最小二乘拟合解谱方法的研究

成都理工大学毕业设计（论文）I最小二乘拟合解谱方法的研究摘要随着探测器和电子技术、计算机技术的高速发展，核辐射测量仪器越来越多的采用能谱分析技术，它可以一次测量获得更多的有用信息，是快速、可靠地确定待测样品中放出各种能量的放射性核素或元素的性质及其强度的重要手段。几十年来，它在核物理研究、原子能各种领域、核防护、环境监测、资源勘查等方面都发挥了巨大的作用。最小二乘拟合解谱的应用有其独到之处，特别是在重峰分析方面，可以用此方法获得我们肉眼分辨不开的重叠峰，得到重峰的相关信息。本文主要介绍用高斯峰形函数（高斯峰）加本底函数拟合实测谱线，用非线性最小二乘拟合法解出拟合参数的方法，并将此方法形成了程序。程序主要包括单峰、多峰分析和重峰分析。程序分析实际的谱线得到的拟合结果可用图像直接绘出以便直观的看出与原始谱线的符合程度，分析所得的峰高，峰位，半高宽，面积等数据信息可保存在文件中，以便于进行后续的分析和研究。关键词：非线性最小二乘；能谱分析；高斯拟合成都理工大学毕业设计（论文）IITheResearchofNonlinearApproximationAnalysisofSpectrumAbstract：Withtherapiddevelopmentofcomputeranddetectorandelectronictechnology,moreandmorenuclearradiationinstrumentsadoptspectrumanalyzingtechnology,whichcangetmoreusefulinformationinonetime,isafastandreliablemethodofdeterminingelementsorelementalpropertiesanditsintensity,theseelementscanemitseveralenergyandformparticularspectrum.Inthepasttensofyears,itplaysabigroleinnuclearphysics,eachfieldofatomicenergy,nuclearprotection,environmentalmonitoringandresourceexploration.Theapplicationofleastsquaremethodtoanalysisspectrumhasitsoriginalpoints,especiallyinmultiplepeaksanalysis,usingthismethodcangetweakpeakswhichwereinvisibleandsubmergedinotherpeaks.Wecanobtainrelevantinformationofsubmergedpeaksbyanalyzingandfittingpeakpositions.Inthepassage,weintroduceamethodoffittingGaussianpeaksandbackgroundandthenderivingfittingparametersbyleastsquaremethod,besides,writingaprogramforthismethod.TheprogrammainlyincludesGaussianpeaks(singlepeakandmulti-peak)fittinganalysisandmultiplepeaksanalysis.Thefittingresultsderivedfromanalyzingactualspectrumlinebytheprogramcanbedrawndirectlyintheformofpicturessoastodetectcoincidenceextentbetweenactualspectrum-lineandtheoriginalspectrum-line,followingdatamessagessuchaspeakheight,peakposition,FWHM,areafromanalysisresultscanbereservedinfilesoastoFollow-upanalysisandresearch.Keywords:nonlinearleastsquares;spectrumanalysis;Gaussianfitting成都理工大学毕业设计（论文）III目录第1章前言..............................................................................................................11.1研究意义.................................................................................................................................11.2国内外研究现状....................................................................................................................11.3主要工作内容........................................................................................................................4第2章谱线的特点......................................................................................................52.1核辐射测量的特点...............................................................................................................52.1.1核辐射是核衰变的产物...................................................................................................52.1.2核辐射的能量具有特征性..............................................................................................52.1.3核素的含量与特征辐射的强度存在正比关系..........................................................52.2仪器谱......................................................................................................................................62.2.1γ射线和物质的相互作用................................................................................................62.2.2统计涨落的影响...............................................................................................................72.2.3其它作用的影响...............................................................................................................8第3章解谱的基本理论..............................................................................................93.1谱数据的获取原理..............................................................................................................93.2高斯拟合法的原理............................................................................................................103.2.1扣除基底求“净”全能峰.................................................................................................103.2.2峰形函数加基线函数同时拟合的峰面积法............................................................123.2.3单峰曲线拟合分析方法.................................................................................................123.2.4重峰的分析方法..............................................................................................................123.3算法介绍..............................................................................................................................133.3.1非线性模型........................................................................................................................133.3.2梯度和海赛矩阵的计算.................................................................................................143.3.3勒温伯格—马阔特方法.................................................................................................16第4章分析软件的设计与实现................................................................................194.1分析软件的功能介绍.........................................................................................................194.2分析软件界面......................................................