基于非线性最小二乘法的多光谱拟合程序：应用于12CH4谱线参数分析

精确的甲烷分子实验光谱参数在大气科学和天文探测等领域有着广泛的应用,特别是谱线的展宽系数及其温度依赖系数对于甲烷分子浓度廓线的研究尤为重要。精密的实验测量是获得准确谱线参数的重要手段。采用实验测量获取谱线参数时,需要在已知实验条件（浓度,温度,总压力,吸收光程以及气体分子种类的混合比等）的情况下,多次扫描同一波段范围得到多组实验室吸收光谱,然后利用基于非线性最小二乘法的拟合程序处理这些光谱,反演获得所需要的光谱参数。然而,一般常用的单光谱拟合程序处理实验光谱既费时又容易引起拟合过程中的误差传递。针对此问题,采用最小二乘拟合技术和Levenberg-Marquardt迭代算法编写了一款适用于处理由可调谐半导体激光吸收光谱技术（TDLAS）所获得的吸收光谱的多光谱拟合程序。该程序可同时处理多张实验光谱,并基于全局拟合方法获得一套光谱参数。详细介绍了该程序的原理、使用方法及数据处理过程。利用多光谱拟合程序中的Voigt线型处理了2 958～2 959 cm-1波数内甲烷（12CH₄）分子6条跃迁谱线的实验光谱,获得了296.0,251.0,223.0,198.0和173.0 K共5组温度下12CH₄分子6条谱线的空气展宽系数。与之前文献报道的该波段内采用单光谱拟合程序得到的相应数据对比结果表明：获得的各温度下的空气展宽系数与参考文献中相应数据差值的百分比处在-4.97%~1.58%之间,两者数据整体符合较好,并且在30组对比数据中,有4组由单光谱拟合程序得到的空气展宽系数的误差值小于由多光谱拟合程序得到的相应数值,有2组数据显示由两种方法获得的误差值相等,其余24组由多光谱拟合程序获得的数据拟合误差小于由单光谱拟合程序获得的相应数值,表明多光谱拟合程序具有良好的可靠性,适用于气体分子吸收光谱的处理。     

用等离子体粒子能谱拟合温度的新方法

用最小二乘法拟合等离子体粒子能谱实验数据时，通常使拟合函数与实验能谱数据之间的误差平方和极小化。如果将能谱实验数据的对数拟合成直线以求得粒子温度，则最好对温度误差的平方和极小化。给出了这种拟合方法的计算公式，并对两种不同方法得到的结果进行了比较。     

基于循环神经网络的缝洞型油藏油井产量预测

利用神经网络的强大非线性映射和拟合能力，构建神经网络产量预测模型，并针对油田生产数据的高误差、易缺省等特性和曲线拟合预测不易收敛的情况，提出了训练数据集扩充方法和改良的均方误差损失函数.在拟合油井产量方面取得了显著的效果.     

磁探针参数的标定

为了标定EAST装置电磁测量系统中的磁探针位置偏差和回路增益,通过分析该装置中的误差源,设计了极向场线圈的通电模式。运用格林函数等算法程序对测量数据进行预处理,利用简化的泰勒线性展开,结合带权重的最小二乘法对数据进行多次循环迭代,拟合出磁探针的位置偏差和回路增益。实验结果表明,使用该方法标定是合理的。     

一种实用的多功能的函数拟合程序

研制了函数拟合程序.本程序主要特点在于可键盘或联机输入实验数据.利用计算机图示功能,手动、或自动拟合,以寻求最佳。本系统能打印出拟合后各参数的最佳值。并能在数字绘图仪上分别画出实验数据和理论曲线或光谱分解后的各分立子谱带。     

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为了标定EAST装置电磁测量系统中的磁探针位置偏差和回路增益,通过分析该装置中的误差源,设计了极向场线圈的通电模式。运用格林函数等算法程序对测量数据进行预处理,利用简化的泰勒线性展开,结合带权重的最小二乘法对数据进行多次循环迭代,拟合出磁探针的位置偏差和回路增益。实验结果表明,使用该方法标定是合理的。     

上转换纳米颗粒荧光寿命测量数据采集与处理

为了测试分析上转换纳米材料(up-conversion nanoparticles, UCNPs)的荧光寿命，设计了一种针对UCNPs进行荧光寿命信号数据高速采集并测量输出的系统。该系统通过MATLAB编写虚拟原始荧光信号并完成滤波和数据拟合，将数据程序脚本嵌入LabVIEW中进行计算和处理，在上位机显示荧光信号波形、拟合数据波形、荧光个数、荧光寿命以及寿命极值等。研究结果表明:该系统软件仿真和数值计算模拟取得了基本一致的结果，在背景噪声一定的情况下，两者误差在3%以内，具有良好的稳定性和准确性。本研究工作对UCNPs荧光寿命测量系统的研发有一定指导价值。     

空间调制干涉光谱成像仪数据误差修正方法

针对空间调制干涉光谱成像仪获取数据的特殊性,提出一种数据误差修正方法,修正了干涉数据的探测器误差和光学系统误差.对于光学系统导致的光场分布不均匀误差,采用多项式拟合的方法从干涉数据中直接获取误差修正数据.利用实际仪器获取的数据对上述方法进行了计算机仿真,得到了较好的误差修正结果.     

ψ(2S)扫描实验中相关数据的拟合及误差处理

文中详细讨论了ψ(2S)扫描实验数据拟合过程中同一反应道不同能量点之间,以及同一能量点不同反应道之间的复杂的相关性问题.利用最大似然函数法得到拟合公式;采用多次抽样拟合的办法避免过多待定参数带来的极小化困难;分析并综合各类误差对拟合参数的影响,从而求得最终的合成误差.文中所阐述的方法是处理实验数据拟合过程中复杂相关性问题的一种有效方法.     

作图法求直线斜率取点远近的探讨

本文以力敏传感器定标数据为例,使用origin软件对数据进行了直线拟合。在作图法拟合的直线上,选取离中值点较远处和较近处坐标点,计算得到靠近两端离中值点较远处坐标点斜率的误差远小于离中值点较远处坐标点斜率,通过误差杆理论分析了其中的缘由。     

瑞利散射多普勒激光雷达风场反演方法

介绍了瑞利散射多普勒激光雷达的风场探测原理和系统结构. 给出了Fabry-Perot(FP)标准具透过率曲线的校准方法. 指出对透过率采用Lorentz或Voigt拟合会产生较大误差,特别是采用Lorentz拟合最大将引起8%的误差. 提出了采用非线性最小二乘法拟合标准具的透过率函数,该方法可以有效消除拟合误差,提高风速测量精度. 考虑到温度不确定度在风场反演过程中的主导影响,提出了同时反演风速和大气温度的非线性迭代算法. 风场反演仿真试验结果表明:在不考虑米散射信号的影响下,该反演算法与传统的反演方法相 关键词： 激光雷达 瑞利散射 多普勒 风     

Parameter Estimation as a Problem in Statistical Thermodynamics

In this work, we explore the connections between parameter fitting and statistical thermodynamics using the maxent principle of Jaynes as a starting point. In particular, we show how signal averaging may be described by a suitable one particle partition function, modified for the case of a variable number of particles. These modifications lead to an entropy that is extensive in the number of measurements in the average. Systematic error may be interpreted as a departure from ideal gas behavior. In addition, we show how to combine measurements from different experiments in an unbiased way in order to maximize the entropy of simultaneous parameter fitting. We suggest that fit parameters may be interpreted as generalized coordinates and the forces conjugate to them may be derived from the system partition function. From this perspective, the parameter fitting problem may be interpreted as a process where the system (spectrum) does work against internal stresses (non-optimum model parameters) to achieve a state of minimum free energy/maximum entropy. Finally, we show how the distribution function allows us to define a geometry on parameter space, building on previous work[1, 2]. This geometry has implications for error estimation and we outline a program for incorporating these geometrical insights into an automated parameter fitting algorithm.     

基于BP神经网络的磁滞回线的曲线拟合

BP神经网络通过调节连接权重可以实现以任意精度逼近非线性函数,利用这一特点可对非线性函数关系进行拟合。本利用BP神经网络对测定磁滞回线实验中的数据进行处理,结果表明该方法处理结果精度高,拟合效果好,计算机处理程序通用。     

多光谱辐射测温的正交多项式回归方法

对于多光谱辐射测温问题,传统的数据处理方法多为最小二乘法、多元线性回归拟合和逐步回归拟合。这些处理方法自身都存在一定的缺陷,使得拟合结果与物体表面真温之间存在一定的误差。文章在可变发射率模型的基础上,提出了对多光谱辐射测温数据处理的另一种新方法——正交多项式回归方法。文章阐述了正交多项式回归的数学基础,并根据钨表面在不同温度下的光谱发射率数据,分别采用逐步回归方法和正交多项式回归方法,对钨表面的真温进行了模拟。通过拟合结果的对比发现用正交多项式回归方法来处理数据,其原理简单、运算量小,拟合结果与表面真温之间的相对误差也较小。得出的结论是用正交多项式回归方法对多光谱辐射测温的数据进行处理,拟合结果比传统方法误差小、速度快、精度高。     

A new ellipse fitting method of the minimum differential-mode noise in the atom interference gravimeter

Ellipse fitting is a useful tool to obtain the differential signal of two atom interference gravimeters. The quality standard of ellipse fitting should be the deviation between the true phase and the fitting phase of the interference fringe. In this paper, we present a new algorithm to fit the ellipse. The algorithm is to minimize the differential noise of two interference gravimeters and obtain a more accurate value of the gravity gradient. We have theoretically derived the expression of the differential-mode noise and implemented the ellipse fitting in the program. This new algorithm is also compared with the classical methods.     

WIDECARS spectra fitting in a premixed ethylene–air flame

WIDECARS measures temperature and mole fractions of most of the major species in ethylene–air flames. One of the issues in implementing this technique is fitting the experimental spectra to theory to obtain flame conditions (temperature, species mole fractions). Individual spectra contain many species resonances, and theory is slow to compute. Libraries of precalculated spectra can be used, but a library of sufficient density for accurate interpolation is large given the many variables. A new fitting algorithm is presented which utilizes a less‐dense library, and additional spectra are calculated during fitting to maintain accuracy. The iterative convergence method converts the problem of minimizing fit error, which converges slowly, to a zero finding problem, which converges reliably, rapidly, and accurately to best fit. Various practical fitting issues, such as the effects of dye laser mode noise and variability, phase‐matching efficiency, and shifts of the spectrum on the spectrometer are addressed. The technique is demonstrated in the analysis of experimental measurements in an equivalence ratio 2.1 ethylene–air flame above the surface of a McKenna burner. Precision errors because of experimental and fitting effects are discussed. Copyright © 2015 John Wiley & Sons, Ltd.     

Volume matching in Tolman models

Since the equations of general relativity are nonlinear, it is not strictly correct to obtain average values by integrating over spatial volumes. Yet this is really what is done in the attempt to fit our rather lumpy universe to a standard cosmological model of uniform density. Consequently, the fitting problem, raised last year by Ellis and Stoeger [1], asks how accurate the average values derived from observational cosmology can be, even without measurement uncertainties. Do they really describe the best-fit Robertson-Walker model to our universe? One of the alternatives to averaging they suggested was that of volume matching. We try to provide a first estimate of the error due to averaging by fitting a Robertson-Walker model to an inhomogeneous Tolman model using realistic density profiles. Comparing the results from volume matching and from averaging, we find that errors are of the order of 10% or more.     

Moessfit

A free data analysis program for Mössbauer spectroscopy was developed to solve commonly faced problems such as simultaneous fitting of multiple data sets, Maximum Entropy Method and a proper error estimation. The program is written in C++ using the Qt application framework and the Gnu Scientific Library. Moessfit makes use of multithreading to reasonably apply the multi core CPU capacities of modern PC. The whole fit is specified in a text input file issued to simplify work flow for the user and provide a simple start in the Mössbauer data analysis for beginners. However, the possibility to define arbitrary parameter dependencies and distributions as well as relaxation spectra makes Moessfit interesting for advanced user as well.     

一个新的空间掩盖效应拟合公式

传统的空间掩盖效应是采用韦伯（Weber）定律来描述的，然而该定律仅考虑了明视觉区，对较弱或较强的光强均不合适。为了更好地描述空间掩盖效应，本文利用信号处理方法，给出了一种新的拟合公式。实验用不同模型拟合Konig与Brodhun的实验数据，证实了提出的模型均方根误差仅为0．0102，小于传统的Weber定律、Weber定律的优选表达式、Guilford模型，以及Chen模型。结果表明，提出的拟合公式在更宽的光强范围内都能与数据很好地拟合，可更广泛地用于工程实践。     

Spreadsheet based analysis of Mössbauer spectra

Using spreadsheet programs to analyse spectral data opens up new possibilities in data analysis. The spreadsheet program contains all the functionality needed for graphical support, fitting and post processing of the results. Unconventional restrictions between fitting parameters can be set up freely, and simultaneous analysis i.e. analysis of many spectra simultaneously in terms of model parameters is straightforward. The free program package Vinda – used for analysing Mössbauer spectra – is described. The package contains support for reading data, calibration, and common functions of particular importance for Mössbauer spectroscopy (f-factors, second order Doppler shift etc.). Methods to create spectral series and support for error analysis is included. Different types of fitting models are included, ranging from simple Lorentzian models to complex distribution models.