α能谱峰形函数及其拟合参数初始值获取
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摘要
根据α能谱的形成机理,建立了一种α能谱峰形函数,提出基于矩估计法确定该峰形函数的拟合参数初始值的方法。以数理统计为基础,分别通过峰形函数和离散谱峰数据计算均值、方差和三阶中心矩建立方程组求解获取拟合参数的初始值。通过连续气溶胶检测仪探测的氡子体α能谱和低本底α能谱仪探测的238Pu面源α能谱对该峰形函数模型和初始值获取方法进行了测试。结果表明:从低重合度到高重合度,该峰形函数模型都能得到较好的应用;基于矩估计法确定该峰形函数的参数初始值能够使该峰形函数较好地拟合α能谱数据。该方法在采用计算机自动α能谱拟合分析中具有较强的实用性。
The weighted nonlinear least squares iterative fitting method is an important method to solve theα-particle spectra.The appropriate spectrum peak shape function model and the initial values of the parameters are the key to the nonlinear least squares iterative fitting.Based on the shaping mechanism ofα-ray spectrum,a kind ofα-ray spectrum peak shape function was established,and the method of determining the initial values of the peak shape function based on the moment estimation was proposed.The mathematical statistics,the mean,variance and third-order central moments of the peak shape function and the discrete spectral peak data were calculated respectively.The initial values of the parameters were obtained by the established equations.The radon daughters' alpha spectra detected by a continuous aerosol detector and 238 Pu surface-sourceα-energy spectra detected by a low-backgroundα-ray spectrometer were used to test the peak shape function model and the initial values acquisition method.The results show that the peak shape function model can be well applied from high-degree overlapping to low-degree overlapping.The initial values of the parameters of the peak shape function obtained by the moment estimation method can make the peak shape function well fit the alpha spectrum data.The method has strong practicability in the computer automatic analysis of alpha spectrum.
The weighted nonlinear least squares iterative fitting method is an important method to solve theα-particle spectra.The appropriate spectrum peak shape function model and the initial values of the parameters are the key to the nonlinear least squares iterative fitting.Based on the shaping mechanism ofα-ray spectrum,a kind ofα-ray spectrum peak shape function was established,and the method of determining the initial values of the peak shape function based on the moment estimation was proposed.The mathematical statistics,the mean,variance and third-order central moments of the peak shape function and the discrete spectral peak data were calculated respectively.The initial values of the parameters were obtained by the established equations.The radon daughters' alpha spectra detected by a continuous aerosol detector and 238 Pu surface-sourceα-energy spectra detected by a low-backgroundα-ray spectrometer were used to test the peak shape function model and the initial values acquisition method.The results show that the peak shape function model can be well applied from high-degree overlapping to low-degree overlapping.The initial values of the parameters of the peak shape function obtained by the moment estimation method can make the peak shape function well fit the alpha spectrum data.The method has strong practicability in the computer automatic analysis of alpha spectrum.
引文
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[13]何晓群.应用回归分析[M].北京:中国人民大学出版社,2015.(He Xiaoqun.Applied regression analysis.Beijing:China Renmin University Press,2015)
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[15]祝强,李少康,徐臻.LM算法求解大残差非线性最小二乘问题研究[J].中国测试,2016,42(3):12-16.(Zhu Qiang,Li Shaokang,Xu Zhen.Study of solving nonlinear least squares under large residual based on Levenberg-Marquardt algorithm.China Measurement and Test,2016,42(3):12-16)
[16]Li Zhe,Tuo Xianguo,Shi Rui,et al.Analytic fitting and simulation methods for characteristic X-ray peaks from Si-PIN detector[J].Nucl Sci Tech,2013,24:060206.
[17]李哲,张译文,孙世峰,等.γ射线闪烁体探测器响应函数模型的研究[J].原子能科学技术,2015,49(8):1354-1358.(Li Zhe,Zhang Yiwen,Sun Shifeng,et al.Study on response function model forγ-ray scintillation detector.Atomic Energy Science and Technology,2015,49(8):1354-1358)
[18]黄金峰,王莹,熊文俊,等.基于Monte-Carlo模拟和峰形拟合的CdZnTe探测器G(E)函数简便计算方法研究[J].原子能科学技术,2017,51(1):165-169.(Huang Jinfeng,Wang Ying,Xiong Wenjun,et al.Study on simple G(E)function calculation method of CdZnTe detector based on Monte-Carlo method and peak shape fitting.Atomic Energy Science and Technology,2017,51(1):165-169)
[19]Park C S,Choi H D,Sun G M,et al.Status of developing HPGeγ-ray spectrum analysis code HYPERGAM[J].Prog Nucl Energ,2008,50(2):389-393.
[2]Lourakis M I A.A brief description of the Levenberg-Marquardt algorithm implemented by levmar[J].Foundat Res Tech,2005,4(1):1-6.
[3]石睿.基于探测器响应函数的α能谱解谱技术研究[D].成都:成都理工大学,2014:33-34.(Shi Rui.Alpha spectrum resolving method based on the detector response function.Chengdu:Chengdu University of Technology,2014:33-34)
[4]Li Zhe,Tuo Xianguo,Shi Rui.A statistical approach to fit Gaussian part of full-energy peaks from Si(PIN)and SDD X-ray spectrometers[J].Sci China Technol Sci,2014,57(1):19-24.
[5]刘永刚.γ能谱谱数据分解方法研究[D].北京:中国地质大学,2011:58-61.(Liu Yonggang.Study onγspectral data analysis methods.Beijing:China University of Geosciences,2011:58-61)
[6]Garcia-Tora1o E,Ace1a M L.Nolin:nonlinear analysis of complex alpha spectra[J].Nucl Instrum Meth A,1981,185(1):261-269.
[7]Bortels G,Collaers P.Analytical function for fitting peaks in alpha-particle spectra from Si detectors[J].Appl Radiat Isotopes,1987,38(10):831-837.
[8]Shi Rui,Tuo Xianguo,Li Huailiang,et al.239Pu alpha spectrum analysis based on PIPS detector response function and variations with vacuum and distance[J].Nucl Sci Tech,2017,28(1):4-10.
[9]胡亮.非线性拟合的初值问题[J].吉首大学学报(自然科学版),2003,24(1):37-39.(Hu Liang.Initial value problem of nonlinear fitting.Journal of Jishou University(Natural Science Edition),2003,24(1):37-39)
[10]艾宪芸.碲锌镉探测器性能分析及其γ谱解析方法研究[D].北京:清华大学,2005:59-64.(Ai Xianyun.Research on the gamma ray spectral response characteristics and relevant spectral analysis methods of cadmium zinc telluride(CdZnTe)detector.Beijing:Tsinghua University,2005:59-64)
[11]张韵华.数值计算方法和算法[M].北京:科学出版社,2000.(Zhang Yunhua.Numerical methods and algorithms.Beijing:Science Press,2000)
[12]Montero M P R,Orellana C J G,Velasco H G,et al.Fast adaptive alpha-particle spectrum fitting algorithm based on genetically estimated initial parameters[J].Appl Radiat Isotopes,2004,60(2):145-149.
[13]何晓群.应用回归分析[M].北京:中国人民大学出版社,2015.(He Xiaoqun.Applied regression analysis.Beijing:China Renmin University Press,2015)
[14]Lampton M.Damping-undamping strategies for the Levenberg-Marquardt nonlinear least-squares method[J].Comput Physics,1997,11(1):110-115.
[15]祝强,李少康,徐臻.LM算法求解大残差非线性最小二乘问题研究[J].中国测试,2016,42(3):12-16.(Zhu Qiang,Li Shaokang,Xu Zhen.Study of solving nonlinear least squares under large residual based on Levenberg-Marquardt algorithm.China Measurement and Test,2016,42(3):12-16)
[16]Li Zhe,Tuo Xianguo,Shi Rui,et al.Analytic fitting and simulation methods for characteristic X-ray peaks from Si-PIN detector[J].Nucl Sci Tech,2013,24:060206.
[17]李哲,张译文,孙世峰,等.γ射线闪烁体探测器响应函数模型的研究[J].原子能科学技术,2015,49(8):1354-1358.(Li Zhe,Zhang Yiwen,Sun Shifeng,et al.Study on response function model forγ-ray scintillation detector.Atomic Energy Science and Technology,2015,49(8):1354-1358)
[18]黄金峰,王莹,熊文俊,等.基于Monte-Carlo模拟和峰形拟合的CdZnTe探测器G(E)函数简便计算方法研究[J].原子能科学技术,2017,51(1):165-169.(Huang Jinfeng,Wang Ying,Xiong Wenjun,et al.Study on simple G(E)function calculation method of CdZnTe detector based on Monte-Carlo method and peak shape fitting.Atomic Energy Science and Technology,2017,51(1):165-169)
[19]Park C S,Choi H D,Sun G M,et al.Status of developing HPGeγ-ray spectrum analysis code HYPERGAM[J].Prog Nucl Energ,2008,50(2):389-393.