分析化学中三阶数据分辨算法及应用的研究

【作者】 曹玉珍；

【导师】 俞汝勤；

【作者基本信息】 湖南大学 ， 分析化学， 2001， 硕士

【摘要】 本论文的绪论部分概述了化学计量学多元分辨与校正这一分支的发展情况以及研究现状，在综述基础上，重点研究了由多样品荧光数据所构成的三阶数据的分辨算法及其应用，着重解决了传统PARAFAC算法的缓慢收敛和对组分数估计敏感等问题。 第一章利用传统PARAFAC算法与三维荧光分析法相结合，同时测定了江、河和湖泊中可能存在的环境污染物萘、1-萘酚和2-萘酚，测定结果表明化学计量学方法在环境检测方面具有广阔的应用前景。此外，本实验的结果为后续算法提供了实际数据。 第二章提出了一个使用惩罚对角化误差修饰的PARAFAC算法（PDE），该算法不仅能加快计算速度，克服传统PARAFAC算法所存在的收敛缓慢问题，而且，当计算时所使用的因子数不小于体系的真实组分数时，对于真实组分的分辨和校正都能获得正确的解，这就部分解决了组分数难以估计的难题。 第三章提出了一个交替最小化协变矩阵误差算法（AMCME），该算法不仅能克服传统PARAFAC算法对组分数估计敏感性，而且能克服PARAFAC算法的缓慢收敛。此外，该算法还克服了ACOMAR算法的收敛较慢，避免了PALS中参数选择的困难。 第四章提出了交替最小化耦合矢量误差和PARAFAC误差（COV-PAR）算法，该算法克服了COVER方法必须在具有先验化学信息的前提下，才能对体系进行分辨和校正。与此同时，该算法也克服了PARAFAC的缓慢收敛和对组分数估计的敏感性。在此基础上，将该算法应用于荧光光谱重叠的水杨酸、龙胆酸和对氨基苯甲酸三种药品混合物体系的分辨，结果令人满意。更多还原

【Abstract】 In the introduction section of this thesis, the development of multivariateresolution and calibration methods in cbemometrics has been reviewed.Algorithms of the resolution for three-way data array constructed by fluorescencedata and their applications have been reseaithed. The problems of slowconvergence and being icnsitivc to the estimation of component number, whichare inevitable while nsing the traditional PARAFAC algorithm are solved.In chapterl, the system of the mixtures of naphthalene, l-naphathol and 2-naphthol, possible pollutants in rivers and lakes, is resolved using the ordinaryPARAFAC algorithm. The satisfactory recovered profiles showed thatchemometrics methods have wide applications in environmental detection.Furthermore, the results of this application supply a real data array for the newalgorithms in the following chapters.In chapter 2, a modified PARAFAC algorithm using penalty diagonalizationerror (PDE) is proposed. This approach can conquer not only the problem of theslow convergence but also that of being sensitive to the estimation of the numberof actual underlying factors, which are inevitable while using the traditionalPARAFAC algorithm.In chapter 3, an alternatively mimmizing covariant matrix error algorithm(AMCME) was developed. This algorithm can overcome the problems of slowconvergence and the estimation of component number of PARAFAC.Furthermore, this algorithm solves the slow convergence and possibledegeneration phenomena of ACOMAR and provides a natural way to avoiding thedifficulty of choosing an appropriate parameter of PALS.Chapter 4 proposed an alternatively minimizing coupled vectors resolution2p___#~2OOlW5~error and PARAFAC error algorithm (COY-PAR), which ovei~omes therequirement of a priori chemical information while using COVER method. Thisapproach can greatly accelerate the computing speed and supply right resolutionsfor the data array provided that the number of the factors used in computation isno less than that of the actual underlying l~ctors. A novel application of thismethod to the resolution of the mixtures of salicylic acid, gentisic acid and p-aminobenzolic acid, whose fluorescence spectrums are overlapping, is performedwith the satisfactory results.更多还原