Interpolation with Specified Error of a Point Series Belonging to a Monotone Curve

The paper addresses the problem of modeling a smooth contour interpolating a point series belonging to a curve containing no special points, which represents the original curve with specified accuracy. The contour is formed within the area of possible location of the parts of the interpolated curve along which the curvature values are monotonously increased or decreased. The absolute interpolation error of the point series is estimated by the width of the area of possible location of the curve. As a result of assigning each intermediate point, the location of two new sections of the curve that lie within the area of the corresponding output section is obtained. When the interpolation error becomes less than the given value, the area of location of the curve is considered to be formed, and the resulting point series is interpolated by a contour that lies within the area. The possibility to shape the contours with arcs of circles specified by characteristics is investigated.     

Solid-perforated panel layout optimization by topology optimization based on unified transfer matrix

This paper presents a numerical method for the optimization of the sequencing of solid panels, perforated panels and air gaps and their respective thickness for maximizing sound transmission loss and/or absorption. For the optimization, a method based on the topology optimization formulation is proposed. It is difficult to employ only the commonly-used material interpolation technique because the involved layers exhibit fundamentally different acoustic behavior. Thus, an optimization method formulation using a so-called unified transfer matrix is newly proposed. The key idea is to form elements of the transfer matrix such that interpolated elements by the layer design variables can be those of air, perforated and solid panel layers. The problem related to the interpolation is addressed and bench mark-type problems such as sound transmission or absorption maximization problems are solved to check the efficiency of the developed method.     

Plate impulse response spatial interpolation with sub-Nyquist sampling

Impulse responses of vibrating plates are classically measured on a fine spatial grid satisfying the Shannon-Nyquist spatial sampling criterion, and interpolated between measurement points. For homogeneous and isotropic plates, this study proposed a more efficient sampling and interpolation process, inspired by the recent paradigm of compressed sensing. Remarkably, this method can accommodate any star-convex shape and unspecified boundary conditions. Here, impulse responses are first decomposed as sums of damped sinusoids, using the Simultaneous Orthogonal Matching Pursuit algorithm. Finally, modes are interpolated using a plane wave decomposition. As a beneficial side effect, these algorithms can also be used to obtain the dispersion curve of the plate with a limited number of measurements. Experimental results are given for three different plates of different shapes and boundary conditions, and compared to classical Shannon interpolation.     

Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes

We developed a new monotone finite volume method for diffusion equations. The second-order linear methods, such as the multipoint flux approximation, mixed finite element and mimetic finite difference methods, are not monotone on strongly anisotropic meshes or for diffusion problems with strongly anisotropic coefficients. The finite volume (FV) method with linear two-point flux approximation is monotone but not even first-order accurate in these cases. The developed monotone method is based on a nonlinear two-point flux approximation. It does not require any interpolation scheme and thus differs from other nonlinear finite volume methods based on a two-point flux approximation. The second-order convergence rate is verified with numerical experiments.     

Speech synthesis by linear interpolation of spectral parameters between dyad boundaries.

A recent study [Olive and Spickenagel, J. Acoust. Soc. Am. 59, 993-996 (1976)] has shown that area parameters derived from linear prediction analysis can be linearly interpolated between dyad boundaries with very little distortion in the resultant synthesized speech. The success of area parameter interpolation raises a question: can other acoustic parameters, such as the power spectrum of the speech waveform, be similarly interpolated? The spectrum is of special interest because speech can be synthesized in real time from spectral parameters on a programmable digital filter. To study this question a speech analysis-synthesis system using spectral parameters (samples of power spectra at different frequencies) was simulated. These parameters were determined from the speech signal at every dyad boundary, and interpolated for intermediate values. Dyad boundaries (representing the limits of transition regions between phonemes) were determined manually. Informal listening tests comparing synthetic speech with and without linear interpolation showed slight degradation in the interpolated speech. This degradation is significantly reduced by using an additional point within the dyad boundaries for interpolation.     

基于Voigt函数的拉曼成像插值方法

拉曼成像是拉曼光谱技术非常重要的一个环节,通过生成光谱数据的伪彩图像,可以得到采集区域中某物质组分的浓度和位置分布信息,当前,拉曼成像技术已经逐渐成为监测生物活性以及物质组分的最优解之一.为了得到清晰的成像效果,采集过程中的数据量不宜过小,否则成像效果差、锯齿感较重,从而导致视觉效果不好.但是,数据量的增加虽然可以得到...     

Conservative form of interpolated differential operator scheme for compressible and incompressible fluid dynamics

The proposed scheme, which is a conservative form of the interpolated differential operator scheme (IDO-CF), can provide high accurate solutions for both compressible and incompressible fluid equations. Spatial discretizations with fourth-order accuracy are derived from interpolation functions locally constructed by both cell-integrated values and point values. These values are coupled and time-integrated by solving fluid equations in the flux forms for the cell-integrated values and in the derivative forms for the point values. The IDO-CF scheme exactly conserves mass, momentum, and energy, retaining the high resolution more than the non-conservative form of the IDO scheme. A direct numerical simulation of turbulence is carried out with comparable accuracy to that of spectral methods. Benchmark tests of Riemann problems and lid-driven cavity flows show that the IDO-CF scheme is immensely promising in compressible and incompressible fluid dynamics studies.     

运动声源多普勒畸变信号的一种时域校正方法

运动声源信号中广泛存在多普勒效应的影响,为了解决其引起的频移、频带扩展问题,提出了一种时域信号校正方法。该方法首先从运动关系和莫尔斯声学理论出发推导得出离散插值时间序列和幅值还原公式,然后对畸变信号进行幅值还原和插值拟合。仿真信号和实验信号处理结果表明多普勒效应带来的频移和频带扩展问题得到了较好的解决,畸变信号得到了有效校正。该方法在时域内对离散信号进行单点操作,与以往的频域处理方法相比具有无需已知声源特征频率、不受频带混叠因素影响的优点,该方法能够处理多频信号,是一种简单有效的多普勒效应消除方法。      

Feature points extraction of different structure for industrial computed tomography image contour

In order to accurately obtain the physical structure and dimension, the feature points extraction must be carried out from the ICT (industrial computed tomography) image contour. Therefore, the discrete data could be transformed into CAD models, and different methods have been developed for the feature points extraction, according to geometric features, the function and shape of mechanical parts. We discussed the feature points extraction methods, and one method is not enough to all the structures, so we must first distinguish the structure as regular and irregular. For the regular structures, by using a positive–negative factor, the curvature estimation method was improved. This method was designed and verified for the actual part, and has an improved accuracy in the feature points extraction. While for the irregular structures we used the polygon approximation method in the feature points extraction. For a complex part composing of several regular structures and irregular structures in the same ICT contour, we divided the whole contour into the regular and irregular structures, then used the corresponding methods for each structure. Last all feature points were extracted. The actual examples showed that the used methods are practical and effective.     

A new interpolation formula in the form of a continued fraction

An interpolation formula in the form of a continued fraction is derived. In the limit case, where the table points are equal, it turns into an expansion of the function into a continued fraction near the point. The formula can be a useful tool for interpolating singular functions. As an application, a series of methods for solving non-linear equations is derived, the first two of them being identical with the methods by Halley and Kiss.     

核燃料棒反光表面条纹自适应中心提取方法

针对水下检测中激光条纹中心难以准确提取的问题,提出了一种适用于水下核燃料棒反光表面的条纹自适应中心提取方法.根据检测环境中存在水体散射及物体表面高反光的特点,去除水下噪点、反光噪点,实现激光条纹分割提取;充分利用BP神经网络曲线拟合及由光条几何信息生成的自适应卷积模板,实现反光区域的轮廓与灰度分布修正,使光条截面灰度分...     

Method for edge contour extraction of a scanning probe microscope image

A method for edge contour extraction of a scanning probe microscope image is proposed. This method is developed to process an image that has the large size irregularity and/or objects bound together. It is based on definition of the local minimum points of brightness data function and permits one to obtain the correct edge contour line. The advantages of the proposed method over traditional methods are demonstrated using model results. This method can be used to process different images.     

Simple adaptive cubic spline interpolation of fluorescence decay functions

Simple method allowing for adaptive cubic spline interpolation of fluorescence decay functions is proposed. In the first step of the method, the interpolated function is integrated using the known adaptive algorithm based on Newton-Cotes quadratures. It is shown that, in this step, application of the Simpson's rule provides the smallest number of calls of the interpolated function. In the second step of the method, a typical cubic spline approximation is used to find values of the interpolated function between the points evaluated in the first step.     

光栅投影三维测量系统标定技术研究

相机与投影仪的标定是影响光栅投影三维测量系统精度的因素之一,且标定所得参数的精度直接影响系统的测量精度。分析标志点边缘成像时的退化模型,提出了基于高斯曲线拟合与边缘局部区域效应相结合的亚像素边缘检测方法,获取高精度边缘,提高标志点检测精度;使用基于透视变换图像矫正的标志点快速排序匹配方法,进行相机快速高精度标定。分析投影仪标定时的相位误差,提出了一种基于径向基的线性插值方式,提高标志点圆心相位获取精度。实验验证,使用上述亚像素边缘检测方式,标志点的边缘残差为0.0871,对比基于高斯曲线的拟合方式,精度提高了41%,相机标定重投影误差均值为0.0524像素;使用上述相位插值方式,投影仪标定重投影误差均值为0.1203像素,对比使用双线性插值方式,标定精度提高23.9%。     

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.     

Adaptive chemistry lookup tables for combustion simulations using optimal B-spline interpolants

Flamelet models, which enable the storing of precomputed detailed chemistry into lookup tables, are widely used in combustion simulations. They allow the computation of accurate results at low computational cost, but standard implementations can lead to numerical problems due to a non-smooth representation, and their applicability is limited by memory requirements. Here, the methods used by a newly developed and optimised lookup table generator based on B-spline interpolation are presented. The creation of smooth representations of flamelet solutions requiring less than one fifth of the number of points in each direction compared to the non-smooth representations of standard lookup tables based on linear interpolation is shown to be possible. The new B-spline interpolation based tables are also applied within a large-eddy simulation of the Swirling Methane/Hydrogen Flame 1 and the results are compared to simulations using lookup tables based on linear interpolation or optimised artificial neural networks. Better performance of the B-spline interpolation based tables with respect to physical accuracy and numerical performance is demonstrated.     

A high order multivariate approximation scheme for scattered data sets

We present a high order multivariate approximation scheme for scattered data sets. Each data point is represented as a Taylor series, and the high order derivatives in the Taylor series are treated as random variables. The approximation coefficients are then chosen to minimize an objective function at each point by solving an equality constrained least squares. The approximation is an interpolation when the data points are given as exact, or a nonlinear regression function when nonzero measurement errors are associated with the data points. Using this formulation, the gradient information on each data point can be used to significantly reduce the approximation error. All parameters of the approximation scheme can be computed automatically from the data points. An uncertainty bound of the approximation function is also produced by the scheme. Numerical experiments demonstrate that although this method is more computationally intensive than traditional methods, it produces more accurate approximation functions.     

弹性力学的插值型重构核粒子法

采用具有离散点插值特性的重构核粒子法形函数, 较精确地重构弹性体 变形的位移试函数, 再与弹性力学的最小势能原理相结合, 形成新的分析弹性力 学平面问题的插值型重构核粒子法. 由于插值型重构核粒子法形函数具有点插值特性和不低于核函数 的高阶光滑性, 因而既克服了多数无网格方法处理本质边界条件的困难, 也保证了较高的数值精度. 与早期的无网格方法相比, 本方法具有精度高、解题规模较小、可直接施加边界条件等优点. 通过对典型弹性力学问题数值模拟, 验证了所提方法的有效性和正确性.     

特定边界跟踪中角点检测研究

针对边界跟踪算法中在角点附近丢失边界信息的问题,对待检测边界中角点的判别和检测方法进行了研究。分析了边界搜索中所扩展的邻域的半径和角点位置的关系,提出了角点存在判据,给出了角点存在区间。提出了寻区间法角点检测算法,用5个已知边界点之间的关系,判断出角点存在的邻域,通过选取合适的邻域半径,使角点存在区间向角点收敛。对测试图像和人侧面轮廓图像的边界利用所提出的算法进行跟踪,测试图像的边界点从19个增长为37个,人侧面轮廓图像边界点从13个增长为21个,新算法准确地检测到轮廓角点和后续种子点,使边界跟踪能够反映所有的边界信息。     

Transient nearfield acoustic holography based on an interpolated time-domain equivalent source method

Transient nearfield acoustic holography based on an interpolated time-domain equivalent source method (ESM) is proposed to reconstruct transient acoustic fields directly in the time domain. Since the equivalent source strengths solved by the traditional time-domain ESM formulation cannot be used to reconstruct the pressure on the source surface directly, an interpolation function is introduced to develop an interpolated time-domain ESM formulation which permits one to deduce an iterative reconstruction process. As the reconstruction process is ill-conditioned and especially there exists a cumulative effect of errors, the Tikhonov regularization is used to stabilize the process. Numerical examples of reconstructing transient acoustic fields from a baffled planar piston, an impulsively accelerating sphere and a cube box, respectively, demonstrate that the proposed method not only can effectively reconstruct transient acoustic fields in the time domain, but also can visualize acoustic fields in the space domain. And, in the first numerical example, the cumulative effect of errors and the validity of using the Tikhonov regularization to suppress the errors are described.