Classical Least-squares Research Articles

DEVELOPMENT AND VALIDATION OF A CHEMOMETRICS ASSISTED SPECTROSCOPIC METHOD FOR THE SIMULTANEOUS ESTIMATION OF GALLIC ACID, ELLAGIC ACID AND CURCUMIN IN POLYHERBAL ANTIDIABETIC FORMULATIONS

Two chemometric methods, Inverse Least Square (ILS) and Classical Least Square (CLS), were applied for the simultaneous estimation of gallic acid, ellagic acid and curcumin in polyherbal antidiabetic formulation. Twenty mixed solutions were prepared for the chemometric calibration as training set and 10 mixed solutions were prepared as validation set. The absorbance data matrix was obtained by measuring the absorbance at 20 different wavelengths, from 241 to 279 nm with the interval of 2 nm (Δλ= 2 nm). The developed calibrations were successfully tested for three antidiabetic polyherbal formulations for their gallic acid, ellagic acid and curcumin contents. Developed methods were validated and root mean square error of precision (RMSEP) was determined. Both chemometric methods in this study can be satisfactorily used for the quantitative analysis in polyherbal dosage forms. The chemometric calculations were performed by using the chemometrics toolbox with MATLAB R2015a software.

Application of open-path Fourier transform infrared spectroscopy (OP-FTIR) to measure greenhouse gas concentrations from agricultural fields

Abstract. Open-path Fourier transform infrared spectroscopy (OP-FTIR) has often been used to measure hazardous or trace gases from hot point sources (e.g. volcano, industrial, or agricultural facilities) but seldom used to measure greenhouse gases (GHGs) from field-scale sources (e.g. agricultural soils). Closed-path mid-IR laser-based N2O, nondispersive-IR CO2 analysers, and OP-FTIR were used to measure concentrations of N2O and CO2 at a maize cropping system during 9–19 June 2014. To measure N2O and CO2 concentrations accurately, we developed a quantitative method of N2O∕CO2 analysis that minimized interferences from diurnal changes of humidity and temperature. Two chemometric multivariate models, classical least squares (CLS) and partial least squares (PLS), were developed. This study evaluated various methods to generate the single-beam background spectra and different spectral regions for determining N2O and CO2 concentrations from OP-FTIR spectra. A standard extractive method was used to measure the actual path-averaged concentrations along an OP-FTIR optical path in situ, as a benchmark to assess the feasibilities of these quantitative methods. Within an absolute humidity range of 5000–20 000 ppmv and a temperature range of 10–35 ∘C, we found that the CLS model underestimated N2O concentrations (bias =-4.9±3.1 %) calculated from OP-FTIR spectra, and the PLS model improved the accuracy of calculated N2O concentrations (bias =1.4±2.3 %). The bias of calculated CO2 concentrations was -1.0±2.8 % using the CLS model. These methods suggested that environmental variables potentially lead to biases in N2O and CO2 estimations from OP-FTIR spectra and may help OP-FTIR users avoid dependency on extractive methods of calibrations.

A maximum correntropy criterion based recursive method for output-only modal identification of time-varying structures under non-Gaussian impulsive noise

This work considers the problem of output-only identification for time-varying structures in a recursive manner under non-Gaussian impulsive noise. Presently, the most existing identification methods are based on classical least-squares (LS) criterion due to its mathematical tractability, computational simplicity and optimality under Gaussian assumption. However, the performance of the LS based methods deteriorates seriously in non-Gaussian situations, especially when responses are corrupted by impulsive noise (outliers) which are frequently encountered in real test cases. To deal with this problem, a maximum correntropy criterion based recursive modal identification method is proposed in this paper, and a class of heavy-tailed alpha-stable distribution is adopted to model non-Gaussian impulsive noise. The effect of the kernel bandwidth parameter in proposed method is discussed and a rational value is given for the model structure selection. Finally, the proposed method is comparatively assessed against its LS counterpart via a numerical example and a laboratory time-varying structure experiment. The comparisons have illustrated the advantages of the proposed method on the modal frequency estimates in terms of estimation accuracy and robustness under the non-Gaussian impulsive noise.

Robust external calibration of terrestrial laser scanner and digital camera for structural monitoring

Abstract In the last two decades, the integration of a terrestrial laser scanner (TLS) and digital photogrammetry, besides other sensors integration, has received considerable attention for deformation monitoring of natural or man-made structures. Typically, a TLS is used for an area-based deformation analysis. A high-resolution digital camera may be attached on top of the TLS to increase the accuracy and completeness of deformation analysis by optimally combining points or line features extracted both from three-dimensional (3D) point clouds and captured images at different epochs of time. For this purpose, the external calibration parameters between the TLS and digital camera needs to be determined precisely. The camera calibration and internal TLS calibration are commonly carried out in advance in the laboratory environments. The focus of this research is to highly accurately and robustly estimate the external calibration parameters between the fused sensors using signalised target points. The observables are the image measurements, the 3D point clouds, and the horizontal angle reading of a TLS. In addition, laser tracker observations are used for the purpose of validation. The functional models are determined based on the space resection in photogrammetry using the collinearity condition equations, the 3D Helmert transformation and the constraint equation, which are solved in a rigorous bundle adjustment procedure. Three different adjustment procedures are developed and implemented: (1) an expectation maximization (EM) algorithm to solve a Gauss-Helmert model (GHM) with grouped t-distributed random deviations, (2) a novel EM algorithm to solve a corresponding quasi-Gauss-Markov model (qGMM) with t-distributed pseudo-misclosures, and (3) a classical least-squares procedure to solve the GHM with variance components and outlier removal. The comparison of the results demonstrates the precise, reliable, accurate and robust estimation of the parameters in particular by the second and third procedures in comparison to the first one. In addition, the results show that the second procedure is computationally more efficient than the other two.

MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.

Multicomponent spectrometric analysis of drugs and their preparations.

Pharmaceutical preparations may contain a single ingredient or multi-ingredients as well as excipients. In multicomponent systems, specific analytical methods are required to determine the concentrations of individual components in the presence of interfering substances. Ultraviolet and visible spectrometric methods have widely been developed for the analysis of drugs in mixtures and pharmaceutical preparations. These methods are based on ultraviolet and visible multicomponent analysis and chemometrics (multivariate data analysis). The commonly used chemometric methods include principal component analysis (PCA); regression involving classical least squares (CLS), partial least squares (PLS), inverse least squares (ILS), principal component regression (PCR), multiple linear regression (MLR), artificial neural networks (ANNs); soft independent modeling of class anthology (SIMCA), PLS-discriminant analysis (DA); and functional data analysis (FDA). In this chapter, the applications of multicomponent ultraviolet and visible, derivative, infrared and mass spectrometric and spectrofluorimetric methods to the analysis of multi-ingredient pharmaceutical preparations, biological samples and the kinetics of drug degradation have been reviewed. Chemometric methods provide an efficient solution to calibration problems in the analysis of spectral data for the simultaneous determination of drugs in multicomponent systems. These methods facilitate the assessment of product quality and enhance the efficiency of quality control systems.

Robust machine learning by median-of-means: Theory and practice

Median-of-means (MOM) based procedures have been recently introduced in learning theory (Lugosi and Mendelson (2019); Lecué and Lerasle (2017)). These estimators outperform classical least-squares estimators when data are heavy-tailed and/or are corrupted. None of these procedures can be implemented, which is the major issue of current MOM procedures (Ann. Statist. 47 (2019) 783–794). In this paper, we introduce minmax MOM estimators and show that they achieve the same sub-Gaussian deviation bounds as the alternatives (Lugosi and Mendelson (2019); Lecué and Lerasle (2017)), both in small and high-dimensional statistics. In particular, these estimators are efficient under moments assumptions on data that may have been corrupted by a few outliers. Besides these theoretical guarantees, the definition of minmax MOM estimators suggests simple and systematic modifications of standard algorithms used to approximate least-squares estimators and their regularized versions. As a proof of concept, we perform an extensive simulation study of these algorithms for robust versions of the LASSO.

Comparative Study of Estimation Methods of the Endpoint Temperature in Basic Oxygen Furnace Steelmaking Process with Selection of Input Parameters

The basic oxygen furnace (BOF) steelmaking process in the steel industry is highly complicated, and subject to variations in raw material composition. During the BOF steelmaking process, it is essential to maintain the carbon content and the endpoint temperature at their set points in the liquid steel. This paper presents intelligent models used to estimate the endpoint temperature in the basic oxygen furnace (BOF) steelmaking process. An artificial neural network (ANN) model and a least-squares support vector machine (LSSVM) model are proposed and their estimation performance compared. The classical partial least-squares (PLS) method was also compared with the others. Results of the estimations using the ANN, LSSVM and PLS models were compared with the operation data, and the root-mean square error (RMSE) for each model was calculated to evaluate estimation performance. The RMSE of the LSSVM model 15.91, which turned out to be the best estimation. RMSE values for the ANN and PLS models were 17.24 and 21.31, respectively, indicating their relative estimation performance. The essential input parameters used in the models can be selected by sensitivity analysis. The RMSE for each model was calculated again after a sequential input selection process was used to remove insignificant input parameters. The RMSE of the LSSVM was then 13.21, which is better than the previous RMSE with all 16 parameters. The results show that LSSVM model using 13 input parameters can be utilized to calculate the required values for oxygen volume and coolant needed to optimally adjust the steel target temperature. (Received July 30, 2018; Accepted September 28, 2018)

A multi-arc approach for chaotic orbit determination problems

Chaotic dynamical systems are characterized by the existence of a predictability horizon, connected to the notion of Lyapunov time, beyond which predictions of the state of the system are meaningless. In order to study the main features of orbit determination in the presence of chaos, Spoto and Milani (Celest Mech Dyn Astron 124:295–309, 2016) applied the classical least-squares fit and differential correction algorithm to determine a chaotic orbit and a dynamical parameter of a simple discrete system—Chirikov standard map (cf. Chirikov in Phys Rep 52:263, 1979)—with observations distributed beyond the predictability horizon. They found a time limit beyond which numerical calculations are affected by numerical instability: the computability horizon. In this article, we aim at pushing forward such inherent obstacle to numerical calculations in chaotic orbit determination by applying the classical and the constrained multi-arc method (cf. Alessi et al. in Mon Not R Astron Soc 423:2270–2278, 2012) to the same dynamical system. These strategies entail the determination of an orbit when observations are grouped in separate observed arcs. For each arc, a set of initial conditions is determined and, in the case of the constrained multi-arc method, all subsequent arcs are constrained to belong to the same trajectory. We show that the use of these techniques in place of the standard least-squares method has significant advantages: Not only can we perform accurate numerical calculations well beyond the computability horizon, in particular, the constrained multi-arc strategy improves considerably the determination of the dynamical parameter.

Surface‐Enhanced Raman Nanoprobes with Embedded Standards for Quantitative Cholesterol Detection

AbstractCholesterol is an essential molecule for many processes in the human body and many diseases such as hypertension, coronary heart disease, atherosclerosis, and lipid metabolism dysfunction can be detected in their early stages by monitoring intracellular cholesterol levels. Herein, metallic surface‐enhanced Raman scattering (SERS) core–shell nanoparticles with an embedded standard are designed for nondestructive detection of H2O2 and cholesterol. A classical least squares (CLS) spectral fitting method allows one to accurately extract the SERS signals of internal standards and target molecules from the multiplexed spectra. The embedded internal standard can be used to calibrate the SERS signals, removing fluctuations induced by differing measurement conditions and local states of the nanoparticles, such as aggregation. Thus, SERS signal reproducibility is improved and a better linear relationship in the working curve of detection is achieved. Using these SERS nanoprobes quantitative detection of H2O2 and cholesterol in solution and inside live cells at a single‐cell level is demonstrated.

Non-destructive characterisation of all-polypropylene composites using small angle X-ray scattering and polarized Raman spectroscopy

Small angle X-ray scattering (SAXS) and polarized Raman spectroscopy were used to examine the structure of unidirectional all-polypropylene composites prepared at different consolidation temperatures. Analysis of the anisotropy of the X-ray scattering pattern provided a way to quantify the disorientation of the crystallites and a direct correlation has been found between a measure of overall orientation and the Young’s modulus of the composites. In the case of the Raman spectroscopic measurements, the molecular orientation state of the reinforcing PP fibres were evaluated by classical least squares (CLS) modelling with real reference spectra. Strong correlation was evinced between the estimated relative degree of orientation of the reinforcing fibres and the Young’s modulus of the multi-layered all-polypropylene composites. Based on these results, both SAXS and Raman spectroscopy are suitable methods to predict the mechanical performance of all-polymer composites, being especially sensitive to manufacturing and application conditions, in a non-destructive way.

Nonlinear least squares with local polynomial interpolation for quantitative analysis of IR spectra

When using spectroscopic instrumentation for quantitative analysis of mixture, spectral intensity non-linearity and peak shift make it challenging for building calibration model. In this study, we investigated the performance of a nonlinear model, namely nonlinear least squares with local polynomial interpolation (NLSLPI). In NLSLPI, the parameters to be optimized are the concentrations of the components. Levenberg-Marquardt (L-M) method is used to solve the nonlinear-least-squares optimization problem and local polynomial interpolation is used to generate the nonlinear function for each component. We tested the robustness of NLSLPI on a computer-simulation dataset. We also compared NLSLPI, in terms of RMSEP, to partial least squares (PLS), classical least squares (CLS) and piecewise classical least squares (PCLS) on a real-world dataset. Experimental results demonstrate the effectiveness of the proposed method.

Five modified classical least squares based models for stability indicating analysis of cyclobenzaprine HCl with its major degradation products: A comparative study

Five modified multivariate calibration models based on classical least squares (CLS) in addition to traditional CLS model are developed and validated for assaying cyclobenzaprine HCl (CZ) with its major degradants; dibenzocycloheptatrienone (DZ) and anthraquinone (AQ), whether in its pure form or in pharmaceutical dosage form. The five models are net analyte processing CLS (NAP-CLS), orthogonal signal correction CLS (OSC-CLS), direct orthogonal signal correction CLS (DOSC-CLS) and hybrid linear analysis following the strategy of Xu and Schechter (HLA-XS) or Goicoechea et al. (HLA-GO). The five modified CLS models in addition to traditional CLS were subjected to a comparative study through manipulation of ultra-violet absorption data in the region of 220–350 nm. Three factor four level experimental design was adopted which results in 16 mixtures calibration set covering various concentrations of CZ, DZ and AQ. An extra validation set, composed of nine mixtures, was prepared for validation of the prediction power of the presented models. Experimental results showed high capability of the proposed modified CLS models for assaying CZ successfully without any interference from the co-existing degradation products (DZ and AQ). A statistical comparison between the results of CZ analysis in its dosage form by the six CLS based models and the reported HPLC method was carried out presenting no significant difference in regards to precision and accuracy. Significance of CLS based models is a consequent of their high quantitative and qualitative power for assaying multi-components mixtures.

Practical Robust Optimization for Least-Squares Problems

The solutions to robust optimization problems are sometimes too conservative because of the focus on worst-case performance. For the least-squares (LS) problem, we describe a way to overcome this by combining the classical formulation with its robust version. We do this by constructing a sequence of problems that are parameterized in terms of the well-estimated aspects of the data. One end of this sequence is the Classical LS, and the other end is a variant of Robust LS that we construct for this purpose. By choosing the right point in the sequence, we are selectively robust only to the poorly estimated aspects of the data. However, we show that better estimation does not imply better prediction. We then transform the problem to align the estimation and prediction objectives, calling it objective matching. This transformation improves prediction while provably retaining the problem structure. Objective matching allows our method (called Unified Least Squares or ULS) to consistently match or outperform other state-of-the-art techniques, including both ridge and LASSO regression, on simulations and real-world data sets.

Classical Least Squares-Assisted Mid-Infrared (MIR) Laser Spectroscopy Detection of High Explosives on Fabrics.

Mid-infrared (MIR) laser spectroscopy was used to detect the presence of residues of high explosives (HEs) on fabrics. The discrimination of the vibrational signals of HEs from a highly MIR-absorbing substrate was achieved by a simple and fast spectral evaluation without preparation of standards using the classical least squares (CLS) algorithm. Classical least squares focuses on minimizing the differences between the spectral features of the actual spectra acquired using MIR spectroscopy and the spectral features of calculated spectra modeled from linear combinations of the spectra of neat components: HEs, fabrics, and bias. Samples in several combinations of cotton fabrics/HEs were used to validate the methodology. Several experiments were performed focusing on binary, ternary, and quaternary mixtures of TNT, RDX, PETN, and fabrics. The parameters obtained from linear combinations of the calculated spectra were used to perform discrimination analyses and to determine the sensitivity and selectivity of HEs with respect to the substrates and to each other. However, discrimination analysis was not necessary to achieve successful detection of HEs on cotton fabric substrates. The RDX signals ( mRDX > 0.02 mg) on cotton were used to calculate the limit of detection (LOD). The signal-to-noise ratios (S/N) calculated from the spectra of cotton dosed with decreasing masses of RDX until S/N ≈ 3 resulted in a LOD of 15-33 µg, depending on the vibrational band used. Linear fits generated by comparing the mass dosed RDX with the fraction predicted were also used to calculate the LOD based on the uncertainty of the blank and the slope. This procedure resulted in a LOD of 58 µg. Probably the most representative value of the method LOD was calculated using an interpolation of a threshold determined using the predicted average value for the blank plus 3.28 times the standard deviations ( p-value threshold) for low surface dosages of RDX (LOD = 40 µg). The contribution demonstrates that to achieve HE detection on fabrics using the proposed algorithm, i.e., determining the presence/absence of HEs on the substrates, the library must contain the spectra of HEs, substrates, and potential interferents or that these spectra be added to the models in the field. If the model does not contain the spectra of the fabric components, there is a high probability of finding false positives for clean samples (no HEs) and a low probability for failed detection in samples with HEs. More work will be required to demonstrate that these new approaches to HE detection work on real-world samples and when contaminating materials are present in the samples.

Development and Validation of Chemometric Spectrophotometric Methods for Simultaneous Determination of Simvastatin and Nicotinic Acid in Binary Combinations.

The development and introduction of combined therapy represent a challenge for analysis due to severe overlapping of their UV spectra in case of spectroscopy or the requirement of a long tedious and high cost separation technique in case of chromatography. Quality control laboratories have to develop and validate suitable analytical procedures in order to assay such multi component preparations. New spectrophotometric methods for the simultaneous determination of simvastatin (SIM) and nicotinic acid (NIA) in binary combinations were developed. These methods are based on chemometric treatment of data, the applied chemometric techniques are multivariate methods including classical least squares (CLS), principal component regression (PCR) and partial least squares (PLS). In these techniques, the concentration data matrix were prepared by using the synthetic mixtures containing SIM and NIA dissolved in ethanol. The absorbance data matrix corresponding to the concentration data matrix was obtained by measuring the absorbance at 12 wavelengths in the range 216 - 240 nm at 2 nm intervals in the zero-order. The spectrophotometric procedures do not require any separation step. The accuracy, precision and the linearity ranges of the methods have been determined and validated by analyzing synthetic mixtures containing the studied drugs. Chemometric spectrophotometric methods have been developed in the present study for the simultaneous determination of simvastatin and nicotinic acid in their synthetic binary mixtures and in their mixtures with possible excipients present in tablet dosage form. The validation was performed successfully. The developed methods have been shown to be accurate, linear, precise, and so simple. The developed methods can be used routinely for the determination dosage form.

Simultaneous Spectrophotometric Determination of Elbasvir and Grazoprevir in a Pharmaceutical Preparation.

Three UV spectrophotometric methods have been developed for the simultaneous determination of two new Food and Drug Administration-approved drugs, elbasvir (EBV) and grazoprevir (GRV), in their combined pharmaceutical dosage form. These methods include dual wavelength (DW), classic least-squares (CLS), and principal component regression (PCR). To achieve the DW method, two wavelengths were chosen for each drug in a way to ensure the difference in absorbance was zero from one drug to the other. GRV revealed equal absorbance at 351 and 315 nm, for which the distinctions in absorbance were measured for the determination of EBV. In the same way, distinctions in absorbance at 375 and 334.5 nm were measured for the determination of GRV. Alternatively, the CLS and PCR models were applied to the spectra analysis because the synchronous inclusion of many unreal wavelengths rather than using a single wavelength greatly increased the precision and predictive ability of the methods. The proposed methods were successfully applied to the assay of these drugs in their pharmaceutical formulation. The obtained results were statistically compared with manufacturing methods. The results conclude that there was no significant difference between the proposed methods and the manufacturing method with respect to accuracy and precision.

Comprehensive Multivariate Analysis of Red Wine Phenolic Composition, Color and Quality Components With Simultaneous Absorbance and Fluorescence Excitation Emission Mapping

The color and phenolic composition of fermented red wines and unfermented grape juice are linked to a variety of quality components including the obvious visual, taste and ‘mouth-feel’ aesthetics. The phenolic composition is a strong indicator of fruit ripeness and can be used to adjust harvesting practices especially during the veraison; notably the phenolic composition can be followed throughout the wine making process to establish quality control and product variation guidelines. Conventional phenolic analysie can be time- and labor intensive with discriminatory analyses usually requiring HPLC or LC-MS instrumentation. Color analyses are typically carried out with conventional UV-VIS spectrophotometry. This study outlines new methodology for calibrating and validating phenolic analysis using a patented simultaneous absorbance and fluorescence excitation-emission mapping (EEM) instrument. Compared to conventional column chromatography, the purely optical calibrated EEM method can provide comprehensive phenolic profiles in a few minutes while concomitantly providing all the information needed for International Commission on Illumination (CIE) tristimulus analyses as well as Hue and Intensity. The study compares the effectiveness and pros and cons of different multivariate analysis techniques of the EEM data, including Principal Components Analysis (PCA), Parallel Factor Analysis (PARAFAC) and Classical Least Squares (CLS). The comparison is evaluated with respect to characterizing and classifying samples as a function of ripening, varietal and process related parameters as well as to possibly screen for adulterants and storage issues such as oxidation or microbial spoilage. This study exemplifes the analysis of several varieties of grape juice and fermented wine samples to illustrate the effectiveness of measuring common phenolic compounds as well as to show the effectiveness of the fingerprinting capabilities for several possible QC related measurements.

Averaging the population projection matrices: Heuristics against uncertainty and nonexistence

In matrix population models, the process of population “projection” through a number of time steps is fundamentally multiplicative, hence the arithmetic mean of the consecutive matrices is of doubtful meaning, while the geometric mean quite corresponds to the multiplication principle. The geometric mean of positive numbers does not bear any problem, but that of matrices does. The “population projection matrices” (PPMs) are rather nonnegative than positive, with the allocation of non-zeros that is predetermined by the life cycle graph (LCG) reflecting the development biology of a given species, and this graph is principally incomplete. The average matrix A should logically have the same fixed pattern of zeros as those to be averaged, and this causes the averaging matrix equation to be overdetermined as a system of element-wise algebraic equations for the unknown positive elements. Therefore, the exact solution to the problem of pattern-geometric averaging does generally not exist, while the classical (least-squares) approximation leads to a significant error. My heuristic approach to finding a better approximate A for the PPMs in the form of L = T(transition) + F(fertility) is to solve the problem in a combined way: the pattern-geometric approximation for the T part and the exact arithmetic mean for F (as population recruitment is an additive process). As a result, the approximation error decreases drastically due to matrix T being always substochastic, while the combined, TF-averaging, method turns out efficient even under ‘reproductive uncertainty’ in data, i.e., for the whole families of feasible matrices F in the sum L = T + {F}. I illustrate the method of TF-averaging with 5 matrices L(t) calibrated for each pair of consecutive years from a 6-year period of observation in a case study of Eritrichium caucasicum, a short-lived perennial herbaceous species. The approximate TF-average enables gaining the ‘age-specific traits from stage-specific models’ (Caswell, 2001, p. 116) that are characteristic of the entire period, and I discuss other motivations/advantages for/of pattern-geometric means in matrix population models.

Identification of Uranium Minerals in Natural U-Bearing Rocks Using Infrared Reflectance Spectroscopy

The identification of minerals, including uranium-bearing species, is often a labor-intensive process using X-ray diffraction (XRD), fluorescence, or other solid-phase or wet chemical techniques. While handheld XRD and fluorescence instruments can aid in field applications, handheld infrared (IR) reflectance spectrometers can now also be used in industrial or field environments, with rapid, nondestructive identification possible via analysis of the solid's reflectance spectrum providing information not found in other techniques. In this paper, we report the use of laboratory methods that measure the IR hemispherical reflectance of solids using an integrating sphere and have applied it to the identification of mineral mixtures (i.e., rocks), with widely varying percentages of uranium mineral content. We then apply classical least squares (CLS) and multivariate curve resolution (MCR) methods to better discriminate the minerals (along with two pure uranium chemicals U3O8 and UO2) against many common natural and anthropogenic background materials (e.g., silica sand, asphalt, calcite, K-feldspar) with good success. Ground truth as to mineral content was attained primarily by XRD. Identification is facile and specific, both for samples that are pure or are partially composed of uranium (e.g., boltwoodite, tyuyamunite, etc.) or non-uranium minerals. The characteristic IR bands generate unique (or class-specific) bands, typically arising from similar chemical moieties or functional groups in the minerals: uranyls, phosphates, silicates, etc. In some cases, the chemical groups that provide spectral discrimination in the longwave IR reflectance by generating upward-going (reststrahlen) bands can provide discrimination in the midwave and shortwave IR via downward-going absorption features, i.e., weaker overtone or combination bands arising from the same chemical moieties.