Classical Least-squares Method Research Articles

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.

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.

Dual input neural networks for positional sound source localization

In many signal processing applications, metadata may be advantageously used in conjunction with a high dimensional signal to produce a desired output. In the case of classical Sound Source Localization (SSL) algorithms, information from a high dimensional, multichannel audio signals received by many distributed microphones is combined with information describing acoustic properties of the scene, such as the microphones’ coordinates in space, to estimate the position of a sound source. We introduce Dual Input Neural Networks (DI-NNs) as a simple and effective way to model these two data types in a neural network. We train and evaluate our proposed DI-NN on scenarios of varying difficulty and realism and compare it against an alternative architecture, a classical Least-Squares (LS) method as well as a classical Convolutional Recurrent Neural Network (CRNN). Our results show that the DI-NN significantly outperforms the baselines, achieving a five times lower localization error than the LS method and two times lower than the CRNN in a test dataset of real recordings.

Demographic Challenges in Poland Understanding Low Fertility

Research background: The phenomenon of low fertility in Poland is a vital subject of demographic analysis. In recent years, not only have there been changes in procreative and family models, but also in the age structure of society. This is particularly significant in the context of population ageing, which is becoming increasingly evident and brings numerous challenges such as increased burden on healthcare systems, a decrease in the active workforce, and the need to secure adequate retirement funds. Despite the desire to have children, many individuals refrain from making such a decision, and the reasons for this choice are diverse. Therefore, it was essential to conduct an analysis of the factors determining fertility in Poland, considering both the economic and social aspects. Understanding how the economic situation, labour market conditions, and changes in social structure impact on the decision-making process regarding childbearing is essential. Purpose of the paper: The objective of this article was to analyse fertility rates in Poland for the period 2004-2020. The conducted research identified the factors influencing the observed state of low generational replacement and determining their intensity. Methodology/Methods/Data sources: The data used in this article were sourced from the Central Statistical Office and covered the years 2004-2020. The study was based on literature concerning demography and econometrics. Three statistical methods were applied in the analysis of fertility in Poland: the Classical Method of Least Squares (CMLS) model, the Fixed Effects (FE) estimator, and the Random Effects (RE) estimator. Fertility analysis was conducted at regional level by dividing Poland into 16 administrative units (voivodeships). A panel model was employed for the analysis, and the results were subjected to Wald, Breusch-Pagan, and Hausman tests to compare the outcomes obtained from different models. Findings: The results of the analysis indicate that the economic situation and the labour market significantly influence the decision to have children in Poland. The trend of low fertility, although showing some increase, is still characteristic of the country compared to other EU nations. The analysis of the factors determining fertility is vital for understanding the decisions of young generations of Poles regarding parenthood.

Extended real-time voltage instability identification method based on synchronized phasor measurements

This paper presents an extended adaptive approach designed to accurately estimate the Thévenin equivalent parameters using phasor measurements at a given bus for measurements lying in any of four quadrants of the PQ-plane. The improvement is achieved by using a new condition to properly update the estimated parameters after an initial guess. Based on an adaptive philosophy, the proposed approach can correctly account for the intrinsic nonlinearities of a power system, can provide a real-time estimation of Thévenin parameters, and does not require network topology knowledge. The method is validated using the Kundur 2-area system, showing estimation improvements compared to the current adaptive approach and the classical recursive least-squares method. The proposed approach is able to estimate both sides of the system with respect to the measurement bus. In addition, a data-driven voltage stability index is developed. To illustrate the performance of the proposed approach in a larger power system, a voltage stability assessment is carried out on the IEEE 39-bus system, considering the action of overexcitation limiters of generators and nonlinear loads. The proposed approach is suitable for applications that require an accurate Thévenin equivalent estimation in real-time, such as for voltage stability assessment. The new approach provides a reliable tool for the system operators to make proper and timely decisions.

Simultaneous Determination of Paracetamol, Ibuprofen, and Caffeine in Tablets by Molecular Absorption Spectroscopy Combined with Classical Least Square Method.

In this paper, the classical least-squares (CLS) method with molecular absorption spectrophotometric measurement was used to determine simultaneously paracetamol (PAR), ibuprofen (IBU), and caffeine (CAF) in tablets. The absorbance spectra of the standard solutions and samples were measured over a wavelength from 220 to 300 nm with a 0.5 nm step. The concentration of PAR, IBU, and CAF in the sample solutions was calculated by using Visual Basic for Applications (VBA) and a program called CLS-Excel written in Microsoft Excel 2016. The method and the CLS-Excel program were tested on mixed standard laboratory samples with different PAR, IBU, and CAF concentration ratios, and they showed only small errors and a satisfying repeatability. An analytical procedure for tablets containing PAR, IBU, and CAF was developed. The reliability of the procedure was proved via the recovery and repeatability of the analysis results with an actual tablet sample and by comparing the mean contents of active substances in the tablets obtained from the analytical procedure with the HPLC method. The procedure is simple with a reduced cost compared with the HPLC standard method.

Advances in mixed cell deconvolution enable quantification of cell types in spatial transcriptomic data

Mapping cell types across a tissue is a central concern of spatial biology, but cell type abundance is difficult to extract from spatial gene expression data. We introduce SpatialDecon, an algorithm for quantifying cell populations defined by single cell sequencing within the regions of spatial gene expression studies. SpatialDecon incorporates several advancements in gene expression deconvolution. We propose an algorithm harnessing log-normal regression and modelling background, outperforming classical least-squares methods. We compile cell profile matrices for 75 tissue types. We identify genes whose minimal expression by cancer cells makes them suitable for immune deconvolution in tumors. Using lung tumors, we create a dataset for benchmarking deconvolution methods against marker proteins. SpatialDecon is a simple and flexible tool for mapping cell types in spatial gene expression studies. It obtains cell abundance estimates that are spatially resolved, granular, and paired with highly multiplexed gene expression data.

Multivariate analytical methods for simultaneous estimation of Atenolol and Hydrochlorothiazide in bulk and tablet dosage form

The present study aimed to develop simple, accurate and precise FTIR and UV spectrophotometric methods for the quantification of Atenolol and Hydrochlorothiazide in bulk and tablet dosage forms. FT-IR method like classical least squares (CLS) was developed within the range of 2366.69-3433.44; 1564.40-1673.30 cm- UV methods like Cramer’s matrix method (method-I) and linear regression analysis (Method II) were developed and they are based upon constructing the matrix set by using molar absorptivity values at 275.60 nm and 270.40 nm. The assay values for FTIR- CLS method were 102% and 108 % for Atenololand Hydrochlorothiazide respectively. Cramer’s matrix method results were found to be 95.15% and 104% for Atenolol and Hydrochlorothiazide respectively and for linear regression method they were found to be 98.50% and 106% (w/w).

Multi-species hydrocarbon measurement using TDLAS with a wide scanning range DFG laser

Tunable diode laser absorption spectroscopy (TDLAS) is a widely used diagnostic technique due to its high sensitivity, fast response, low cost, and other merits. Hydrocarbon detection is a field of great interest in the application of tunable diode lasers as hydrocarbons are fundamental molecules in many industrial processes. Many tunable diode lasers are only suitable for single species detection due to the short scanning range and in real situations. However, different hydrocarbon species tend to exist simultaneously. Here we present a laser system based on the difference-frequency generation (DFG) method for simultaneous hydrocarbon mixtures detection. The direct absorption spectra of different hydrocarbons covering various groups (e.g., alkane, olefin, and aromatic) were measured. The measurements of the concentration dependence of absorbance for each molecule were carried out. The R2 values were larger than 0.997, which demonstrated the system can measure hydrocarbons covering different molecular classes accurately. The mixture components were identified using the independent component analysis and quantitative analysis was performed using the classical least-squares method. Future studies will focus on the validation of the system in actual processes.

Assessment of the uncertainty in spatial-correlation models for earthquake ground motion due to station layout and derivation method

The evaluation of the aggregate risks to spatially distributed infrastructures and portfolios of buildings requires quantification of the estimated shaking over a region. To characterize the spatial dependency of ground motion intensity measures (e.g. peak ground acceleration), a common geostatistical tool is the semivariogram. Over the past decades, different fitting approaches have been proposed in the geostatistics literature to fit semivariograms and thus characterize the correlation structure. A theoretically optimal approach has not yet been identified, as it depends on the number of observations and configuration layout. In this article, we investigate estimation methods based on the likelihood function, which, in contrast to classical least-squares methods, straightforwardly define the correlation without needing further steps, such as computing the experimental semivariogram. Our outcomes suggest that maximum-likelihood based approaches may outperform least-squares methods. Indeed, the former provides correlation estimates, that do not depend on the bin size, unlike ordinary and weighted least-squares regressions. In addition, maximum-likelihood methods lead to lower percentage errors and dispersion, independently of both the number of stations and their layout as well as of the underlying spatial correlation structure. Finally, we propose some guidelines to account for spatial correlation uncertainty within seismic hazard and risk assessments. The consideration of such dispersion in regional assessments could lead to more realistic estimations of both the ground motion and corresponding losses.

A Modified Least-Squares Method for Quantitative Analysis in Raman Spectroscopy

Quantitative spectral analysis is highly demanded in many applications such as pharmaceutical research, biological sample analysis, and food quality control, in which Raman spectroscopy has been established as a label-free analytical tool. In an attempt to address the challenge faced by the classical least-squares method during the quantification of analyte concentrations, which is induced by potential inaccuracy or variations in the spectral library, we propose a modified least-squares method that accounts for such variations as individual Gaussian functions with variable parameters. Both the spectral library and the analyte concentrations are updated during iterations. The method is validated on both simulated data with multiple Gaussian peaks and experimental measurements from phantoms of chemical mixtures and K562 leukemia cells.

Identification by means of a genetic algorithm of nonlinear damping and stiffness of continuous structures subjected to large-amplitude vibrations. Part I: single-degree-of-freedom responses

A procedure is presented to identify the nonlinear damping and stiffness parameters of a single-degree-of-freedom (SDOF) model from large-amplitude vibrations of harmonically forced continuous systems, in absence of internal resonances. Cubic nonlinear damping is introduced in the SDOF model in addition to the classical viscous one. The parameter estimation relies on the harmonic balance method. It is shown that the mean value, the first and the second harmonics are needed for a softening response, although often only the first harmonic is experimentally measured with accuracy. The identification methodology is thus split between (i) purely hardening and (ii) softening behaviour. The absence of coupling enables for an independent estimation of the nonlinear stiffness from the backbone curve, followed by an evaluation of damping at resonance. For the purely hardening case, the classical least-squares method is applied by using experimentally measured first harmonic. For the softening case, a novel cascade procedure consists in (i) a single-term harmonic balance parameter estimation used as initiation of (ii) a minimization of the distance between data and a two-term harmonic balance model by means of a genetic algorithm. These procedures are validated by parameter identification on synthetic (numerically generated) and experimental frequency-responses. In particular, the identified nonlinear damping model is compared to level-adjusted linear viscous damping with a different coefficient identified at any level of harmonic force, demonstrating its ability to account for the evolution of damping with the vibration amplitude. The identification of one-to-one internal resonances is treated in a companion paper.

A new strategy for calibrating indicator displacement assay (IDA)-based sensor systems

A novel strategy for calibrating Indicator Displacement Assay (IDA)-based sensors is presented herein. The main idea is to replace the instrumental measurement responses by the equilibrium concentration of spectroscopically active species which can be obtained by the Classical Least Squares (CLS) method. Also, coupling the Indirect Hard Modelling (IHM) and CLS methods for the calibration model resulted in a reduction of matrix effects.According to Beer’s law, the measured multivariate spectrum of a mixture is the sum of contributions of all spectroscopically active components via their concentrations and pure spectra. Concentrations of a few components are usually the fundamental variables in a measured spectrum in several sensors or wavelengths. In IDA systems, the equilibrium concentrations of indicator and indicator-receptor species are the fundamental variables that can be an alternative for instrumental responses as the input data for regression methods. These fundamental variables can be exploited from the recorded spectra of the mixtures when the pure spectra of the active species are known. Using dramatically reduced number of input variables without the need for any variable selection method is the main advantage of this idea over conventional calibration methods that use variable selected spectroscopic signals. This strategy can be applied for systems in which the active species are known. Accordingly, for IDA-based sensors with determined pure response to indicator and indicator-receptor complex, the free concentrations of active species can be resolved by the Classical Least Squares (CLS) method.The pure analytical responses are altered in mixtures due to the intermolecular interactions caused by matrix effect in real experimental dataset. So, the free concentrations of spectroscopically active species are not resolved correctly by the CLS method. To tackle the issue of nonlinearity of data due to the matrix effect, the Indirect Hard Modelling (IHM) can be applied to correctly resolve the fundamental variables. The applicability of the presented idea is successfully validated by simulated and real sensor array systems.

SIMULTANEOUS SPECTROPHOTOMETRIC DETERMINATION AND CLASSICAL LEAST SQUARES METHOD: A SIMPLE EXPERIMENT TO INTRODUCE THE CONCEPT OF MULTIVARIATE CALIBRATION

We herein present an experiment where the concentrations of tartrazine, sunset yellow and amaranth in samples containing these three food dyes are determined by system of equations (SE) and classical least squares (CLS) multivariate calibration methods using light absorption data. Firstly, concentrations are obtained by means of the well-known SE method, that is, by solving a set of three linear equations in which the Beer-Lambert’s proportionality coefficients are obtained from analytical curves. Then, it is shown that the CLS method is a natural extension to SE, with an arbitrarily large number of equations. Nevertheless, within the CLS method, the unknown coefficients are found using mixtures with known concentrations of each dye. In order to introduce the students to the basics of algorithms and numerical computations, data treatment is performed in a command-line fashion using a freely available software. Advantages of multivariate calibration models over univariate ones are made clear, and the performance of the CLS and SE methods is compared based on the root-mean-square error

Assessment of chosen GRACE-related gravity models based on the GOCE satellite precise science orbit

Eight selected geopotential models obtained through the International Center for Global Earth Models were used in the dynamic orbit determination process of the satellite of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission. For the estimation of various GOCE orbital arc variants, the following gravity models were taken into account: HUST-GRACE2016S, ITU_GRACE16, ITSG-GRACE2014S, ITSG-GRACE2014K, TONGJI-GRACE01, EIGEN-51C, EIGEN5S, EGM2008. The official kinematic and reduced-dynamic precise science orbit (PSO) of the GOCE satellite received via the European Space Agency was adopted as the reference orbit. Cartesian coordinates of the GOCE satellite in this orbit were treated as pseudo-observations in the estimation process using the classical least-squares method. The estimated orbital arcs were fitted to the corresponding arcs of the reference orbit. This allowed the values of 3D root-mean-square (RMS) of the distance between the estimated and reference arcs to be computed. The averages for these 3D RMS values, computed for ten and fifty orbital arcs, made it possible to compare the orbital performance of selected gravity models. Additionally, the fit to both types of the GOCE PSO, i.e., the kinematic orbit and the reduced-dynamic orbit made it possible to compare their quality. Investigation of the gravity model performance was also the opportunity to describe the effectiveness of dynamic orbit determination solutions, depending on the estimated arc lengths, type of reference orbit and the use (or not) of the background models.

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)

Photoacoustic spectroscopy with mica and graphene micro-mechanical levers for multicomponent analysis of acetic acid, acetone and methanol mixture

Multilayer graphene and mica cantilevers as part of an optical microphone in combination with CO2 laser emitting in the range of 9–11 μm were employed in a multicomponent analysis of a mixture of acetone, acetic acid and methanol by photoacoustic spectroscopy. Using these elements, the detection limits of mica circle cantilever were 0.54, 0.80 and 24.8 ppm for acetic acid, methanol and acetone, respectively; these limits were approximately 5 times lower than the detection limit of the highest-class microphone used in this study. The multicomponent analysis was performed using five selected CO2 laser lines and a classical method of least squares. Despite the inaccuracies of our system, very good agreement between the concentration of acetic acid calculated from the photoacoustic signal and from weighing of concentration standards (~3%) was found when measuring the signal in a 10:1:1 mixture of acetone:acetic acid:methanol at five selected laser lines. The absorption coefficient of acetic acid at 10.24 μm was almost 500 times higher than that of acetone, which showed the good ability of this method to detect acetic acid in a high background of acetone, which can be beneficial in the medical analysis of breath.

Least-Squares Method in the Theory of Matrix Differential-Algebraic Boundary-Value Problems

We use the scheme of the classical least-squares method for the construction of approximate pseudosolutions of a linear matrix boundary-value problem for a system of differential-algebraic equations.

Application of Bayesian analysis to the doubly labelled water method for total energy expenditure in humans.

RationaleThe doubly labelled water (DLW) method is the reference method for the estimation of free‐living total energy expenditure (TEE). In this method, where both 2H and 18O are employed, different approaches have been adopted to deal with the non‐conformity observed regarding the distribution space for the labels being non‐coincident with total body water. However, the method adopted can have a significant effect on the estimated TEE.MethodsWe proposed a Bayesian reasoning approach to modify an assumed prior distribution for the space ratio using experimental data to derive the TEE. A Bayesian hierarchical approach was also investigated. The dataset was obtained from 59 adults (37 women) who underwent a DLW experiment during which the 2H and 18O enrichments were measured using isotope ratio mass spectrometry (IRMS).ResultsTEE was estimated at 9925 (9106‐11236) [median and interquartile range], 9646 (9167–10540), and 9,638 (9220–10340) kJ·day−1 for women and at 13961 (12851–15347), 13353 (12651–15088) and 13211 (12653–14238) kJ·day−1 for men, using normalized non‐Bayesian, independent Bayesian and hierarchical Bayesian approaches, respectively. A comparison of hierarchical Bayesian with normalized non‐Bayesian methods indicated a marked difference in behaviour between genders. The median difference was −287 kJ·day−1 for women, and −750 kJ·day−1 for men. In men there is an appreciable compression of the TEE distribution obtained from the hierarchical model compared with the normalized non‐Bayesian methods (range of TEE 11234–15431 kJ·day−1 vs 10786–18221 kJ·day−1). An analogous, yet smaller, compression is seen in women (7081–12287 kJ·day−1 vs 6989–13775 kJ·day−1).ConclusionsThe Bayesian analysis is an appealing method to estimate TEE during DLW experiments. The principal advantages over those obtained using the classical least‐squares method is the generation of potentially more useful estimates of TEE, and improved handling of outliers and missing data scenarios, particularly if a hierarchical model is used.

Earth orientation parameters from VLBI determined with a Kalman filter

This paper introduces the reader to our Kalman filter developed for geodetic VLBI (very long baseline interferometry) data analysis. The focus lies on the EOP (Earth Orientation Parameter) determination based on the Continuous VLBI Campaign 2014 (CONT14) data, but also earlier CONT campaigns are analyzed. For validation and comparison purposes we use EOP determined with the classical LSM (least squares method) estimated from the same VLBI data set as the Kalman solution with a daily resolution. To gain higher resolved EOP from LSM we run solutions which yield hourly estimates for polar motion and dUT1 = Universal Time (UT1) – Coordinated Universal Time (UTC). As an external validation data set we use a GPS (Global Positioning System) solution providing hourly polar motion results.Further, we describe our approach for determining the noise driving the Kalman filter. It has to be chosen carefully, since it can lead to a significant degradation of the results. We illustrate this issue in context with the de-correlation of polar motion and nutation.Finally, we find that the agreement with respect to GPS can be improved by up to 50% using our filter compared to the LSM approach, reaching a similar precision than the GPS solution. Especially the power of erroneous high-frequency signals can be reduced dramatically, opening up new possibilities for high-frequency EOP studies and investigations of the models involved in VLBI data analysis.We prove that the Kalman filter is more than on par with the classical least squares method and that it is a valuable alternative, especially on the advent of the VLBI2010 Global Observing System and within the GGOS frame work.