共查询到18条相似文献,搜索用时 125 毫秒
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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。 相似文献
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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。 相似文献
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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。 相似文献
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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%. 相似文献
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《现代测量与实验室管理》2020,(2)
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。 相似文献
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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。 相似文献
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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。 相似文献
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R. B. Deshpande B. K. Shankaramurthy C. P. Revankar 《International journal for numerical methods in engineering》1976,10(2):457-463
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. 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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Benjamin Lenoir 《Optimization and Engineering》2014,15(3):609-617
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. 相似文献
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周兆经 《中国计量学院学报》1993,(2)
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。 相似文献