Classical Least-squares Research Articles

Parameter estimation in vapor-liquid equilibrium modeling of compounds related to biodiesel production using opposite point-based differential evolution algorithm.

Biodiesel stands out as the most favorable alternatives to fossil-derived diesel, offering a multitude of environmental benefits. At various stages of biodiesel production, the separation processes necessitate thermodynamic models with the capability to correlate and predict phase equilibria of mixtures. In this study, application of the classical differential evolution (DE) and its new enhanced version, the OPDE algorithm, for modeling vapor-liquid equilibrium (VLE) associated with components related to biodiesel production is presented. The algorithms were analysed and contrasted in terms of their performance, in estimating parameters for Wilson, NRTL and UNIFAC models. Additionally, classical least-squares (LS) and error-in-variable (EIV) approaches were examined and compared. Also, VLE datasets for a specific system have been merged, and parameters have been estimated. The findings suggest that parameters obtained through LS approach align with those reported in literature, indicating faster convergence in all problems. In contrast, the EIV approach achieved a higher objective function value compared to the LS approach, exhibiting low deviation. OPDE outperformed DE in terms of performance. The enhancement in RMSTD value has been found within range 91%-99% for EIV approach. Further, novel findings derived from some of the studied VLE datasets are presented.

Advanced UV Spectrophotometry-Classical Least Squares Determination of Paracetamol, Phenylpropanolamine HCl, and Chlorpheniramine Maleate in Tablet Dosage Form

This study aims to develop and validate an advanced UV spectrophotometry- Classical Least Squares (CLS) for the simultaneous determination of Paracetamol (PA), Phenylpropanolamine HCl (PH), and Chlorpheniramine Maleate (CH) in tablet dosage form. The method involves the preparation of standard solutions of the three compounds across their respective concentration ranges 3-9 µg/mL for PA, 170-512 µg/mL for PH, and 7-19 µg/mL for CH. The CLS spectrophotometry UV method was applied to these spectra to construct calibration, which were then used to predict the concentrations of PA, PH, and CH in tablet dosage form. Validation of the method demonstrated excellent linearity, precision, and accuracy, with recovery rates of 99.26% for PA, 100.06% for PH, and 99.41% for CH. Sensitivity analysis revealed Limits of Detection (LOD) of 0.10 µg/mL for PA, 1.20 µg/mL for PH, and 0.30 µg/mL for CH, and Limits of Quantification (LOQ) of 0,30 µg/mL for PA, 4.00 µg/mL for PH, and 1.50 µg/mL for CH. The method’s robustness and reliability make it an excellent choice for routine quality control of these compounds in pharmaceutical tablet formulations.

Spectral induced polarization tomography inversion: Hybridizing homotopic continuation with Bayesian inversion

Induced polarization tomography offers the potential to better characterize the subsurface structures by considering spectral content from data acquisition over a broad frequency range. Spectral induced polarization (SIP) tomography is generally defined as a nonlinear inverse problem commonly solved through deterministic gradient-based methods. To this end, the spectral parameters, i.e., direct current resistivity, chargeability, relaxation time, and frequency exponent, are resolved by individually or simultaneously inverting all frequency data, followed by fitting a generalized Cole-Cole model to the inverted complex resistivities. Due to the high correlation between the Cole-Cole model parameters and a lack of knowledge about the initial approximation of the spectral parameters, using the classical least-squares methods may lead to inaccurate solutions and impede reliable uncertainty analysis. To cope with these limitations, we introduce a new approach based on a hybrid application of a globally convergent homotopic continuation method and a Bayesian inference to reconstruct the distribution of the subsurface spectral parameters. The homotopic optimization, owing to its fast and global convergence, is first implemented to invert multifrequency SIP data sets aimed at retrieving the complex-valued resistivity. Then, Bayesian inversion based on a Markov chain Monte Carlo (MCMC) sampling method, along with a priori information including the lower and upper bounds of the prior distributions, is used to invert the complex resistivity for the Cole-Cole model parameters. By applying the MCMC inversion algorithm, a full nonlinear uncertainty appraisal can be provided. We numerically evaluate the performance of our method using synthetic and real data examples in the presence of topographical effects. Numerical results prove that the homotopic continuation method outperforms the classic, smooth inversion algorithm in the sense of approximation accuracy and computational efficiency. In addition, we determine that our hybrid inversion strategy provides reliable representations of the main features and structure of the earth’s subsurface in terms of the spectral parameters.

Fast Sparse Discriminative K-Means for Unsupervised Feature Selection.

Embedded feature selection approach guides subsequent projection matrix (selection matrix) learning through the acquisition of pseudolabel matrix to conduct feature selection tasks. Yet the continuous pseudolabel matrix learned from relaxed problem based on spectral analysis deviates from reality to some extent. To cope with this issue, we design an efficient feature selection framework inspired by classical least-squares regression (LSR) and discriminative K-means (DisK-means), which is called the fast sparse discriminative K-means (FSDK) for the feature selection method. First, the weighted pseudolabel matrix with discrete trait is introduced to avoid trivial solution from unsupervised LSR. On this condition, any constraint imposed into pseudolabel matrix and selection matrix is dispensable, which is significantly beneficial to simplify the combinational optimization problem. Second, the l2,p -norm regularizer is introduced to satisfy the row sparsity of selection matrix with flexible p . Consequently, the proposed FSDK model can be treated as a novel feature selection framework integrated from the DisK-means algorithm and l2,p -norm regularizer to optimize the sparse regression problem. Moreover, our model is linearly correlated with the number of samples, which is speedy to handle the large-scale data. Comprehensive tests on various data terminally illuminate the effectiveness and efficiency of FSDK.

PINNslope: Seismic data interpolation and local slope estimation with physics informed neural networks

Interpolation of aliased seismic data constitutes a key step in a seismic processing workflow to obtain high-quality velocity models and seismic images. Building on the idea of describing seismic wavefields as a superposition of local plane waves, we propose to interpolate seismic data by using a physics informed neural network (PINN). In the proposed framework, two feed-forward neural networks are jointly trained using the local plane wave differential equation as well as the available data as two terms in the objective function: a primary network assisted by positional encoding is tasked with reconstructing the seismic data, whereas an auxiliary, smaller network estimates the associated local slopes. Results on synthetic and field data validate the effectiveness of the proposed method in handling aliased (coarsely sampled) data and data with large gaps. Our method compares favorably against a classic least-squares inversion approach regularized by the local plane-wave equation as well as a PINN-based approach with a single network and precomputed local slopes. We find that introducing a second network to estimate the local slopes, whereas at the same time interpolating the aliased data enhances the overall reconstruction capabilities and convergence behavior of the primary network. Moreover, an additional positional encoding layer embedded as the first layer of the wavefield network confers to the network the ability to converge faster, improving the accuracy of the data term.

Gradient-Based Optimization Method for Experimental Modal Parameter Estimation with Finite Element Model

This paper presents a novel gradient-based optimization algorithm for improving the accuracy of experimentally estimated modal parameters with the assistance of finite element models. Initially, we recast the discrete vibration response equation into a matrix form and formulate the parameter estimation problem in modal analysis as an optimization problem. Then the problem is solved with a gradient-based iterative algorithm, which explicitly exhibits the closed form of gradients used in optimization. Initial values for this iteration are parameters derived from finite element models, since every important engineering structure should be analyzed with a finite element model before it is constructed. Subsequently, the performance of this algorithm is validated by both pure numerical experiments, which simulate the physical world, and experiments using real measurement data gathered by sensors in the real physical world. The algorithm’s performance is further enhanced by incorporating gradient clipping and an adaptive iteration threshold. As a comparison, a discussion on classical least-squares time-domain method for the problem is provided. For practical applications, the Shi–Tomasi corner detection and Lucas–Kanade optical flow methods are deployed to detect corner points from videos taken during the vibration of a structure and track the motion of these points in the videos.

Resolution of overlapping spectra using chemometric manipulations of UV-spectrophotometric data for the determination of Atenolol, Losartan, and Hydrochlorothiazide in pharmaceutical dosage form

Simultaneous determination of atenolol (ATN), losartan potassium (LOS), and hydrochlorothiazide (HCZ) in presence of HCZ impurity B was conducted by chemometric approaches and radial basis function network (RBFN) using UV-spectrophotometry without preliminary separation. Three chemometric models namely, classical least-squares (CLS), principal component regression (PCR), and partial least-squares (PLS) along with RBFN were utilized using the ternary mixtures of the three drugs. The multivariate calibrations were obtained by measuring the zero-order absorbance of the mixtures from 250 to 270 nm at the interval of 0.2 nm. The models were built covering the concentration range of (4.0 to 20.0), (3.8 to 20.2), and (0.9 to 50.1) μg mL−1 for ATN, LOS, and HCZ, respectively. The regression coefficient was calculated between the actual and predicted concentrations of the 3 drugs using CLS, PCR, PLS and RBFN. The accuracy of the developed models was evaluated using the root mean square error of prediction (RMSEP) giving satisfactory results. The proposed methods were simple, accurate, precise and were applied efficiently for the quantitation of the three components in laboratory-prepared mixtures, and in dosage form showing good recovery values. In addition, the obtained results were compared statistically with each other using ANOVA test showing non-significant difference between them.

Development and Evaluation of Chemometric Models for the Estimation of Sumatriptan in the Presence of Naproxen and a Degradation Product Using UV Spectrophotometry.

Chemometrics is a discipline that allows the spectral resolution of drugs in a pharmaceutical formulation along with degradation product and it is an alternative to chromatographic methods. Sumatriptan (SUM) is co-formulated with naproxen (NAP) and used in acute migraine attacks. SUM, which has physiological importance, has not been subjected to any stability-indicating chemometric approaches yet, so there is a need for an accurate and safe method for the assay of the cited drug in its preparations. The greenness and blueness assessment was applied using different ecological metrics, including the Green Analytical Procedure Index (GAPI), Analytical Greenness Metric (AGREE), Analytical Eco-Scale (AES) and new "blueness" evaluation using the Blue Applicability Grade Index (BAGI) tool. SUM was determined in pharmaceutical formulation along with NAP and in presence of alkali-induced degradation product with simple and cost-effective multivariate approaches using spectrophotometric data. Three chemometric approaches were applied for the stability-indicating determination of SUM in the presence of NAP. Classical least-squares (CLS), partial least-squaresregression (PLS), and principal components regression (PCR)-three multivariate calibration numerical models that were applied to the UV spectra of the mixtures-were used to achieve the best resolution. Sumatriptan was analyzed with mean accuracies for PLS (100.29% ± 1.318) and for PCR (100.60% ± 1.564). The presented methods were compared and validated for their quantitative analyses. Moreover, statistical comparison between the results obtained by the proposed models and the official methods showed no significant differences. The proposed multivariate calibrations were accurate and specific for quantitative analysis of the studied component. PLS is the best method that has the capacity for qualitative analysis of SUM and it is suitable for routine analysis and stability studies of SUM in QC laboratories. Various ecological assessment metrics confirmed the long-standing eco-friendliness of the suggested models. Severally overlapped mixtures of SUM along with co-formulated drug NAP and an alkali-induced degradation product were analyzed by three chemometric approaches. The analytical performance of PLS and PCR was compared and validated in terms of root-mean-square error of calibration (RMSEC), SE of prediction, and recoveries. PLS gave the highest predicted concentrations with the lowest RMSEC and root-mean-square error of prediction. The standard addition was applied for accuracy assessment and the results were compared to those of official methods. Proposed models determined SUM in synthetic mixtures and pharmaceutical formulation in QC laboratories and stability studies. Ecological evaluation tools for measuring the environmental friendliness of chemicals were utilized for the first time in the analysis of SUM.

Four chemometric models enhanced by Latin hypercube sampling design for quantification of anti-COVID drugs: sustainability profiling through multiple greenness, carbon footprint, blueness, and whiteness metrics

Montelukast sodium (MLK) and Levocetirizine dihydrochloride (LCZ) are widely prescribed medications with promising therapeutic potential against COVID-19. However, existing analytical methods for their quantification are unsustainable, relying on toxic solvents and expensive instrumentation. Herein, we pioneer a green, cost-effective chemometrics approach for MLK and LCZ analysis using UV spectroscopy and intelligent multivariate calibration. Following a multilevel multifactor experimental design, UV spectral data was acquired for 25 synthetic mixtures and modeled via classical least squares (CLS), principal component regression (PCR), partial least squares (PLS), and genetic algorithm-PLS (GA-PLS) techniques. Latin hypercube sampling (LHS) strategically constructed an optimal validation set of 13 mixtures for unbiased predictive performance assessment. Following optimization of the models regarding latent variables (LVs) and wavelength region, the optimum root mean square error of cross-validation (RMSECV) was attained at 2 LVs for the 210–400 nm spectral range (191 data points). The GA-PLS model demonstrated superb accuracy, with recovery percentages (R%) from 98 to 102% for both analytes, and root mean square error of calibration (RMSEC) and prediction (RMSEP) of (0.0943, 0.1872) and (0.1926, 0.1779) for MLK and LCZ, respectively, as well bias-corrected mean square error of prediction (BCMSEP) of -0.0029 and 0.0176, relative root mean square error of prediction (RRMSEP) reaching 0.7516 and 0.6585, and limits of detection (LOD) reaching 0.0813 and 0.2273 for MLK and LCZ respectively. Practical pharmaceutical sample analysis was successfully confirmed via standard additions. We further conducted pioneering multidimensional sustainability evaluations using state-of-the-art greenness, blueness, and whiteness tools. The method demonstrated favorable environmental metrics across all assessment tools. The obtained Green National Environmental Method Index (NEMI), and Complementary Green Analytical Procedure Index (ComplexGAPI) quadrants affirmed green analytical principles. Additionally, the method had a high Analytical Greenness Metric (AGREE) score (0.90) and a low carbon footprint (0.021), indicating environmental friendliness. We also applied blueness and whiteness assessments using the high Blue Applicability Grade Index (BAGI) and Red–Green–Blue 12 (RGB 12) algorithms. The high BAGI (90) and RGB 12 (90.8) scores confirmed the method's strong applicability, cost-effectiveness, and sustainability. This work puts forward an optimal, economically viable green chemistry paradigm for pharmaceutical quality control aligned with sustainable development goals.

Spider chart, greenness and whiteness assessment of experimentally designed multivariate models for simultaneous determination of three drugs used as a combinatory antibiotic regimen in critical care units: Comparative study

In this study, five earth-friendly spectrophotometric methods using multivariate techniques were developed to analyze levofloxacin, linezolid, and meropenem, which are utilized in critical care units as combination therapies. These techniques were used to determine the mentioned medications in laboratory-prepared mixtures, pharmaceutical products and spiked human plasma that had not been separated before handling. These methods were named classical least squares (CLS), principal component regression (PCR), partial least squares (PLS), genetic algorithm partial least squares (GA-PLS), and artificial neural network (ANN). The methods used a five-level, three-factor experimental design to make different concentrations of the antibiotics mentioned (based on how much of them are found in the plasma of critical care patients and their linearity ranges). The approaches used for levofloxacin, linezolid, and meropenem were in the ranges of 3–15, 8–20, and 5–25 µg/mL, respectively. Several analytical tools were used to test the proposed methods' performance. These included the root mean square error of prediction, the root mean square error of cross-validation, percentage recoveries, standard deviations, and correlation coefficients. The outcome was highly satisfactory. The study found that the root mean square errors of prediction for levofloxacin were 0.090, 0.079, 0.065, 0.027, and 0.001 for the CLS, PCR, PLS, GA-PLS, and ANN models, respectively. The corresponding values for linezolid were 0.127, 0.122, 0.108, 0.05, and 0.114, respectively. For meropenem, the values were 0.230, 0.222, 0.179, 0.097, and 0.099 for the same models, respectively. These results indicate that the developed models were highly accurate and precise. This study compared the efficiency of artificial neural networks and classical chemometric models in enhancing spectral data selectivity for quickly identifying three antimicrobials. The results from these five models were subjected to statistical analysis and compared with each other and with the previously published ones. Finally, the whiteness of the methods was assessed by the recently published white analytical chemistry (WAC) RGB 12, and the greenness of the proposed methods was assessed using AGREE, GAPI, NEMI, Raynie and Driver, and eco-scale, which showed that the suggested approaches had the least negative environmental impact. Furthermore, to demonstrate solvent sustainability, a greenness index using a spider chart methodology was employed.

Development of a Versatile Lipid Core for Nanostructured Lipid Carriers (NLCs) Using Design of Experiments (DoE) and Raman Mapping.

The objective of this study was to develop a versatile lipid core for the 'brick-dust type of drugs' (poorly water-soluble and poorly lipid-soluble drugs). In the first step, excipients of different polarities were classified according to their behavior in aqueous solutions. Subsequently, binary mixtures were prepared with cetyl palmitate (Crodamol™ CP pharma, Campinas, São Paulo, Brazil) as the solid lipid, and its miscibility with other excipients was evaluated using Raman mapping and classical least squares (CLS). Based on the results, the excipients Crodamol™ CP pharma (hydrophobic), Super Refined™ DMI (dimethyl isosorbide; hydrophilic, Mill Hall, PA, USA), and Super Refined™ Lauryl Lactate (lauryl lactate, medium polarity, Mill Hall, PA, USA) were chosen to compose the lipid core. The ideal proportion of these excipients was determined using a mixture design and the standard deviation (STD) of image histograms as the response variables. After statistical evaluation of the DoE results, the final composition was determined, and drugs with different logP (0 to 10) and physicochemical characteristics were evaluated in the optimized mixture. The drugs butamben (Sigma-Aldrich Co., Spruce Street, St. Louis, MO, USA), tacrolimus (NutriFarm, São Paulo, Brazil), atorvastatin calcium, and resveratrol (Botica da Terra, Campinas, Brazil) presented a homogeneous distribution in the optimized lipid core, indicating that this is a promising system to be used in nanostructured lipid carrier (NLC) formulations of such types of drugs.

Quantitative and qualitative analysis of cell culture media powders for mammalian cells by Raman microscopy

Cell culture media are essential for large-scale recombinant protein production using mammalian cell cultures. The composition and quality of media significantly impact cell growth and product formation. Analyzing media poses challenges due to complex compositions and undisclosed exact compositions. Traditional methods like NMR and chromatography offer sensitivity but require time-consuming sample preparation and lack spatial information. Raman chemical mapping characterizes solids, but its use in cell culture media analysis is limited so far. We present a chemometric evaluation for Raman maps to qualify and quantify media components, evaluate powder homogeneity, and perform lot-to-lot comparisons. Three lots of a marketed cell culture media powder were measured with Raman mapping technique. Chemometrics techniques have outlined a strategy to extract information from complex data. First, a spectral library has been structured. In addition to the 23 spectra for presumed ingredients, we obtained another 9 pure components with Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS). Then the Spectral Angle Mapper-Orthogonal Projection (SAM-OP) algorithm revealed whether references actually occur in the mapped media powders. Finally, a quantification was provided by Classical Least Squares (CLS) modelling. Quantities of 18 significant amino acids mostly correlated with the reference method. The proposed method can be generally applied even for such complicated samples. Leveraging Raman mapping and innovative chemometric methods enhance recombinant protein production by improving the understanding of the spatial distribution and composition of cell culture media in mammalian cell cultivations.

Visualization and identification of components in a gigantic spherical dolomite concretion by Raman imaging in combination with MCR or CLS methods

The combination of Raman imaging and multivariate curve resolution (MCR) or classical least squares (CLS) has allowed us to explore the distribution and identification of components in a gigantic spherical dolomite concretion. It has been found by the MCR and CLS analyses of imaging data that the concretion contains dolomite, kerogen, anatase, quartz, plagioclase, and carbon materials with considerably large distribution of dolomite. The existence of these components has also been confirmed by the point-by-point analysis of imaging data. The distributions of these components were clearly observed by Raman images. Of note is that the amount of carbon materials is considerably large, and they are buried among the matrix sedimentary grains in the concretion, suggesting that there exist soft tissues with biological origin. Moreover, one of the loading spectra of CLS shows intense bands in the region of 3000–2800 cm−1, and bands at ca. 1658, ca. 1585, 1455, 1323, and 1261 cm−1. These bands indicate the existence of decomposed organic materials in the concretion. Raman imaging of concretions provides direct evidence that concretions are of biological organic origin.

Multiplexed Surface Protein Detection and Cancer Classification Using Gap-Enhanced Magnetic-Plasmonic Core-Shell Raman Nanotags and Machine Learning Algorithm.

Cancer is the second leading cause of death attributed to disease worldwide. Current standard detection methods often rely on a single cancer marker, which can lead to inaccurate results, including false negatives, and an inability to detect multiple cancers simultaneously. Here, we developed a multiplex method that can effectively detect and classify surface proteins associated with three distinct types of breast cancer by utilizing gap-enhanced Raman scattering nanotags and machine learning algorithm. We synthesized anisotropic magnetic core-gold shell gap-enhanced Raman nanotags incorporating three different Raman reporters. These multicolor Raman nanotags were employed to distinguish specific surface protein markers in breast cancer cells. The acquired signals were deconvoluted and analyzed using classical least-squares regression to generate a surface protein profile and characterize the breast cancer cells. Furthermore, computational data obtained via finite-difference time-domain and discrete dipole approximation showed the amplification of the electric fields within the gap region due to plasmonic coupling between the two gold layers. Finally, a random forest classifier achieved an impressive classification and profiling accuracy of 93.9%, enabling effective distinguishing between the three different types of breast cancer cell lines in a mixed solution. With the combination of immunomagnetic multiplex target specificity and separation, gap-enhancement Raman nanotags, and machine learning, our method provides an accurate and integrated platform to profile and classify different cancer cells, giving implications for identification of the origin of circulating tumor cells in the blood system.

Visual detection of microplastics using Raman spectroscopic imaging.

As a new type of pollutant in the marine environment and terrestrial ecosystems, microplastics have attracted widespread attention. Assessing the ecological risk of microplastics relies on accurately detecting small-sized particles in the environment. Microplastics exhibit unique "fingerprint" characteristics in Raman spectroscopy, making them suitable for rapid identification. In this study, we achieved visualization of microplastics through pseudo-color images generated by Raman spectroscopy imaging. Pseudo-color imaging maps were generated by selecting characteristic peaks and the classical least-squares fitting method was used to visually represent the distribution of different microplastics. The study explored the potential of Raman spectroscopy and its mapping mode in distinguishing various types of mixed microplastics and demonstrated that this approach can identify microplastics in complex environmental samples. Specifically, a cloud-point extraction followed by membrane filtration method was successfully applied to identifying mixed-component microplastics. In summary, the category, quantity, location, and differentiation of microplastics can be accurately analyzed by Raman spectroscopy, which provides a basis for assessing their ecological risk.

Extended least squares (ELS) and generalized least squares (GLS) for clutter suppression in hyperspectral images: A theoretical description

Hyperspectral imaging (HSI) has been demonstrated to be useful for estimating spatial distributions of different chemical constituents on surfaces and in imaged scenes, as well as for detecting anomalies and known targets that may be present. In target detection, the objective is to find pixels that contain significant signal attributable to a known “target” spectrum. Unfortunately, measured images are often dominated by “non-target” interference signals with unknown spectra that vary image-to-image. To be effective, target detection algorithms must account for the non-target signal, commonly referred to as “clutter.” The utility of HSI for target detection in spatially complex scenarios can be attributed to two aspects associated with the sensing system: 1) The target can dominate the measured signal in a few individual pixels, although it may have only a minor contribution to the overall signal, and 2) HSI measures many pixels relevant for characterizing clutter that can be used in clutter suppression algorithms to account for interferences.Clutter suppression enables the detection of minor signal sources in HSI, resulting in a sensing system uniquely suited to highly variable environmental scenarios. Popular clutter suppression methods such as extended least squares (ELS) and generalized least squares (GLS) can be described as extensions of the classical least squares (CLS) model. The main advantage of these methods is that they are fast and easy to train on an image-to-image basis providing highly sensitive, image-specific target detection systems. However, the optimization of such models affects the sensitivity and selectivity of the detection. In an effort to assist practitioners interested in clutter suppression, this paper presents a detailed description of the theoretical aspects of ELS and GLS methods used for target detection on hyperspectral images. The concepts are demonstrated with practical examples of the detection of an acrylonitrile butadiene styrene (ABS) particle in sand based on a single near infrared hyperspectral image.

Identification of time-varying inertia tensor parameters of a space solar power satellite based on a robust weighted recursive algorithm under impulsive disturbance

Considering changes in the structural size and mass caused by the on-orbit assembly process in a planar space solar power satellite, this study proposes an improved robust recursive algorithm to identify the time-varying inertia tensor parameters of the system. In this algorithm, to decrease the effect of impulsive disturbance on inertial parameter identification during the on-orbit assembly and improve computational accuracy, robust weighted factor and multi-innovation theory are involved. Then, the time-varying inertia tensor parameters of this large flexible structure are identified based on the distributed measurement results of multiple attitude sensors. The simulation results indicate that the proposed algorithm improves the identification accuracy and has better robustness than the original method under the impulsive disturbance. The relative values of the average relative error caused by the impulsive disturbance under the proposed algorithm are approximately 27.8–73.0% less than those under the original method. Additionally, the results also demonstrate that the proposed algorithm has higher noise immunity than the classical recursive least-squares method in a time-varying system. When the impulsive disturbance and zero-mean Gaussian white noise are applied to the system, compared with the conventional recursive least-squares method, the proposed algorithm yields lower absolute and relative values of the average relative error by approximately 4.2% and 44.9%, respectively.

A globally convergent estimator of the parameters of the classical model of a continuous stirred tank reactor

In this paper we provide the first solution to the challenging problem of designing a globally convergent estimator for the parameters of the standard model of a continuous stirred tank reactor. Because of the presence of non-separable exponential nonlinearities in the system dynamics that appear in Arrhenius law, none of the existing parameter estimators is able to deal with them in an efficient way and, in spite of many attempts, the problem was open for many years. To establish our result we propose a novel procedure to obtain a suitable nonlinearly parameterized regression equation and introduce a radically new estimation algorithm—derived applying the Immersion and Invariance methodology—that is applicable to these regression equations. A further contribution of the paper is that parameter convergence is exponential and is guaranteed with weak excitation requirements. To achieve this remarkable property we rely on the utilization of a recently introduced parameter estimator that seamlessly combines a classical least-squares search with the dynamic regressor extension and mixing estimation procedure.

Comparative Study of Augmented Classical Least Squares Models for UV Assay of Co-Formulated Antiemetics Together with Related Impurities.

The classical least squares (CLS) model and three augmented CLS models are adopted and validated for the analysis of pyridoxine HCl (PYR), cyclizine HCl (CYC), and meclizine HCl (MEC) in a quinary mixture with two related impurities: the CYC main impurity, Benzhydrol (BEH), which has carcinogenic and hepatotoxic effects, and the MEC official impurity, 4-Chlorobenzophenone (BEP). The proposed augmented CLS models are orthogonal signal correction CLS (OSC-CLS), direct orthogonal signal correction CLS (DOSC-CLS), and net analyte processing CLS (NAP-CLS). These models were applied to quantify the three active constituents in their raw materials and their corresponding dosage forms using their UV spectra. To evaluate the CLS-based models sensibly, we design a comparative study involving two sets: the training set to construct models and the validation set to assess the prediction abilities of these models. A five-level, five-factor calibration design was established to produce 25 mixtures for the calibration set. In addition, 16 experiments were performed for a test set distributed equally between the in-space and out-space samples. The primary criterion for comparing the models' performance was the validation set's root mean square error of prediction (RMSEP) value. Finally, augmented CLS models showed acceptable results for assaying the three analytes. The results were compared statistically with the reported HPLC methods; however, the DOSC-CLS model proved the best for assaying the dosage forms.

Characterization of Radix Angelicae sinensis by Fluorescence and Near-Infrared Spectroscopies

Angelica sinensis (Oliv.) diels is a perennial herbaceous plant. Its dried root, referred to as radix Angelicae sinensis (RAS), has been used for edible and medicinal purposes. This study is dedicated to spectroscopic characterization and quality detection of RAS powder material or aqueous solution using fluorescence excitation–emission matrix and near-infrared (NIR) spectroscopies. It is the first time that the fluorescence combined with net analyte signal–classical least-squares was able to accurately determine two active substances in 131 RAS batches from five geographical origins in Gansu, China. The concentrations of Z-ligustilide and L-tryptophan were 1.17 ± 0.43 mg g−1 and 0.59 ± 0.19 mg g−1, respectively. A satisfactory NIR-principal discriminant variate model was achieved, enabling the RAS batches to be discriminated by the location. The correct discrimination rates reached 100% for calibration and 87.50% for validation. The work provides an alternative and holistic strategy for reliable fingerprint authentication of RAS materials and helps promote its utility.