Desenvolvimento e aplicação de metodos quimiometricos de ordem superior




Two of the multi-way methods presented in this work were developed in psychometrics for psychological studies. On being applied in chemical data these methods demand on refinements to accommodate the variation present in the chemical data. Although the development of such kind of refinements there are some variation within the data which cannot be described by the multi-way methods. In this way, the main focus of the thesis is to describe the relationship between the parts of the data that can be described or not by the methods, in other words, how one can extract meaningful information from multi-way data set. Three topics are studied: Second order calibration; curve resolution and multi-way exploratory data analysis. In the second order calibration the influence of experimental behaviour over the multi-way structure of the data and how it affects the calibration results is evaluated. In the curve resolution, the variation of the data that cannot be accomodated by the methods, interfere on the choice of the number of curves to be resolved and a validadtion procedure is used on such choice. On the exploratory data analysis two problems are studied: In the first, it is suggested a methodology to discriminate the part of the data that can be described by the Multi Way methods from that one which cannot be described. In the second, a similar problem is treated where a smoothing method is used. With the current popularity of second-order (or hyphenated) instruments, there now exists a number of chemometric techniques for the so-called second-order calibration problem, i.e. that of quantifying an analyte of interest in the presence of one (or more) interferent(s). Second-order instruments produce data of varying complexity, one particular phenomenon sometimes encountered being that of rank overlap (or rank deficiency), where the overall rank of the data is not equal to the sum of the ranks of the contributing species. One of the purpose of the present work is to evaluate the performance of two second-order calibration methods, a least squares-based and an eigenvalue-based solution, in terms of their quantitative ability and stability, as applied to flow injection analysis (FIA) data which exhibits rank overlap. In the presence of high collinearity in the data, the least squares methods is found to give a more stable solution. Two-mode component analysis (TMCA) is used to investigate the reasons for this difference in terms of the chemical properties of the species analyzed. The success of the second-order calibration in general is found to depend strongly on the associated pKa values. Chromophores identification in biological samples often demands on the physical separation of the compounds, which can be difficult. Although there are several advantages of hyphenated spectroscopic techniques on substances identification, complex mixtures of chromophores presenting overlapped spectra cannot be identified directly. This work presents a chemometric application to compounds identification in biological samples by spectroscopic hyphenated techniques using a curve resolution method. The PARAllel FACtor analysis model (PARAFAC), which has no rotational indeterminacy, was used for curve resolution of excitation-emission spectra of human dental tartars. PARAFAC was applied under constraints (i.e unimodality and non-negativity) and evaluated with a validation procedure. The resolved profiles are porphyrinic like spectra presenting the excitation band maxima in 407, 416 and 431nm in the Soret band region (390-440nm) of these substances. The original methods proposed by Ledyard R. Tucker during the 1960s presented the rotational freedom problem, making the interpretation of results obtained by these methods rather difficult to be carried out. On the proposal of making the multi-way data analysis more acceptable, this work suggests a methodology for extracting meaningful information from the data set. For that, the proposed methodology is based on the decomposition of the data set in 3-way blocks by using Tucker Models. With the aim of keeping in one block the similar information about data properties, it is proposed decomposition based on a Constrained Tucker Model, where the core array has some of its elements fixed to zero. This methodology is successfully applied to a data set formed by physical and physico chemical properties of starches of four cassava cultivars, harvested at different ages during the period usually taken for harvest of industrial uses. The PARAFAC model has been used in several applications in chemistry, e.g. for overlapped spectra resolution, second order calibration and others. In general, the PARAFAC method uses a vector space approach by considering the resulting matrices from the decomposition as a collection of vectors. This work presents a PARAFAC application where the decomposition resulting factors are considered as being functions. The functional objects used to link PARAFAC method and functional analysis are spline functions. The methodology used to promote the Spline-PARAFAC decomposition is based on Bro-Sidiropoulos approach for the unimodality constraint. One of the advantages of using splines is the possibility of achieving smoothing on the decomposed components. The amount of smoothing applied on the components is controlled in the presented methodology by a penalty parameter or by the number of basis functions. Thus Spline-PARFAC requires the calculation of the parameter l and the number basis, which were found in this work by using an Ordinary Cross Validation OCV. The Spline-PARAFAC was applied to a carbon monoxide data set, which corresponds to concentrations measured every hour during the years of 1997 and 1999 in the São Paulo city in Brazil. Each data set was arranged in a Three Way Array of dimension (24 hoursx5 daysx52 weeks). The Spline-PARAFAC presented a good performance producing smoothed profiles which describe the dally variation of emitted gas and the seasonal effects during the year.


quimica analitica planejamento experimental

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