57 resultados para least squares method
Resumo:
A aplicação de técnicas espectroscópicas que utilizam a radiação infravermelha (NIRS-Near Infrared Spectroscopy e DRIFTS-Diffuse Reflectance Fourier Transformed Spectroscopy) na análise inorgânica do solo tem sido proposta desde a década de 1970, mas até os dias atuais são raros os métodos implementados rotineiramente no Brasil. Isso deve-se à dificuldade em construir modelos de calibração, por meio de métodos estatísticos multivariados, utilizando-se amostras reais de solo, de constituição complexa, que varia geograficamente e de acordo com o manejo. Por isso, os objetivos deste trabalho foram construir modelos de calibração em NIRS e DRIFTS para a quantificação das frações de argila e areia, em amostras de solos de classes diferentes - Latossolo Vermelho (predominante), Nitossolo, Argissolo Vermelho e Neossolo Quartzarênico - e avaliar qual dessas duas técnicas é mais adequada para essa finalidade, assim como a interferência do agrupamento de amostras e da seleção de variáveis espectrais na qualidade desses modelos. Para isso, valores de referência obtidos pelo método do densímetro, método largamente utilizado nos laboratórios de análise de solo, foram correlacionados com valores de absorbância em NIRS e DRIFTS pela ferramenta estatística PLS (Partial Least Squares), obtendo-se altos coeficientes de determinação (R²), de 0,95, 0,90 e 0,91 para argila, silte e areia, respectivamente, na validação externa. Isso confirma a aplicabilidade das técnicas espectroscópicas na análise granulométrica do solo para fins agrícolas. O agrupamento das amostras segundo a localização e a seleção de variáveis espectrais pouco influenciou na qualidade dos modelos. A técnica espectroscópica mais indicada para essa finalidade foi a DRIFTS.
Resumo:
The least square method is analyzed. The basic aspects of the method are discussed. Emphasis is given in procedures that allow a simple memorization of the basic equations associated with the linear and non linear least square method, polinomial regression and multilinear method.
Resumo:
The aim of this work is to present a tutorial on Multivariate Calibration, a tool which is nowadays necessary in basically most laboratories but very often misused. The basic concepts of preprocessing, principal component analysis (PCA), principal component regression (PCR) and partial least squares (PLS) are given. The two basic steps on any calibration procedure: model building and validation are fully discussed. The concepts of cross validation (to determine the number of factors to be used in the model), leverage and studentized residuals (to detect outliers) for the validation step are given. The whole calibration procedure is illustrated using spectra recorded for ternary mixtures of 2,4,6 trinitrophenolate, 2,4 dinitrophenolate and 2,5 dinitrophenolate followed by the concentration prediction of these three chemical species during a diffusion experiment through a hydrophobic liquid membrane. MATLAB software is used for numerical calculations. Most of the commands for the analysis are provided in order to allow a non-specialist to follow step by step the analysis.
Resumo:
Genetic algorithm was used for variable selection in simultaneous determination of mixtures of glucose, maltose and fructose by mid infrared spectroscopy. Different models, using partial least squares (PLS) and multiple linear regression (MLR) with and without data pre-processing, were used. Based on the results obtained, it was verified that a simpler model (multiple linear regression with variable selection by genetic algorithm) produces results comparable to more complex methods (partial least squares). The relative errors obtained for the best model was around 3% for the sugar determination, which is acceptable for this kind of determination.
Resumo:
The objective of this work was to accomplish the simultaneous determination of some chemical elements by Energy Dispersive X-ray Fluorescence (EDXRF) Spectroscopy through multivariate calibration in several sample types. The multivariate calibration models were: Back Propagation neural network, Levemberg-Marquardt neural network and Radial Basis Function neural network, fuzzy modeling and Partial Least Squares Regression. The samples were soil standards, plant standards, and mixtures of lead and sulfur salts diluted in silica. The smallest Root Mean Square errors (RMS) were obtained with Back Propagation neural networks, which solved main EDXRF problems in a better way.
Resumo:
Dilutions of methylmetacrylate ranging between 1 and 50 ppm were obtained from a stock solution of 1 ml of monomer in 100 ml of deionised water, and were analyzed by an absorption spectrophotometer in the UV-visible. Absorbance values were used to develop a calibration model based on the PLS, with the aim to determine new sample concentrations. The number of latent variables used was 6, with the standard errors of calibration and prediction found to be 0,048 ml/100 ml and 0,058 ml/100 ml. The calibration model was successfully used to calculate the concentration of monomer released in water, where complete dentures were kept for one hour after polymerization.
Resumo:
In this work, a partial least squares regression routine was used to develop a multivariate calibration model to predict the chemical oxygen demand (COD) in substrates of environmental relevance (paper effluents and landfill leachates) from UV-Vis spectral data. The calibration models permit the fast determination of the COD with typical relative errors lower by 10% with respect to the conventional methodology.
Resumo:
In this work, the artificial neural networks (ANN) and partial least squares (PLS) regression were applied to UV spectral data for quantitative determination of thiamin hydrochloride (VB1), riboflavin phosphate (VB2), pyridoxine hydrochloride (VB6) and nicotinamide (VPP) in pharmaceutical samples. For calibration purposes, commercial samples in 0.2 mol L-1 acetate buffer (pH 4.0) were employed as standards. The concentration ranges used in the calibration step were: 0.1 - 7.5 mg L-1 for VB1, 0.1 - 3.0 mg L-1 for VB2, 0.1 - 3.0 mg L-1 for VB6 and 0.4 - 30.0 mg L-1 for VPP. From the results it is possible to verify that both methods can be successfully applied for these determinations. The similar error values were obtained by using neural network or PLS methods. The proposed methodology is simple, rapid and can be easily used in quality control laboratories.
Determinação de misturas de sulfametoxazol e trimetoprima por espectroscopia eletrônica multivariada
Resumo:
In this work a multivariate spectroscopic methodology is proposed for quantitative determination of sulfamethoxazole and trimethoprim in pharmaceutical associations. The multivariate model was developed by partial least-squares regression, using twenty synthetic mixtures and the spectral region between 190 and 350 nm. In the validation stage, which involved the analysis of five synthetic mixtures, prediction errors lower that 3% were observed. The predictive capacity of the multivariate models is seriously affected by spectral changes induced by pH variations, a fact that acquires a great significance in the analysis of real samples (pharmaceuticals) that contain chemical additives.
Resumo:
Two spectrophotometric methods are described for the simultaneous determination of ezetimibe (EZE) and simvastatin (SIM) in pharmaceutical preparations. The obtained data was evaluated by using two different chemometric techniques, Principal Component Regression (PCR) and Partial Least-Squares (PLS-1). In these techniques, the concentration data matrix was prepared by using the mixtures containing these drugs in methanol. The absorbance data matrix corresponding to the concentration data matrix was obtained by the measurements of absorbances in the range of 240 - 300 nm in the intervals with Δλ = 1 nm at 61 wavelengths in their zero order spectra, then, calibration or regression was obtained by using the absorbance data matrix and concentration data matrix for the prediction of the unknown concentrations of EZE and SIM in their mixture. The procedure did not require any separation step. The linear range was found to be 5 - 20 µg mL-1 for EZE and SIM in both methods. The accuracy and precision of the methods were assessed. These methods were successfully applied to a pharmaceutical preparation, tablet; and the results were compared with each other.
Resumo:
In this work an analytical methodology for the determination of relevant physicochemical parameters of prato cheese is reported, using infrared spectroscopy (DRIFT) and partial least squares regression (PLS). Several multivariate models were developed, using different spectral regions and preprocessing routines. In general, good precision and accuracy was observed for all studied parameters (fat, protein, moisture, total solids, ashes and pH) with standard deviations comparable with those provided by the conventional methodologies. The implantation of this multivariate routine involves significant analytical advantages, including reduction of cost and time of analysis, minimization of human errors, and elimination of chemical residues.
Resumo:
The main objective of the present work is represented by the characterization of the physical properties of industrial kraft paper (i.e. transversal and longitudinal tear resistance, transversal traction resistance, bursting or crack resistance, longitudinal and transversal compression resistance (SCT (Compressive Strength Tester) and compression resistance (RCT-Ring Crush Test)) by near infrared spectroscopy associated to partial least squares regression. Several multivariate models were developed, many of them with high prevision capacity. In general, low prevision errors were observed and regression coefficients that are comparable with those provided by conventional standard methodologies.
Resumo:
Genetic algorithm and multiple linear regression (GA-MLR), partial least square (GA-PLS), kernel PLS (GA-KPLS) and Levenberg-Marquardt artificial neural network (L-M ANN) techniques were used to investigate the correlation between retention index (RI) and descriptors for 116 diverse compounds in essential oils of six Stachys species. The correlation coefficient LGO-CV (Q²) between experimental and predicted RI for test set by GA-MLR, GA-PLS, GA-KPLS and L-M ANN was 0.886, 0.912, 0.937 and 0.964, respectively. This is the first research on the QSRR of the essential oil compounds against the RI using the GA-KPLS and L-M ANN.
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Direct infusion electrospray ionization mass spectrometry in the negative ion mode, ESI(-)-MS and Fourier transform infrared spectroscopy (FTIR) were used together with partial least squares (PLS) as a tool to determine B3 adulteration (B3 - mixture of 3% v/v of biodiesel in diesel) with kerosene and residual oil.
Resumo:
Mid-infrared spectroscopy and chemometrics were used to identify adulteration in roasted and ground coffee by addition of coffee husks. Consumers' sensory perception of the adulteration was evaluated by a triangular test of the coffee beverages. Samples containing above 0.5% of coffee husks from pure coffees were discriminated by principal component analysis of the infrared spectra. A partial least-squares regression estimated the husk content in samples and presented a root-mean-square error for prediction of 2.0%. The triangular test indicated that were than 10% of coffee husks are required to cause alterations in consumer perception about adulterated beverages.