数据拟合算法分析及C语言实现

数据拟合在很多地方都有应用,主要用来处理实验或观测的原始离散数据。通过拟合可以更好的分析和解释数据。在引用前人的算法基础上,采用正交多项式最小二乘法进行曲线拟合,通过实验对算法进行了分析,并给出了C语言实现的代码。     

剪切压电陶瓷块微位移测量及非线性修正

通过搭建的剪切压电陶瓷块微位移测量系统,进行了5个不同目标电压的剪切压电陶瓷微位移测量实验,对实验数据分别进行二阶、三阶、四阶最小二乘拟合后进行非线性修正实验,其中采用三阶最小二乘拟合进行修正时效果最好,其位移1 050 nm行程时最大非线性误差为3 nm。对所得三阶最小二乘拟合多项式的系数进行样条插值拟合,从而实现对不同目标位移的非线性修正,其中位移900 nm行程时最大非线性误差为4 nm,仅为原始非线性误差的11%。     

基于最小二乘法拟合的流量计不确定度分析方法

为确定标准表法流量标准装置中非固定流量点使用的标准流量计的不确定度,使用最小二乘法对其流量和仪表系数测量数据进行拟合,计算拟合曲线的标准偏差,分析流量计的不确定度。最小二乘法拟合分别采用不同次数的多项式和分式进行,并对拟合曲线进行比较。结果表明线性拟合操作简单,但拟合效果随测量数据的线性关系程度区别较大;曲线拟合随着模型次数增加拟合效果越好,不确定度越小,但高次多项式存在效果不佳的情况;分式拟合能较好地实现低次高精度的曲线拟合,在非线性关系数据的应用效果优于多项式拟合,能够满足流量计的不确定度要求。     

高精确度智能仪器大范围测量中的数据解算方法

以单片机为核心的智能化仪器难以实现高精确度、大范围测量,尤其是输出量与输入量在不同区间呈不同的函数关系时,在单片机上难以实现其运算,为此本文把输出量划分为若干个区间段,在不同区间段内采用多项式校正理论和最小二乘法拟合方法,给出了在不同区间段内多项式校正的数学模型,并在此基础上阐述了提高校正数据精度的有效措施。     

汽－液平衡的一种有效算法

以活化碳酸钠溶液吸收二氧化碳的汽－液平衡分压为例，用最小二乘法和正交多项式，将一元拟合与二元拟合结合在一起，建立了汽－液平衡的一种有效算法，与实测数据拟合的很好，最大相对误差不超过３％．     

土壤湿度传感器非线性误差补偿方法

PHSL-S土壤湿度传感器具有高度非线性,严重影响土壤水分含量的测量准确性。本文介绍了一种基于最小二乘法和多项式拟合的土壤湿度传感器非线性误差补偿方法。首先介绍了非线性误差补偿原理,构建了基于多项式拟合的土壤湿度传感器非线性误差补偿器(即传感器逆模型),通过综合评价拟合函数性能参数,确定补偿器的阶数;利用最小二乘法,求解出了传感器补偿器的参数。利用PHSL-S传感器土壤湿度检测系统进行实验,结果表明,这种基于最小二乘法和多项式拟合的土壤湿度传感器非线性误差小于5%,证实了该方法的有效性。     

EPE动态冲击曲线拟合函数对比

目的针对多项式函数拟合发泡聚乙烯泡沫(EPE)动态冲击曲线不准确的问题,构建精确且简洁的数学模型以解决此问题。方法选用对勾函数、双指数函数及常见的二次、三次多项式函数对实验数据进行拟合,拟合点共8个。改变实验材料的密度、厚度及实验的跌落高度,对比分析4种数学模型的拟合效果。结果双指数函数和对勾函数的拟合度均可达到0.98以上,二次和三次多项式函数拟合度低于0.9,且拟合效果不稳定,在拟合曲线的最低点误差较大。结论与双指数函数相比,对勾函数的参数较少,拟合效果相近时,在实际应用中更易推广。     

基于三维点云螺纹中轴线的拟合方法研究

螺纹中轴线的精确测定是决定螺纹三维测量结果是否准确的重要因素之一。中轴线的倾斜、偏移会对工件坐标系的建立、螺纹的三维重构、参数检验等测量操作引入误差。基于三维点云的最小二乘拟合算法,开展了螺纹中轴线的拟合方法研究。根据螺纹表面点云数据,利用螺纹表面与中轴线的特征关系建立最小二乘数学模型,通过计算点云数据的三维凸包滤除螺纹自身三维结构带来的拟合误差,使螺纹中轴线的测定更精准。通过仿真实验,基于三维点云的最小二乘拟合算法拟合的直线与三维点云的距离方差为0.34,在旋合长度范围内与投影法确定的直线两端最大距离为0.15μm,符合三维测量高精度标准,基于三维点云的最小二乘拟合算法可以快速、准确地拟合螺纹中轴线。     

磁保持继电器短耐试验通电时间的波动问题研究

针对磁保持继电器在短时耐受试验中得到的通电时间数据表现出杂乱无章波动现象的问题,利用正交多项式拟合方法对试验数据进行了拟合,并研究了所得拟合曲线的特点。结果表明,5次正交多项式能有效地反应出这些试验数据的分布特征,揭示了隐含在数据中的规律,分析了可能导致这种现象的原因,为更准确的产品试验与检测提供了有力的保障。     

传感器标定的非线性校正研究

针对传感器输入输出存在的非线性误差;本文利用曲线拟合法中的最小二乘拟合、多项式曲线拟合及神经网络拟合三种方法来对某压力传感器标定实验所得的数据进行非线性校正,并对拟合后的数据进行非线性分析;结果表明,通过以上三种曲线拟合方法都可以对传感器标定的数据进行校正,但神经网络拟合后的线性度相对最小二乘和多项式拟合后的线性度要小,非线性校正效果显著.此类方法简捷,实用,可对所有非线性系统进行校正,具有较高的应用价值.     

Comparison of curve fitting techniques

Various methods of curve fitting used in solving aero-thermodynamic problems of turbomachines have been compared. The first and second derivatives predicted by using orthogonal polynomial fits are much more accurate than those obtained by using spline fits (with different boundary conditions) and method of least squares.     

电容式水分传感器的非线性特性与改善方法

电容法水分快速测定仪是最常用的现场水分快速检测设备之一,但由于非线性影响,电容法水分检测的准确性受到限制.本文介绍了电容式水分传感器的工作原理,探讨了非线性影响因素,建立了非线性影响的数学模型,提出了较全面的硬件改善措施和利用最小二乘法确定传感器输出特性多项式回归模型的软件补偿方法.设计实践表明,利用本研究方法对电容式水分传感器进行非线性补偿效果良好.     

Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms

Four modal methods of reconstructing a wavefront from its difference fronts based on Zernike polynomials in lateral shearing interferometry are currently available, namely the Rimmer-Wyant method, elliptical orthogonal transformation, numerical orthogonal transformation, and difference Zernike polynomial fitting. The present study compared these four methods by theoretical analysis and numerical experiments. The results show that the difference Zernike polynomial fitting method is superior to the three other methods due to its high accuracy, easy implementation, easy extension to any high order, and applicability to the reconstruction of a wavefront on an aperture of arbitrary shape. Thus, this method is recommended for use in lateral shearing interferometry for wavefront reconstruction.     

A versatile analytical expression for the inverse Abel transform applied to experimental data with noise

A method for reconstruction of radially distributed plasma emission coefficients from projections with noise is proposed. The method represents the projections based on overlapping piecewise polynomial least squares fitting to take the inversion. Parameters that affect the inversion accuracy are analyzed and discussed in detail. Results for profiles with various shapes are presented and compared with those obtained with other methods. It is shown that for data with different numbers of points and different levels of noise, our method is more accurate and yields markedly better results for very sparse data. In addition, excellent results have been obtained from experimental intensities of an arc plasma without filtering of noise.     

The Fitting of Power Series,Meaning Polynomials,Illustrated on Band-Spectroscopic Data

The prototype of fitting polynomials to equally-spaced data—in which the equalspacing is theoretically precise and the data is accurate to many decimal places—arises in the analysis of band spectra. A hard look at such examples forces us to reexamine our thinking on such diverse issues as: How to formulate such problems, the use of robust/resistant techniques in polynomial regression, which coordinates to use and why, the basic properties of linear least squares, choices in stopping a fit, and improved ways to describe our answers.

Our results and attitudes apply rather directly to other situations where we are fitting a sum of functions of a single variable. When two or more different variables, subject to error, blunder, or omission, underlie the carriers to be considered, regression/fitting problems are likely to need not only the considerations presented here, but others as well. To a varying extent, the same will be true of nonlinear fitting/regression problems.     

商业轮转胶印最佳实地密度研究与应用

在标准印刷条件下,使用GATF测试版在商业轮转上印刷轻涂纸,根据相对反差K与实地密度的关系,基于最小二乘法多项式拟合得到了回归方程,研究了商业轮转胶印的最佳实地密度。研究结果表明:墨层较薄时,则实地密度小,色彩平淡;墨层过厚会导致网点增大过度,印刷品暗调并级。     

A general approach of least squares estimation and optimal filtering

The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the method as well as numerical considerations are discussed. Then two particular cases are considered: the usual least squares method and the Generalized Least Squares method. In both cases, the estimator and its variance are characterized in the time domain and in the Fourier domain. Finally, the equivalence of the Generalized Least Squares method and the optimal filtering technique using a matched filter is established.     

用多项式模型和自适应滤波估计瞬时频率

本文论述了非平稳信号瞬时频率(IF)的估计方法,包括基干最小均方误差(LMS)算法或递推最小二乘(RLS)算法的自适应IF估计方法和基于信号相位多项式模型的IF估计方法。对各种估计方法的估计方差与理论方差下限进行了比较。说明了,基于互Wigner分布的估计方法所需信噪比(SNR)门限值最低。在低SNR、短信号记录的情况下,用多项式相位模型与最大似然法可以获得比较可靠的IF估计。