixth deals with the interpretability problem of first-order Takagi-Sugeno systems and interpolation issues, developing a special two-model configuration. The seventh describes an expert system for defining an athlete's aerobic and anaerobic thresholds that successfully mimics decision-making by sport medicine professionals, with system functionality based on fuzzy comparison measures, generalized means, fuzzy membership functions, and differential evolution. The eighth applies a differential evolution algorithm-based method to training radial basis function networks with variables including centers, weights, and widths. The ninth compares two floating-point-encoded evolutionary algorithms – differential evolution and a generalized generation gap model – using a set of problems with different characteristics. The tenth proposes a new approach for monitoring break tendency of paper webs on modern paper machines, combining linguistic equations and fuzzy logic in a case-based reasoning framework. As the Guest Editor of this Special Issue, I thank the contributors and reviewers for their time and effort in making this special issue possible. I am also grateful to the JACIII editorial board, especially Prof. Kaoru Hirota, the Editors-in-Chief and Managing Editor Kenta Uchino, and the staff of Fuji Technology Press for the opportunity to participate in this work. I also thank Prof. Kaoru Hirota for organizing the reviewing of my paper.

Performance of a mixed Lagrange time delay estimation autoregressive (MLTDEAR) model for single‐image signal‐ to‐noise ratio estimation in scanning electron microscopy

A novel technique based on the statistical autoregressive (AR) model has recently been developed as a solution to estimate the signal-to-noise ratio (SNR) in scanning electron microscope (SEM) images. In another research study, the authors also developed an algorithm by cascading the AR model with the Lagrange time delay (LTD) estimator. This technique is named the mixed Lagrange time delay estimation autoregressive (MLTDEAR) model. In this paper, the fundamental performance limits for the problem of single-image SNR estimation as derived from the Cramer-Rao inequality is presented. We compared the experimental performances of several existing methods--the simple method, the first-order linear interpolator, the AR-based estimator as well as the MLTDEAR method--with respect to this performance bound. In a few test cases involving different images, the efficiency of the MLTDEAR single-image estimation technique proved to be significantly better than that of the other three methods. Study of the effect of different SEM setting conditions that affect the autocorrelation function curve is also discussed.

Robust image signal‐to‐noise ratio estimation using mixed lagrange time delay estimation autoregressive model

A new technique based on the statistical autoregressive (AR) model has recently been developed as a solution to signal-to-noise (SNR) estimation in scanning electron microscope (SEM) images. In the present study, we propose to cascade the Lagrange time delay (LTD) estimator with the AR model. We call this technique the mixed Lagrange time delay estimation autoregressive (MLTDEAR) model. In a few test cases involving different images, this model is found to present an optimum solution for SNR estimation problems under different noise environments. In addition, it requires only a small filter order and has no noticeable estimation bias. The performance of the proposed estimator is compared with three existing methods: simple method, first-order linear interpolator, and AR-based estimator over several images. The efficiency of the MLTDEAR estimator, being more robust with noise, is significantly greater than that of the other three methods.