LEAST-SQUARES METHOD-BASED FEATURE FITTING AND EXTRACTION IN REVERSE ENGINEERING

The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.

ON THE BREAKDOWNS OF THE GALERKIN AND LEAST-SQUARES METHODS

The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.

基于LMS Virtual Lab对多孔同心式液压脉动衰减器的优化研究

多孔同心式液压脉动衰减器采用穿孔管作为压力脉动的衰减部件,通过改变穿孔管的阻抗特性,避开系统的流固耦合谐振点。传统的衰减器在低频段衰减效果良好,但在中频和高频效果欠佳。通过改变穿孔管内部穿孔段的孔径、管壁厚度、穿孔率来优化衰减器在中频和高频段的衰减效果。在LMS Virtual.Lab Acoustics的管道声学有限元模块中应用了传递导纳函数,通过常温下衰减器的传递损失计算,得到衰减器在中频和高频段良好的衰减性能,并通过两负载法进行实验论证。

Solution of shallow-water equations using least-squares finite-element method

A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.

Least-squares finite-element method for shallow-water equations with source terms

Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.

NEGATIVE NORM LEAST-SQUARES METHODS FOR THE INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS

The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.

基于LM方法的麻花钻刃带宽度测量研究

提出一种基于二值化的麻花钻刃带宽度检测方法。首先对目标边缘进行锐化,然后用巴特沃斯高通滤波提取边缘信息;其次通过改进的大津二值化算法对疑似边缘点进行阈值分割,获取边缘点坐标;再次使用列文伯格-马夸尔特(LM)方法对边缘附近的点进行拟合,得到刃带宽度曲线并求其拐点,求取麻花钻刃带宽度的数据。最后进行对比实验,用LM方法对未处理的M35直径2.5 cm的刃带图像进行处理得到刃带宽度1.467 mm,测量误差0.467 mm。改进后的测量结果为0.853 mm,测量误差为0.147 mm。

Monte Carlo method for evaluation of surface emission rate measurement uncertainty

The aim of this study is to evaluate the uncertainty of 2πα and 2πβ surface emission rates using the windowless multiwire proportional counter method.This study used the Monte Carlo method (MCM) to validate the conventional Guide to the Expression of Uncertainty in Measurement (GUM) method.A dead time measurement model for the two-source method was established based on the characteristics of a single-channel measurement system,and the voltage threshold correction factor measurement function was indirectly obtained by fitting the threshold correction curve.The uncertainty in the surface emission rate was calculated using the GUM method and the law of propagation of uncertainty.The MCM provided clear definitions for each input quantity and its uncertainty distribution,and the simulation training was realized with a complete and complex mathematical model.The results of the surface emission rate uncertainty evaluation for four radioactive plane sources using both methods showed the uncertainty’s consistency E_(n)<0.070 for the comparison of each source,and the uncertainty results of the GUM were all lower than those of the MCM.However,the MCM has a more objective evaluation process and can serve as a validation tool for GUM results.

Optimization of Random Feature Method in the High-Precision Regime

Machine learning has been widely used for solving partial differential equations(PDEs)in recent years,among which the random feature method(RFM)exhibits spectral accuracy and can compete with traditional solvers in terms of both accuracy and efficiency.Potentially,the optimization problem in the RFM is more difficult to solve than those that arise in traditional methods.Unlike the broader machine-learning research,which frequently targets tasks within the low-precision regime,our study focuses on the high-precision regime crucial for solving PDEs.In this work,we study this problem from the following aspects:(i)we analyze the coeffcient matrix that arises in the RFM by studying the distribution of singular values;(ii)we investigate whether the continuous training causes the overfitting issue;(ii)we test direct and iterative methods as well as randomized methods for solving the optimization problem.Based on these results,we find that direct methods are superior to other methods if memory is not an issue,while iterative methods typically have low accuracy and can be improved by preconditioning to some extent.

Reduced-order method for nuclear reactor primary circuit calculation

Accurate real-time simulations of nuclear reactor circuit systems are particularly important for system safety analysis and design.To effectively improve computational efficiency without reducing accuracy,this study establishes a thermal-hydraulics reduced-order model(ROM)for nuclear reactor circuit systems.The full-order circuit system calculation model is first established and verified and then used to calculate the thermal-hydraulic properties of the circuit system under different states as snapshots.The proper orthogonal decomposition method is used to extract the basis functions from snapshots,and the ROM is constructed using the least-squares method,effectively reducing the difficulty in constructing the ROM.A comparison between the full-order simulation and ROM prediction results of the AP1000 circuit system shows that the proposed ROM can improve computational efficiency by 1500 times while achieving a maximum relative error of 0.223%.This research develops a new direction and perspective for the digital twin modeling of nuclear reactor system circuits.

An Adaptive Least-Squares Mixed Finite Element Method for Fourth Order Parabolic Problems

A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.

LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR A CLASS OF STOKES EQUATION

A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces.

Least-Squares Finite Element Method for the Steady Upper-Convected Maxwell Fluid

In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.

Complex derivatives valuation: applying the Least-Squares Monte Carlo Simulation Method with several polynomial basis

Background:This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.The standard approach in the option pricing literature is to choose the basis arbitrarily.By comparing four different polynomial basis we show that the choice of basis interferes in the option's price.Methods:We assess Least-Squares Method performance in pricing four different American Asian Options by using four polynomial basis:Power,Laguerre,Legendre and Hermite A.To every American Asian Option priced,three sets of parameters are used in order to evaluate it properly.Results:We show that the choice of the basis interferes in the option's price by showing that one of them converges to the option's value faster than any other by using fewer simulated paths.In the case of an Amerasian call option,for example,we find that the preferable polynomial basis is Hermite A.For an Amerasian put option,the Power polynomial basis is recommended.Such empirical outcome is theoretically unpredictable,since in principle all basis can be indistinctly used when pricing the derivative.Conclusion:In this article The Least-Squares Monte Carlo Method performance is assessed in pricing four different types of American Asian Options by using four different polynomial basis through three different sets of parameters.Our results suggest that one polynomial basis is best suited to perform the method when pricing an American Asian option.Theoretically all basis can be indistinctly used when pricing the derivative.However,our results does not confirm these.We find that when pricing an American Asian put option,Power A is better than the other basis we have studied here whereas when pricing an American Asian call,Hermite A is better.

基于改进增益型自适应LMS算法的谐波检测方法

基于自适应噪声对消原理的谐波电流检测方法相对其他检测方法来说,具有实现简单、鲁棒性强等特点。该方法利用信号处理中的自适应干扰对消原理,将电网电压信号作为参考输入,负载电流作为原始输入,从负载中实时消除与电压波形相同的基波有功电流分量(或基波电流),从而得到负载电流中所有谐波与基波电流无功分量之和。再配合有源电力滤波器(APF),由补偿装置注入一个与谐波和基波电流无功分量之和大小相等极性相反的补偿电流,达到抑制谐波与基波电流无功分量的目的。提出了一种基于改进增益型自适应谐波电流的检测方法,该方法采用的反馈量不同于以往方法中的误差信号,而是将误差信号经过数学转换,使其转换成一个能真正反映系统跟踪误差的信号,并将其作为自适应滤波器权系数迭代的反馈量。通过Matlab证明该方法能够在保持较小的稳态失调的情况下也具有较快的动态响应速度。

用LMS法建立长沙市3～11岁儿童体质指数生长曲线

目的建立长沙市3～11岁儿童体质指数生长百分位曲线。方法测量18 214名儿童的身高、体重,计算每个儿童的体质指数值,应用LMS方法对体质指数百分位数进行拟合。结果获得了按年龄的L、M、S 3个参数并计算出长沙市3～11岁儿童体质指数百分位曲数。结论 LMS法拟合曲线效果良好,长沙市男、女儿童体质指数与世界卫生组织资料及全国水平存在差异。

用LMS法建立长沙市3～11岁儿童体质量生长曲线

目的了解长沙市3～11岁儿童体质量的分布特征,建立体质量生长百分位曲线,为儿童超重、肥胖和消瘦的预防、治疗及BMI筛查参考值的建立提供依据。方法采用随机整群抽样方法,抽取长沙市20所幼儿园及15所小学18 214名儿童,测量入选儿童的体质量,并记录性别和年龄,采用LMS方法拟合儿童体质量百分位数。结果获得了各年龄段的L、M、S 3个参数并计算出了长沙市3～11岁体质量百分位曲数;长沙市男女儿童体质量总体上高于全国平均水平:大部分年龄段男童体质量高于全国平均水平,各年龄段女童体质量均高于全国平均水平。结论 LMS法拟合的儿童体质量生长曲线、拟合值与实测值误差很小,拟合效果良好;长沙市3～11岁儿童体质量与全国水平均存在差异。

用LMS法建立长沙市3～11岁儿童身高生长曲线

目的建立长沙市3～11岁儿童身高生长百分位曲线。方法测量长沙市18 214名3～11岁儿童的身高,应用LMS方法对身高百分位数进行拟合。结果获得了按年龄的L、M和S 3个参数并计算出长沙市3～11岁儿童身高百分位曲数。结论 LMS法拟合曲线效果良好,长沙市3～11岁儿童身高与世界卫生组织及全国水平存在差异。

基于谱减和LMS的自适应语音增强

针对宽带噪声背景下的语音增强问题,将短时语音视为非平稳或宽平稳信号,基于谱减法和自适应滤波的最小均方(LMS)算法,提出了一种FIR型自适应滤波算法(SSLMS):用减谱法由短时噪声观测语音估计期望信号,作为滤波器输出信号的参考信号;用滤波器的输出与参考信号的差值为误差信号,用LMS算法求得滤波器权系数修正量,并修正滤波器。权系数最速下降调整中,采用了归一化LMS、符号LMS、块LMS技术,以简化保证权系数收敛的步长选择、减少权系数修正的运算量,从而提高自适应速度。对不同的语音在各种信噪比下仿真实验,并与改进的谱减法比较,结果表明,该法增强效果优于谱减法;在信噪比为3dB时该法的增强效果仍然令人满意。

基于LMS工作模态测试的齿轮箱性能分析

基于LMS测试分析系统,对某试验齿轮箱进行工作模态测试和分析;采用最小二乘复频域法对齿轮箱各阶模态进行参数识别,并对工作模态分析过程中额外输入峰进行了辨识,剔除了谐波引起的虚假模态;通过对测试结果进行分析及讨论,发现齿轮安装偏心导致齿轮啮合频率及其谐波的分布;根据各阶模态振型的特性,对齿轮箱运行状况进行评价,提出对该齿轮箱结构设计的改进措施。