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.

Fitting method of pseudo-polynomial for solving nonlinear parametric adjustment

The optimal condition and its geometrical characters of the least square adjustment were proposed. Then the relation between the transformed surface and least squares was discussed. Based on the above, a non iterative method, called the fitting method of pseudo polynomial, was derived in detail. The final least squares solution can be determined with sufficient accuracy in a single step and is not attained by moving the initial point in the view of iteration. The accuracy of the solution relys wholly on the frequency of Taylor’s series. The example verifies the correctness and validness of the method. [

Three-Step Predictor-Corrector of Exponential Fitting Method for Nonlinear Schroedinger Equations

We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.

Displacement Response Reconstruction of Slender Flexible Structures Based on Cubic Spline Fitting Method

How to reconstruct a dynamic displacement of slender flexible structures is the key technology to develop smart structures and structural health monitoring(SHM), which are beneficial for controlling the structural vibration and protecting the structural safety. In this paper, the displacement reconstruction method based on cubic spline fitting is put forward to reconstruct the dynamic displacement of slender flexible structures without the knowledge of modeshapes and applied loading. The obtained strains and displacements are compared with the results calculated by ABAQUS to check the method's validity. It can be found that the proposed method can accurately identify the strains and displacement of slender flexible structures undergoing linear vibrations, nonlinear vibrations, and parametric vibrations. Under the concentrated force, the strains of slender flexible structures will change suddenly along the axial direction. With locally densified measurement points, the present reconstruction method still works well for the strain concentration problem.

Study on Coal Consumption Curve Fitting of the Thermal Power Based on Genetic Algorithm

Coal consumption curve of the thermal power plant can reflect the function relationship between the coal consumption of unit and load, which plays a key role for research on unit economic operation and load optimal dispatch. Now get coal consumption curve is generally obtained by least square method, but which are static curve and these curves remain unchanged for a long time, and make them are incompatible with the actual operation situation of the unit. Furthermore, coal consumption has the characteristics of typical nonlinear and time varying, sometimes the least square method does not work for nonlinear complex problems. For these problems, a method of coal consumption curve fitting of the thermal power plant units based on genetic algorithm is proposed. The residual analysis method is used for data detection;quadratic function is employed to the objective function;appropriate parameters such as initial population size, crossover rate and mutation rate are set;the unit’s actual coal consumption curves are fitted, and comparing the proposed method with least squares method, the results indicate that fitting effect of the former is better than the latter, and further indicate that the proposed method to do curve fitting can best approximate known data in a certain significance, and they can real-timely reflect the interdependence between power output and coal consumption.

DMPFIT: A Tool for Atomic-Scale Metrology via Nonlinear Least-Squares Fitting of Peaks in Atomic-Resolution TEM Images

Despite the wide availability and usage of Gatan’s DigitalMicrograph software in the electron microscopy community for image recording and analysis, nonlinear least-squares fitting in DigitalMicrograph is less straightforward. This work presents a ready-to-use tool, the DMPFIT software package, written in DigitalMicrograph script and C++ language, for nonlinear least-squares fitting of the intensity distribution of atomic columns in atomic-resolution transmission electron microscopy (TEM) images with a general two-dimensional (2D) Gaussian model. Applications of the DMPFIT software are demonstrated both in atomic-resolution conventional coherent TEM (CTEM) images recorded by the negative spherical aberration imaging technique and in high angle annular dark field (HAADF) scanning TEM (STEM) images. The implemented peak-finding algorithm based on the periodicity of 2D lattices enables reliable and convenient atomic-scale metrology as well as intuitive presentation of the resolved atomic structures.

嗜热链球菌JM108发酵动力学模型的建立

本研究以嗜热链球菌JM108的生长和代谢为研究对象,以建立随时间变化模型,模拟细菌的生长、产物合成以及底物消耗的动力学变化。在M17培养基中接种嗜热链球菌JM108,每隔2 h对发酵体系内的嗜热链球菌JM108活菌数、乳酸含量以及葡萄糖含量进行测定,采用3种经典模型Logistic模型、Boltzmann模型和SGompertz模型对实验值进行非线性拟合。非线性拟合结果表明,Logistic模型最适合用于描述细菌生长动力学、乳酸生成动力学和葡萄糖消耗动力学,其R2值分别为0.9974、0.9947和0.9964,均大于0.99,拟合值与实验值的误差均小于15%,拟合良好,表明所建立的动力学模型能够较好地预测发酵过程的动态变化。嗜热链球菌JM108生长量动力学方程为:y=8.59+-2:39/1+(x/2.32)^(0.02);乳酸生成量动力学方程为:y=1.05+-1:061+(x/3.67)^(3.23);葡萄糖消耗量动力学方程为:y=0.02+0.151+(x/3.47)^(3.90)。建立嗜热链球菌JM108的发酵动力学模型,为描述发酵的动力学特征提供了理论支持。

基于X射线光电子能谱的NCM正极材料中过渡金属化学态判断和定量分析:挑战及解决方法

X射线光电子能谱(XPS)在锂离子电池镍钴锰酸锂(LiNi_(x)Co_(y)Mn_(1-x-y)O_(2),NCM)正极材料的分析中有着重要应用,然而NCM中Ni、Co、Mn过渡金属主峰与俄歇峰相互重叠使这三种元素的化学态识别和定量分析变得困难。以LiNi_(0.8)Co_(0.1)Mn_(0.1)O_(2)(NCM811)为例,分析了XPS谱图中过渡金属主峰与俄歇峰的干扰问题,并提出一个基于非线性最小二乘拟合的算法对相互重叠时的过渡金属2p峰进行分峰拟合。通过比较不同化学态的Ni/Co/Mn参考样品,选取Ni(OH)_(2)、NiOOH、LiCoO_(2)、MnO_(2)作为拟合参考谱图。与常规的高斯/洛伦兹拟合方法相比,建立的非线性最小二乘拟合方法无需手动调整拟合参数,使得XPS谱图拟合过程不依赖于操作者,可重复性得到提高,并验证了这种拟合方法在NCM811正极材料XPS谱图分析中的有效应用,将过渡金属的主峰和其他元素的俄歇峰进行分离,为Ni、Co、Mn过渡金属主峰与俄歇峰相互重叠的化学态识别和定量分析难题提供了可参考的解决方案。

2维超大行程快反镜的分段非线性拟合标定

为了实现集高速扫描与精确指向功能于一体的2维超大行程快速反射镜(快反镜)的高重复定位精度与分辨率,采用分段标定方法,设计了2维超大行程快反镜角度标定系统;对多项式拟合法进行优化得到分段式非线性拟合法,并对标定模型进行了理论分析和实验测试。结果表明,在±5°范围内,传统的多项式拟合法标定误差最高达1.7 mrad,而优化后的分段式非线性拟合法在±5°标定的拟合误差小于8.2μrad,x、y轴分辨率分别可达4.6μrad和5.6μrad,x、y轴重复定位精度分别为19.4μrad和9.6μrad。此研究对精确控制2维超大行程快反镜有重要的作用。

一种新型角度传感器及其非线性补偿技术

为了解决传统电阻式、磁式等角度传感器存在磨损严重、易受电磁干扰的问题,设计了一种基于激光光斑图像识别的角度传感器,采用灰度重心法计算出光斑的中心点像素坐标,根据光斑中心点像素坐标来计算当前输入的角度值。采用傅里叶曲线拟合法,将中心点像素坐标和输入角度值拟合成一条平滑的曲线。并采用改进的反向传播(BP)神经网络算法对输入、输出曲线存在的非线性进行补偿。实验结果表明:进行非线性补偿后的角度传感器的非线性误差为1.017,降低了1.069。其迟滞性、灵敏度、分辨率和平均测量误差分别为±2.65%、2.428/(°)、2560像素/(°)和0.6°。

The Convergence of Least-Squares Progressive Iterative Approximation for Singular Least-Squares Fitting System

Data fitting is an extensively employed modeling tool in geometric design. With the advent of the big data era, the data sets to be fitted are made larger and larger, leading to more and more least-squares fitting systems with singular coefficient matrices. LSPIA (least-squares progressive iterative approximation) is an efficient iterative method for the least-squares fitting. However, the convergence of LSPIA for the singular least-squares fitting systems remains as an open problem. In this paper, the authors showed that LSPIA for the singular least-squares fitting systems is convergent. Moreover, in a special case, LSPIA converges to the Moore-Penrose (M-P) pseudo-inverse solution to the least- squares fitting result of the data set. This property makes LSPIA, an iterative method with clear geometric meanings, robust in geometric modeling applications. In addition, the authors discussed some implementation detail of LSPIA, and presented an example to validate the convergence of LSPIA for the singular least-squares fitting systems.

A unified approach for least-squares surface fitting

This paper presents a novel approach for least-squares fitting of complex surface to measured 3D coordinate points by adjusting its location and/or shape. For a point expressed in the machine reference frame and a deformable smooth surface represented in its own model frame, a signed point-to-surface distance function is defined, and its increment with respect to the differential motion and differential deformation of the surface is derived. On this basis, localization, surface reconstruction and geometric variation characterization are formulated as a unified nonlinear least-squares problem defined on the product space SE(3)×Km. By using Levenberg-Marquardt method, a sequential approximation surface fitting algorithm is developed. It has the advantages of implementational simplicity, computational efficiency and robustness. Applications confirm the validity of the proposed approach.

Data-based model free hysteresis identification for a nonlinear structure

In the last two decades, the damage detection for civil engineering structures has been widely treated as a modal analysis problem and most of the currently available vibration-based system identification approaches are based on modal parameters, namely the natural frequencies, mode shapes and damping ratios, and/or their derivations, which are suitable for linear systems. Nonlinearity is generic in engineering structures. For example, the initiation and development of cracks in civil engineering structures as typical structural damages are nonlinear process. One of the major challenges in damage detection, early warning and damage prognosis is to obtain reasonably accurate identification of nonlinear performance such as hysteresis which is the direct indicator of damage initiation and development under dynamic excitations. In this study, a general data-based identification approach for hysteretic performance in form of nonlinear restoring force using structural dynamic responses and complete and incomplete excitation measurement time series was proposed and validated with a 4-story frame structure equipped with smart devices of magneto-theological （MR） damper to simulate nonlinear performance. Firstly, as an optimization method, the least-squares technique was employed to identify the system matrices of an equivalent linear system of the nonlinear structure model basing on the exci- tation force and the corresponding vibration measurements with impact test when complete and incomplete excitations; and secondly, the nonlinear restoring force of the structure was identified and compared with the test measurements fi- nally. Results show that the proposed data-based approach is capable of identifying the nonlinear behavior of engineering structures and can be employed to evaluate the damage initiation and development of different structure under dynamic loads.

砂岩单轴压缩黏弹塑性分数阶蠕变模型研究

为建立参数少、计算简便、蠕变过程描述准确的蠕变模型,基于岩石力学及分数阶理论,引入分数阶软体元件,将其与弹性、塑性、黏性元件相结合,得到了创新的黏弹塑性蠕变模型,推导蠕变模型的本构方程,并对砂岩单轴压缩蠕变试验数据进行参数辨识、曲线拟合和对比分析,进而对蠕变模型进行验证。结果表明:引入的分数阶软体元件应变随时间呈幂函数趋势增长,可表征非线性蠕变阶段,详细地分析了弹性元件、塑性元件、黏性元件及分数阶软体元件在蠕变过程中不同阶段发挥的作用;推导得到模型在ε·(t→∞)=0(σ<σ_(s))、ε·(t→∞)>0(σ<σ_(s))、ε·(t→∞)>0(σ≥σ_(s))情况下的本构方程,以及计算简便的参数辨识方法,试验数据拟合曲线的拟合度均在0.9以上,验证了蠕变模型的合理性和科学性;所建立的六参数黏弹塑性分数阶模型能全面地描述蠕变的整个过程,并且与其他模型对比模型参数更少、计算量更小。

光强非线性响应下的光致热弹光谱光强修正

提出了基于光强非线性响应的光致热弹光谱光强修正方法,实现了激光光强的准确修正。控制DFB激光器工作于波长调制模式,设置激光调制频率为16369.75 Hz,通过光纤放大器增强其出射光强非线性项的幅值,光束经多次反射池后汇聚于石英音叉根部激发光热信号,采用数字锁相放大器解调得到对应的谐波信号,通过多项式拟合谐波信号背景,反演得到与浓度及光强分别对应的谐波信号。实验结果表明,当光强从22.03 mW变化至3.16 mW,谐波信号背景幅值与光强具有良好的线性关系,线性相关系数大于0.998,归一化后的谐波信号幅值波动小于0.37%。针对甲烷测量,系统在较大的浓度范围内具有良好的线性响应,谐波信号信噪比表明系统的最低检测限达0.22×10-6。该研究为光致热弹光谱的光强修正提供了一种新的方法,可有效提高LITES系统在长期测量应用中的稳定性。

光透过式测量下轴承内圈投影轮廓的方程描述和拟合方法

针对轴承内圈沟道曲率半径及沟道位置尺寸的机械式测量方法存在定位要求高,不易实现准确定位、测量效率低等问题,提出了一种基于视觉的光透过式测量方法,同时对该方法的测量原理、数学模型及误差影响因素进行了研究。运用数学方法求取了将几种误差影响因素进行叠加后轴承内圈各部分投影轮廓的曲线方程,给出了参数求解过程。在此基础上,研究了针对测量投影数据的拟合方法,以最小二乘法和非线性曲线拟合法分别拟合上端面和两侧面投影轮廓,求解出偏转角度α、β及相关拟合参数,对沟道投影轮廓采用非线性优化算法进行求解,并得出沟道曲率半径及沟道位置尺寸及误差。仿真结果表明,在不同的误差因素α、β下,该测量方法的测量精度可达到与提取的轮廓点坐标数据精度一致,可行性高。

基于多元非线性拟合模型的冷链物流配送成本分析

针对生鲜食品冷链物流配送成本增加的问题,采用多元非线性数值拟合模型对其进行研究。基于层次分析法,对冷链物流配送成本的主要构成部分以及主要影响因素进行分析,利用N元M次正交多项式非线性拟合模型构建生鲜食品冷链物流配送成本模型,并对计算结果进行分析与讨论。研究结果表明,采用6元5次正交多项式非线性拟合模型计算冷链物流配送成本,分析结果合理,且该模型能够较好地定量处理损耗成本、生鲜食品价值、冷藏车装载率、顾客需求量、配送时间窗及顾客满意度对冷链物流配送成本的非线性影响。

无需公共点的高精度激光跟踪仪自标定方法

多台激光跟踪仪组成的测量系统能够得到高精度的坐标观测值,在加速器准直工程领域应用十分广泛。该系统需要自标定仪器中心的距离,目前基于球面拟合的自标定方法虽然测量效率较高,但是其精度有限。为了提高其精度,分析基于拟合的自标定方法精度较低的主要原因,提出了基于三角形结构的自标定方法,定量对比了新方法和基于球心拟合方法的精度。新方法建立非线性误差模型进行参数迭代求解,能够应用于激光跟踪仪的三维自标定。通过模拟仿真和实测实验,证明了该方法比基于球心拟合的自标定方法在精度上有了大幅度提升。文中算法无需增加额外设备,改进了原先基于球心拟合方法并提高其自标定精度,具有一定的工程应用价值。

液相色谱中线性溶剂强度模型的快速建立

目的通过一组单线性梯度洗脱实验获取线性溶剂强度模型的参数值,为色谱图的预测提供所必须的参数值。方法首先,在实验中固定流动相组成的起始和结束值,通过改变梯度洗脱的时间,从而改变梯度的斜率(B)。测定溶质在这些梯度条件下的保留时间,计算其流出色谱柱时所对应的流动相组成(φR)。然后,将描述φR与B之间关系的数学公式对实验数据进行非线性拟合,从而获取线性溶剂强度模型的参数值。拟合基于Levenberg-Marquardt算法,通过Excel中的Visual Basic for Applications(VBA)语言编程实现。结果计算机程序的可靠性通过实验进行验证。以12种芳环化合物为分离的对象,以C18柱为固定相,含1%乙酸的甲醇-水溶液为流动相,应用所编写的程序对单线性梯度洗脱实验数据进行处理,获取溶剂强度模型的参数值。然后,根据所得到的参数值预测多线性梯度洗脱条件下的色谱图,得到的理论色谱图与实验色谱图吻合。结论所建立的方法可快速准确地获取线性溶剂强度模型的参数值,具有良好的实用价值。

光纤法珀传感器的改进型相位生成载波法解调

为解决相位生成载波-反正切解调算法(PGC-Atan)的非线性失真问题,搭建了基于改进型PGC-Atan算法的非本征型法珀传感器(EFPI)解调系统。首先,理论分析了载波相位调制深度(C)偏离最优值、伴生调幅、载波相位延迟等非线性因素对经典PGC-Atan算法中参与反正切运算的正弦与余弦两路信号的影响。然后,针对外调制或伴生调幅较小的情况,提出了一种基于系数补偿的改进型PGC-Atan算法(PGC-CC-Atan)。该算法通过构造与C值和载波相位延迟有关的系数,消除反正切运算中的非线性参数。针对内调制情况,提出了一种基于椭圆拟合的改进型PGC-Atan算法(PGCEF-Atan)。该算法通过基于分块矩阵的最小二乘法拟合椭圆并提取3个椭圆参数,进而将受非线性因素影响的正弦与余弦两路信号校正为正交信号。最后,通过仿真验证了改进型算法的正确性,并采用高调制特性的垂直腔面发射激光器(VCSEL)和常规腔长的EFPI等搭建PGC解调系统,对比经典PGC-Atan算法与两种改进型算法的解调性能,证实了改进型算法非线性失真抑制的有效性。实验结果表明:一定C值范围内,两种改进型算法可在非线性因素影响下有效解调。PGC-EF-Atan算法相较于PGC-CC-Atan算法,解调信纳比提升了11.602 dB,总谐波失真降低了10.951%。两种改进型算法中,PGC-EF-Atan算法对非线性失真的抑制效果更好,且解调线性度良好,准确度高。