【作者】 胡乐乾；

【导师】 吴海龙； 俞汝勤；

【作者基本信息】 湖南大学 ， 分析化学， 2006， 博士

【摘要】 在化学计量学的理论和方法体系中,三维数据分析和定量构效关系是两个非常重要的研究领域,本论文通过对这两个领域的研究热点的追踪分析,选取了其中几个重要的问题进行了探索和应用研究,主要涉及以下几个方面:一、三维化学数据解析的方法和应用研究(第一章-第五章):三维化学数据解析方法因其能够在未知干扰存在下实现对感兴趣成分的定性定量分析而受到广泛的重视。传统的三维数据解析方法如平行因子分析由于收敛速度慢,容易出现衰退解,对拟合模型需要的化学秩敏感等不足影响了它的应用。近年来发展的交替三线性分解算法(ATLD)克服了传统平行因子分析算法收敛速度慢、对化学秩预估计值不敏感等不足,为三维数据分析算法在化学中的应用注入了新的生机。但是交替三线性分解算法在解决小样品量测时可能出现求解不稳定问题,为了弥补这一不足,同时能够保留其优点,本文结合平行因子-交替最小二乘算法,提出了交替不对称三线性分解算法(AATLD)。模拟的和真实的三维二阶校正数据试验均显示出该算法在浓度模出现比较严重的共线性时可以取得与平行因子分析方法相媲美的结果,同时其收敛速度远远快于平行因子分析算法,而且作为一种不对称算法,相对于交替三线性分解算法而言,可以很好地解决小样品校正问题,并在一定程度上能够克服二阶衰退,从而实现在现代分析化学中实际复杂体系的直接快速定量分析。在应用一种三维化学数据解析算法处理三维数据之前,首先要做的就是估计三维化学数据的化学秩。同二维数据的秩估计相比,三维化学的秩估计更加困难。基于已有的三维数据秩估计方法存在的不足,结合直接三线性分解的思想,代替如传统的利用特征值进行秩估计的思路,提出了伪样品特征矢量提取和投影技术估计三维数阵化学秩的新方法。模拟的和真实的三维二阶校正数据显示该方法运算速度快、结果可靠、不需要人为设定判别标准等优点。由于三维试验数据来源较为复杂,任何一种秩估计方法都不能保证在所有的情况下都能给出复杂体系的正确因子数,本文又提出了利用简单的线性变换方法结合蒙特卡罗技术提出了秩估计方法。该方法利用两个子空间,一个来源于原始三维数据本身,一个由原始三维数据经线性变化后产生,结合投影技术估计三维数据的化学秩。为了使结果更稳健,应用蒙特卡罗方法,用多组子空间确定复杂体系的化学秩。同其他三维数阵秩估计方法相比,该算法具有计算量小、运算速度快、结果更可靠,不需要事先制定判别标准等优点。在体液中的药物分析是现代生命医学领域面临的一个重要的问题,传统方法采用色谱分离技术来实现这一目的,通常情况下通过调整色谱柱或者色谱条件分更多还原

【Abstract】 In the field of chemometrics, studying multi-way data analysis and quantitative structure-activity relationship are the most active areas with practical significance. Work in this paper focuses on the methodolodies three-way data analysis and the application of three-way data analysis and quantitative structure-activity relationship in pharmacology. The main results are summarized as follows:1. Three-way data analysis (Chapter 1 to Chapter 5): An alternating asymmetric trilinear decomposition for three-way data arrays analysis (AATLD) method was introduced. The new proposed algorithm combines the merit of PARAFAC-alternating least squares (PARAFAC-ALS) and alternating trilinear decomposition (ATLD). It retains the second-order advantage of quantization for analyte(s) of interest even in the presence of potentially unknown interferents. In contrast with the traditional PARAFAC, ATLD and PARAFAC -ALS, by using simulated and real three-way data arrays of second–order calibration, it was showed that the new proposed algorithm performs better when the data are heavily collinear e.g., the large condition number of the loading matrix A, B and C. Even with heavily collinear simulated data set, it was also found that the AATLD algorithm is faster than others on obtaining solutions with chemical meaning. In the same time, it can obtain satisfactory result with the small samples data arrays.Determining the rank of a trilinear data array is a first step to further the later trilinear component decomposition. Different with estimating the rank of bilinear data, it is more difficult to decide the significant component number to fit exactly the three-way data arrays using trilinear decomposition. A rank-estimating method specifically for trilinear data array was proposed. It utilizes the idea of direct trilinear decomposition (DTLD) to compress the cube matrix into two pseudo samples matrices, and then decompose them by singular value decomposition. Two eigenvectors combining with the projection technique are devised to estimate the rank of trilinear data arrays. Simulated trilinear data arrays with homoscedastic and heteroscedastic noises, different noise level, high collinearity and real three-way data arrays have been used to illustrate the feasibility of the proposed method respectively. Comparing with the other factor-determining methods, it was showed that the new method can give more reliable results in the different conditions. A simple linear transform incorporating Monte Carlo simulation approach (LTMC) to estimating the chemical更多还原