Second-order advantage achieved by unfolded-partial least-squares/residual bilinearization modeling of excitation-emission fluorescence data presenting inner filter effects

A second-order multivariate calibration approach, based on a combination of unfolded-partial least-squares with residual bilinearization (U-PLS/RBL), has been applied to fluorescence excitation-emission matrix data for multicomponent mixtures showing inner filter effects. The employed chemometric algorithm is the most successful one regarding the prediction of analyte concentrations when significant inner filter effects occur, even in the presence of unexpected sample components, which require strict adherence to the second-order advantage. Results for simulated fluorescence excitation-emission data are described, in comparison with the classical approach based on parallel factor analysis and other second-order algorithms, including generalized rank annihilation, bilinear least squares combined with residual bilinearization and multivariate curve resolution-alternating leastsquares. A set of experimental data was also studied, in which calibration was performed with fluorescence excitation-emission matrices for samples containing mixtures of chrysene (the analyte of interest) and benzopyrene (which produced strong inner filter effect across the useful wavelength range). Prediction was made on validation samples with a qualitative composition similar to the calibration set, and also on test samples containing an unexpected component (pyrene). In this latter case, U-PLS/RBL showed a unique success for the analysis of the calibrated component chrysene, achieving the useful second-order advantage.     

Nonlinear four-way kinetic-excitation-emission fluorescence data processed by a variant of parallel factor analysis and by a neural network model achieving the second-order advantage: malonaldehyde determination in olive oil samples

Four-way data were obtained by recording the kinetic evolution of excitation-emission fluorescence matrices for the product of the Hantzsch reaction between the analyte malonaldehyde and methylamine. The reaction product, 1,4-disubstituted-1,4-dihydropyridine-3,5-dicarbaldehyde, is a highly fluorescent compound. The nonlinear nature of the kinetic fluorescence data has been demonstrated, and therefore the four-way data were processed with parallel factor analysis combined with a nonlinear pseudounivariate regression, based on a quadratic polynomial fit, and also with a recently introduced neural network methodology, based on the combination of unfolded principal component analysis, residual trilinearization, and radial basis functions. The applied chemometric strategies are not only able to adequately model the nonlinear data but also to successfully determine malonaldehyde in olive oil samples. This is possible since the experimentally recorded four-way data, modeled with the above-mentioned advanced chemometric approaches, permit the achievement of the second-order advantage. This allows us to predict the analyte concentration in a complex background, in spite of the nonlinear behavior and in the presence of uncalibrated interferences. The present work is a new example of the use of higher-order data for the resolution of a complex nonlinear system, successfully employed in the context of food chemical analysis.     

Time-alignment of bidimensional chromatograms in the presence of uncalibrated interferences using parallel factor analysis: Application to multi-component determinations using liquid-chromatography with spectrofluorimetric detection

A new methodology for the alignment of matrix chromatographic data is proposed, based on the decomposition of a three-way array composed of a test and a reference data matrix using a suitably initialized and constrained parallel factor (PARAFAC) model. It allows one to perform matrix alignment when the test data matrix contains unexpected chemical interferences, in contrast to most of the available algorithms. A series of simulated analytical systems is studied, as well as an experimental one, all having calibrated analytes and also potential interferences in the test samples, i.e., requiring the second-order advantage for successful analyte quantitation. The results show that the newly proposed method is able to properly align the different data matrix, restoring the trilinearity which is required to process the calibration and test data with second-order multivariate calibration algorithms such as PARAFAC. Recent models including unfolded partial least-squares regression (U-PLS) and N-dimensional PLS (N-PLS), combined with residual bilinearization (RBL), are also applied to both simulated and experimental data. The latter one corresponds to the determination of the polycyclic aromatic hydrocarbons benzo[b]fluoranthene and benzo[k]fluoranthene in the presence of benzo[j]fluoranthene as interference. The analytical figures of merit provided by the second-order calibration models are compared and discussed.     

Screening of oil samples on the basis of excitation-emission room-temperature phosphorescence data and multiway chemometric techniques. Introducing the second-order advantage in a classification study

Room-temperature phosphorescence excitation-emission matrices and multiway methods have been analyzed as potential tools for screening oil samples, based on full matrix information for polyaromatic hydrocarbons. Crude oils obtained from different sources of similar geographic origin, as well as light and heavy lubricating oils, were analyzed. The room-temperature phosphorescence matrix signals were processed by applying multilayer perceptron artificial neural networks, parallel factor analysis coupled to linear discriminant analysis, discriminant unfolded partial least-squares, and discriminant multidimensional partial least-squares (DN-PLS). The ability of the latter algorithm to classify the investigated oils into four categories is demonstrated. In addition, the combination of DN-PLS with residual bilinearization allows for a proper classification of oils containing unsuspected compounds not present in the training sample set. This second-order advantage concept is applied to a classification study for the first time. The employed approach is fast, avoids the use of laborious chromatographic analysis, and is relevant for oil characterization, identification, and determination of accidental spill sources.     

Second-order advantage achieved with four-way fluorescence excitation-emission-kinetic data processed by parallel factor analysis and trilinear least-squares. Determination of methotrexate and leucovorin in human urine

Four-way fluorescence data recorded by following the kinetic evolution of excitation-emission fluorescence matrices (EEMs) have been analyzed by parallel factor analysis and trilinear least-squares algorithms. These methodologies exploit the second-order advantage of the studied data, allowing analyte concentrations to be estimated even in the presence of an uncalibrated fluorescent background. They were applied to the simultaneous determination of the components of the anticancer combination of methotrexate and leucovorin in human urine samples. Both analytes were converted into highly fluorescent compounds by oxidation with potassium permanganate, and the kinetics of the reaction was continuously monitored by recording full EEM of the samples at different reaction times. A commercial fast scanning spectrofluorometer has been used for the first time to measure the four-way EEM kinetic data. The rapid scanning instrument allows the acquisition of a complete EEM in 12 s at a wavelength scanning speed of 24 000 nm/min. The emission spectra were recorded from 335 to 490 nm at 5-nm intervals, exciting from 255 to 315 nm at 6-nm intervals. Ten successive EEMs were measured at 72-s intervals, to follow the fluorescence kinetic evolution of the mixture components. Good recoveries were obtained in synthetic binary samples and also in spiked urine samples. The excitation, emission, and kinetic time profiles recovered by both chemometric techniques are in good agreement with experimental observations.     

Chemometrics-assisted excitation-emission fluorescence spectroscopy on nylon membranes. Simultaneous determination of benzo[a]pyrene and dibenz[a,h]anthracene at parts-per-trillion levels in the presence of the remaining EPA PAH priority pollutants as interferences

This work presents a novel approach for the simultaneous ultratrace determination of benzo[ a]pyrene and dibenzo[ a,h]anthracene, the two most carcinogenic polycyclic aromatic hydrocarbons (PAHs), in a very interfering environment, combining the recently discovered ability of the nylon membrane to strongly retain and concentrate PAHs on its surface, the sensitivity of molecular fluorescence, and the selectivity of second-order chemometric algorithms. The fluorescence excitation-emission matrices, directly measured on a nylon-membrane surface, are processed by applying parallel factor analysis (PARAFAC) and unfolded partial least-squares coupled to residual bilinearization (U-PLS/RBL). The superiority of U-PLS/RBL to quantify BaP and DBA at concentrations below 10 ng L (-1) in the presence of the remaining 14 US EPA (United States Environmental Protection Agency) PAHs at total concentrations ranging from 1400 and 14,000 ng L (-1) is demonstrated. The present method successfully faces this complex challenge without using organic solvents, which are to known produce environmental contamination. Finally, the high sensitivity of the present method avoids preconcentration and elution steps, considerably decreasing the analysis time and the experimental errors. Because the instrumental involved in the determination is nonsophisticated, the experiments could be carried out in routine laboratories.     

A test field for the second-order advantage in bilinear least-squares and parallel factor analyses: fluorescence determination of ciprofloxacin in human urine

The analytical performances of two algorithms, the recently introduced bilinear least-squares (BLLS) and the popular parallel factor analysis (PARAFAC), are compared as regards second-order fluorescence data recorded for the determination of the fluoroquinolone antibiotic ciprofloxacin in human urine samples. The applied chemometric methodologies employ different strategies for exploiting the so-called second-order advantage, which allows one to obtain individual concentrations of calibrated analytes in the presence of any number of uncalibrated (urine) components. Analysis of a spiked urine test set (in the analyte concentration range 0-200 mg L(-1)) showed that BLLS provides results of slightly better quality than PARAFAC. Satisfactory results have been obtained on comparing the concentrations predicted for a series of real urine samples with those furnished by liquid chromatography. The limit of detection of the fluorescence-based methods is approximately 5 mg L(-1).     

Statistical analysis of excitation–emission matrices for laser-induced fluorescence spectroscopy

An algorithm for statistical processing of the set of multicomponent excitation–emission matrices for laser-induced fluorescence spectroscopy is proposed that is based on principal component analysis. It is shown for the first time that the fluorescence emission and excitation spectra of unknown fluorophores in optically thin samples can be calculated. Using the proposed algorithm, it is possible to pass from principal components with alternating signs to positive quantities corresponding to the spectra of real substances. The method is applied to a mixture of three fluorescent dyes, and it is demonstrated that the obtained spectra of principal components well reproduce the spectra of initial dyes.     

Estimating the rate constant in second-order kinetics using hard-soft-net analyte signal (HS-NAS) method

Rank deficiency is the major problem associated with the chemometrics modeling of the second-order chemical reactions of the form of A + B → C. In this article, the application of the hard-soft-net analyte signal (HS-NAS), as a newly proposed method in our research group, is described for modeling of second-order reactions. This combined hard-soft method is based on the net analyte signal (NAS) concept, which is defined as a part of total signal that is directly related to the concentration of the component of interest. Therefore, concentration changes versus time can be obtained by calculating NAS for any chemical species involved in the reaction without requiring any pure component spectra or extra runs. The power of the method was verified by applying it to the resolution of simulated data sets containing noises added at different levels. The resolution of the second-order reaction between amoxicillin and 1, 2-naphthoqoinone was also tested as a real chemical system.     

三维荧光二阶校正法用于水样中培氟沙星和 氧氟沙星的同时测定

提出三维荧光二阶校正法,用于环境水样中氟喹诺酮类抗生素培氟沙星和氧氟沙星的同时定量分析.即在激发波长为230～400 nm,发射波长为360～580 nm范围内,测定样品(包含校正样、验证样、测试样)的三维荧光光谱,构建三维荧光响应数据阵;经数据处理后,采用交替三线性分解算法进行分解,得到与物质相关的相对激发、相对发射和相对浓度谱信息;通过对浓度信息进行单变量校正,获得校正曲线,进一步预测真实浓度.结果表明,培氟沙星和氧氟沙星的平均回收率分别为(101.1±5.3)％,(99.7±4.7)％,检测限分别为2.14,4.34 ng/mL,定量限分别为6.49,13.16 ng/mL.三维荧光二阶校正法可以在未知干扰物共存下,同时定量分析环境水样中培氟沙星和氧氟沙星,实现二阶优势.     

Second-order calibration of excitation-emission matrix fluorescence spectra for the determination of N-phenylanthranilic acid derivatives

A spectrofluorimetric method has been developed for the quantitative determination of mefenamic, flufenamic, and meclofenamic acids in urine samples. The method is based on second-order data multivariate calibration (unfolded partial least squares (unfolded-PLS), multi-way PLS (N-PLS), parallel factor analysis (PARAFAC), self-weighted alternating trilinear decomposition (SWATLD), and bilinear least squares (BLLS)). The analytes were extracted from the urine samples in chloroform prior to the determination. The chloroform extraction was optimized for each analyte, studying the agitation time and the extraction pH, and the optimum values were 10 minutes and pH 3.5, respectively. The concentration ranges in chloroform solution of each of the analytes, used to construct the calibration matrix, were selected in the ranges from 0.15 to 0.8 microg mL-1 for flufenamic and meclofenamic acids and from 0.25 to 3.0 microg mL-1 for mefenamic acid. The combination of chloroform extraction and second-order calibration methods, using the excitation-emission matrices (EEMs) of the three analytes as analytical signals, allowed their simultaneous determination in human urine samples, in the range of approximately 80 mg L-1 to 250 mg L-1, with satisfactory results for all the assayed methods. Improved results over unfolded-PLS and N-PLS were found with PARAFAC, SWATLD, and BLLS, methods that exploit the second-order advantage.     

Data-driven modal surrogate model for frequency response uncertainty propagation

A method is developed for propagation of model parameter uncertainties into frequency response functions based on a modal representation of the equations of motion. Individual local surrogate models of the eigenfrequencies and residue matrix elements for each mode are trained to build a global surrogate model. The computational cost of the global surrogate model is reduced in three steps. First, modes outside the range of interest, necessary to describe the in-band frequency response, are approximated with few residual modes. Secondly, the dimension of the residue matrices for each mode is reduced using principal component analysis. Lastly, multiple surrogate model structures are employed in a mixture. Cheap second-order multivariate polynomial models and more expensive Gaussian process models with different kernels are used to model the modal data. Leave-one-out cross-validation is used for model selection of the local surrogate models. The approximations introduced allow the method to be used for modally dense models at a small computational cost, without sacrificing the global surrogate model’s ability to capture mode veering and crossing phenomena. The method is compared to a Monte Carlo based approach and verified on one industrial-sized component and on one assembly of two car components.     

Unfolded partial least-squares with residual quadrilinearization: A new multivariate algorithm for processing five-way data achieving the second-order advantage. Application to fourth-order excitation-emission-kinetic-pH fluorescence analytical data

Unfolded partial least-squares in combination with residual quadrilinearization (U-PLS/RQL), is developed as a new latent structured algorithm for the processing of fourth-order instrumental data. In order to check its analytical predictive ability, fluorescence excitation-emission-kinetic-pH data were measured and processed. The concentration of the fluorescent pesticide carbaryl was determined in the presence of the pesticides fuberidazole and thiabendazole as uncalibrated interferents, in the first example of fourth-order multivariate calibration. The hydrolysis of the analyte was followed at different pH values using a fast-scanning spectrofluorimeter, recording the excitation-emission fluorescence matrices during its evolution to produce 1-naphthol, which does also emit fluorescence. A set of test samples containing the above mentioned fluorescent contaminants was analyzed with the new model, comparing the results with those from parallel factor analysis (PARAFAC). The newly developed U-PLS/RQL model provides better figures of merit for analyte quantitation (average prediction error, 7 μg L⁻¹, relative prediction error, 5%, calibration range, 50-250 μg L⁻¹), and is considerably simpler than PARAFAC in its implementation. The latter, however, furnishes important physicochemical information regarding the chemical process under study, although this requires the data to be unfolded into an array of lower dimensions, due to the lack of quadrilinearity of the experimental data.     

First and second-order derivatives for CP and INDSCAL

In this paper we provide the means to analyse the second-order differential structure of optimization functions concerning CANDECOMP/PARAFAC and INDSCAL. Closed-form formulas are given under two types of constraint: unit-length columns or orthonormality of two of the three component matrices. Some numerical problems that might occur during the computation of the Jacobian and Hessian matrices are addressed. The use of these matrices is illustrated in three applications.     

Computing sensitivity and selectivity in parallel factor analysis and related multiway techniques: the need for further developments in net analyte signal theory

Sensitivity and selectivity are important figures of merit in multiway analysis, regularly employed for comparison of the analytical performance of methods and for experimental design and planning. They are especially interesting in the second-order advantage scenario, where the latter property allows for the analysis of samples with a complex background, permitting analyte determination even in the presence of unsuspected interferences. Since no general theory exists for estimating the multiway sensitivity, Monte Carlo numerical calculations have been developed for estimating variance inflation factors, as a convenient way of assessing both sensitivity and selectivity parameters for the popular parallel factor (PARAFAC) analysis and also for related multiway techniques. When the second-order advantage is achieved, the existing expressions derived from net analyte signal theory are only able to adequately cover cases where a single analyte is calibrated using second-order instrumental data. However, they fail for certain multianalyte cases, or when third-order data are employed, calling for an extension of net analyte theory. The results have strong implications in the planning of multiway analytical experiments.     

Multiway partial least-squares coupled to residual trilinearization: a genuine multidimensional tool for the study of third-order data. Simultaneous analysis of procaine and its metabolite p-aminobenzoic acid in equine serum

A new third-order multivariate calibration approach, based on the combination of multiway-partial least-squares with a separate procedure called residual trilinearization (N-PLS/RTL), is presented and applied to multicomponent analysis using third-order data. The proposed chemometric algorithm is able to predict analyte concentrations in the presence of unexpected sample components, which require strict adherence to the second-order advantage. Results for the determination of procaine and its metabolite p-aminobenzoic acid in equine serum are discussed, based on kinetic fluorescence excitation-emission four-way measurements and application of the newly developed multiway methodology. Since the analytes are also the reagent and product of the hydrolysis reaction followed by fast-scanning fluorescence spectroscopy, the classical approach based on parallel factor analysis is challenged by strong linear dependencies and multilinearity losses. In comparison, N-PLS/RTL appears an appealing genuine multiway alternative that avoids the latter complications, yielding analytical results that are statistically comparable to those rendered by related unfolded algorithms, which are also able to process four-way data. Prediction was made on validation samples with a qualitative composition similar to the calibration set and also on test samples containing unexpected equine serum components.     

A comparison of several trilinear second-order calibration algorithms

A comprehensive and systematic strategy for evaluating the performances of several trilinear second-order calibration algorithms is presented in this paper, in particular with a view of practical applications. Several trilinear second-order calibration methods such as PARAFAC, ATLD, SWATLD and APTLD, which have the “second-order advantage” and are gaining widespread acceptance in the field of chemometrics, were compared. Based on different input parameters including noise level, initial value, number of estimated components and collinearity in simulated and real data, the performances of these methods were evaluated in terms of predicting ability, consistency of resolved and real profiles, fitness obtained by selected components and speed of convergence. The obtained results give a reevaluation of the position and role of these trilinear second-order calibration methods in chemometrics and provide a guidance in practical applications for solving complicated quantitative analysis problems in analytical chemistry. It is useful and helpful to choose, for example, which algorithm would be more suitable for predicting the concentration of the analyte(s) of interest even in the presence of unknown interferents in complex systems.     

Polarization sensing with visual detection

We describe a new approach to fluorescence sensing which relies on visual determination the polarization. The sensing device consists of a fluorescent probe, which changes intensity in responses to the analyte, and an oriented fluorescent film, which is not affected by the analyte. An emission filter is selected to observe the emission from both the film and the sensing fluorophore. Changes in the probe intensity result in changes in the polarization of the combined emission from the sensor and reference. The degree of polarization can be detected visually using a dual polarizer with adjacent sections oriented orthogonally to each other. The emission passing through the dual polarizer is viewed with a second analyzing polarizer. This analyzer is rotated manually to yield equal intensities from both sides of the dual polarizer. This approach was used to measure the concentration of RhB in intralipid and to measure pH using 6-carboxyfluorescein. The analyzer angle is typically accurate to 1 degree, providing pH values accurate to +/- 0.1 pH unit at the midpoint of the titration curve. We also describe a method of visual polarization sensing that does not require an oriented film and that can use the same fluorophore for the sample and reference. These approaches to visual sensing are generic and can be applied to a wide variety of analytes for which fluorescent probes are available. Importantly, the devices are simple, with the only electronic component being the light source.     

Stability of second-order nonlinear optical properties in sol–gel matrix bearing silylated chalcone and disperse red 1

We report the syntheses of two triethoxysilanes for thin film fabrication. One silane (SGDR1) contains disperse red 1 (DR1) which is a second-order nonlinear optical (NLO) active chromophore. The other silane (SGCHC) bears a chalcone derivative. In order to improve the poor temporal stability of second-order NLO effects in the resulting poled sol–gel film, photo-crosslink was induced between the double bonds in chalcone units after mixing SGDR1 and SGCHC. Under UV exposure, the photocrosslink was studied with UV–visible absorption and IR vibrational spectroscopy. The decaying behavior of the molecular order parameter (A₂) after corona poling was investigated using polarized absorption spectroscopy (PAS). Second-order non-linear optical properties of the sample were studied using second-harmonic generation (SHG) and linear electro-optic (E/O) signal measurement. Poled and UV-cured film of SGDR1/SGCHC exhibited much better stability than thermally poled sample with respect to the molecular order parameter and linear electro-optic effect.     

A new finite element scheme for instability analysis of thin shells

This paper describes a new finite element scheme for the analysis of instability phenomena of arbitrary thin shells. A computationally efficient procedure is proposed for calculating the non-linear stiffness and tangential stiffness matrices for a doubly-curved quadrilateral element defined by co-ordinate lines. The essential feature is the explicit addition of the non-linear terms into the rigid-body motion of the element. Thus the non-linear and tangential element stiffness matrices can easily be generated by transforming the generalized element stiffness matrix for linear analysis, and the non-linear terms of these matrices are separated into a number of component terms multiplied by the rigid-body rotations. These component terms can be stored permanently and used to calculate efficiently the non-linear and tangential stiffness matrices at each iteration. Illustrative examples are presented which confirm the validity of the present approach in the analysis of instability phenomena of thin plates and shells.