Loading Matrix Research Articles

Finite element simulation of the effect of particle shape and thermal residual stress on the tensile properties of NbCp/Fe composites

To optimize the microstructure and properties of NbCp/Fe composites, this study considered factors such as load transfer, plastic strain, matrix damage, and interface debonding. A two-dimensional finite element model was constructed using ABAQUS software. Random adsorption algorithm was used to realize the random distribution of particles within the representative volume element, and interface damage was described using a cohesive zone model. The effects of particle shape and thermal residual stress on the tensile properties of NbCp/Fe composites were investigated. The results show that circular particles uniformly distribute the stress during the tensile process, effectively enhancing the tensile properties of the composites. Conversely, triangular particles, with obvious sharp corners, reduce their tensile properties, particularly in the presence of thermal residual stresses, which further aggravates the stress concentration between the particles and the matrix. This leads to a decrease in the strength and toughness of the material.

Selecting the number of factors in approximate factor models using group variable regularization

. We propose a novel method for the estimation of the number of factors in approximate factor models. The model is based on a penalized maximum likelihood approach incorporating an adaptive hierarchical lasso penalty function that enables setting entire columns of the factor loadings matrix to zero, which corresponds to removing uninformative factors. Additionally, the model is capable of estimating weak factors by allowing for sparsity in the non zero columns. We prove that the proposed estimator consistently estimates the true number of factors. Simulation experiments reveal superior selection accuracies for our method in finite samples over existing approaches, especially for data with cross-sectional and serial correlations. In an empirical application on a large macroeconomic dataset, we show that the mean squared forecast errors of an approximate factor model are lower if the number of included factors is selected by our method.

Structured prior distributions for the covariance matrix in latent factor models

Factor models are widely used for dimension reduction in the analysis of multivariate data. This is achieved through decomposition of a p×p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p \ imes p$$\\end{document} covariance matrix into the sum of two components. Through a latent factor representation, they can be interpreted as a diagonal matrix of idiosyncratic variances and a shared variation matrix, that is, the product of a p×k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p \ imes k$$\\end{document} factor loadings matrix and its transpose. If k≪p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k \\ll p$$\\end{document}, this defines a parsimonious factorisation of the covariance matrix. Historically, little attention has been paid to incorporating prior information in Bayesian analyses using factor models where, at best, the prior for the factor loadings is order invariant. In this work, a class of structured priors is developed that can encode ideas of dependence structure about the shared variation matrix. The construction allows data-informed shrinkage towards sensible parametric structures while also facilitating inference over the number of factors. Using an unconstrained reparameterisation of stationary vector autoregressions, the methodology is extended to stationary dynamic factor models. For computational inference, parameter-expanded Markov chain Monte Carlo samplers are proposed, including an efficient adaptive Gibbs sampler. Two substantive applications showcase the scope of the methodology and its inferential benefits.

Assessment of cumulative incidences of mung bean crop production in lowlands of south Ethiopia through multiple factor analysis

Ethiopian farmers face a combination of risks in agricultural production during a single crop season. However, cumulative incidence assessment of the risks in the agriculture was not researched. Thus, this study aimed at assessing the cumulative incidence components in the production of the mung bean crop in the lowlands of South Ethiopia. A cross-sectional study was used with 384 mung bean farmers selected from lowlands of Gamo, Gofa and Wolaita zones. Thirteen original risk types were used to be categorized into a few factors through multiple factor analysis. Factor analysis identified latent variables with an Eigenvalues greater than one. The economic risk factor, the climate-related risk factor, and the systematic risk factor were the first three factors that explain 92.87 % of the inertia cumulatively. The rotated factor loading matrix indicated that under factor one, the encountered risks are an increase in the price of inputs, an increase in the price of food, and financial incidence, which accounted 50 % of the total variance. Under factor two extended dry spells, crop diseases, and wild animals’ damage and livestock diseases and deaths variables that accounted for 23.24 % of the total variance. The risk types categorized under systematic risks were social risks and political risks that accounted for 19.61 % of the total variance of risks encountered by mung bean farmers in the study area. Therefore, disentangling systematic risks is important by providing much-needed information to mung bean farmers and policymakers regarding systematic risk management priorities.

Research on cable dynamic response of a catenary anchor leg mooring system based on ANCF

This paper presents a dynamic analysis model for a catenary anchor leg mooring (CALM) system based on the absolute nodal coordinate formulation (ANCF) method, combined with continuum mechanics and finite element theory. This model uses absolute slope coordinates instead of traditional angle coordinates to better describe the large deformation and large displacement of the cables. The paper derives the element mass matrix, generalized stiffness matrix, and the element external load matrix, including the Morison force transformed into the ANCF framework, based on the virtual work principle. The accuracy and reliability of the ANCF program are validated using static and dynamic beam models, as well as submerged tether models. Furthermore, a comparative analysis of the ANCF mooring cable model with OpenFAST and MoorDyn accentuates the program's practical value in real engineering applications. Finally, we systematically analyzed the dynamic characteristics of a CALM single-point mooring system, revealing that the mooring forces in the cables significantly influence the high-frequency motion of the buoy. Additionally, the reduction in the length of the mooring cables, to an appropriate extent, enhances the stability of the system, which further attests to the effectiveness and practicality of the ANCF model that has been developed.

UV-A assisted catalytic wet peroxide oxidation: Activity of iron minerals in the degradation of DEET

The widespread use of insect repellent N,N’-diethyltoluamide (DEET), along with its low biodegradability, has made this an ubiquitous contaminant in waterbodies. This work explores the elimination of DEET (10 mg/L) in aqueous matrices employing natural iron minerals ilmenite (FeTiO3), hematite (Fe2O3), goethite (Fe(OOH)) and magnetite (Fe3O4) as low-cost catalysts in UV-assisted Catalytic Wet Peroxide Oxidation, using UV-A LEDs (λ: 395 nm) as radiation source in a 500 mL useful-volume reactor. Under the studied conditions, magnetite presented a higher activity, significantly superior to that of the other minerals. A parametric study evaluating the effect of the catalyst load, initial pH, H2O2 dose, UV irradiance and water matrix was performed. Magnetite is able to carry out DEET degradation working at circumneutral pH (pH: 5) with outstanding results in terms of DEET removal even in complex matrices such as river water and WWTP effluent. Furthermore, the catalyst presented an excellent stability. Still, under the optimal operating conditions of this study ([Fe3O4]: 500 mg/L, [H2O2]0: 61.1 mg/L, pH0: 5, T: 25ºC, t: 120 min), only 27.8% mineralization was reached in ultrapure water. Nonetheless, the remaining organic compounds are mainly short-chain organic acids (malonic, oxalic, acetic and formic acids), which account for 98.7% of the residual organic carbon. These compounds, which are readily biodegradable, present a lower phytotoxicity than that of DEET, demonstrating the potential of UV-CWPO for the elimination of this emerging contaminant.

A new factor analysis model for factors obeying a Gamma distribution

The traditional factor analysis model assumes that the factors obey a normal distribution, which is not appropriate in fields whose data are nonnegative. For this kind of problem, we construct a more practical factor model, assuming that the factors obey a Gamma distribution. We develop a new factor analysis model and discuss its true loading matrix. Then we study its parameter estimation with the maximum likelihood estimation (MLE) method based on an Expectation-Maximization (EM) algorithm, where step E is realized by the Metropolis-Hastings (M-H) algorithm in the Markov Chain Monte Carlo (MCMC) method. We use the new model to empirically study real data, and evaluate its information extraction ability, using the defined true loading matrix to calculate the true loading of the factor. We compare the new model and traditional factor analysis models on simulated and real data, respectively, whose results show that the new model has better information extraction ability for nonnegative data when the number of factors is the same.

Degradation of the cytostatic drug bicalutamide by photo-assisted catalytic wet peroxide oxidation

The presence of cytostatic drugs, such as bicalutamide (BICA), in aquatic compartments reveals the necessity of developing efficient processes for their elimination in wastewater treatment plants (WWTP). This work explores for the first time the use of natural magnetite as a low-cost catalyst in the photo assisted — catalytic wet peroxide oxidation (UV-CWPO) of BICA. For this purpose, real WWTP secondary effluents were spiked with 100 μg/L BICA and subjected to UV-CWPO. Preliminary runs comparing UV photolysis, UV/H2O2, CWPO and UV-CWPO confirmed the synergistic effect of UV radiation and the CWPO process employing magnetite. Afterwards, a parametric study was performed evaluating the influence of the pH, catalyst load, H2O2 dosage, temperature and water matrix. Under optimum operating conditions (pH 0: 6, [magnetite]: 375 mg/L and [H2O2]: 75 mg/L), 99.7 % BICA degradation and 60.7 % mineralization were reached after 30 min in WWTP effluent. UV-CWPO also proved to be effective in hospital wastewater. Catalyst activity was studied in 5 consecutive runs, showing great stability for both BICA removal and TOC elimination. Finally, phytotoxicity tests revealed a lower toxicity in the UV-CWPO effluent compared to the untreated stream. Hence, UV-CWPO proved to be a feasible to eliminate risky cytostatic drugs in relevant environmental matrices.

Identification of Bletilla striata and related decoction pieces: a data fusion method combining electronic nose, electronic tongue, electronic eye, and high-performance liquid chromatography data.

Introduction: We here describe a new method for distinguishing authentic Bletilla striata from similar decoctions (namely, Gastrodia elata, Polygonatum odoratum, and Bletilla ochracea schltr). Methods: Preliminary identification and analysis of four types of decoction pieces were conducted following the Chinese Pharmacopoeia and local standards. Intelligent sensory data were then collected using an electronic nose, an electronic tongue, and an electronic eye, and chromatography data were obtained via high-performance liquid chromatography (HPLC). Partial least squares discriminant analysis (PLS-DA), support vector machines (SVM), and back propagation neural network (BP-NN) models were built using each set of single-source data for authenticity identification (binary classification of B. striata vs. other samples) and for species determination (multi-class sample identification). Features were extracted from all datasets using an unsupervised approach [principal component analysis (PCA)] and a supervised approach (PLS-DA). Mid-level data fusion was then used to combine features from the four datasets and the effects of feature extraction methods on model performance were compared. Results and Discussion: Gas chromatography-ion mobility spectrometry (GC-IMS) showed significant differences in the types and abundances of volatile organic compounds between the four sample types. In authenticity determination, the PLS-DA and SVM models based on fused latent variables (LVs) performed the best, with 100% accuracy in both the calibration and validation sets. In species identification, the PLS-DA model built with fused principal components (PCs) or fused LVs had the best performance, with 100% accuracy in the calibration set and just one misclassification in the validation set. In the PLS-DA and SVM authenticity identification models, fused LVs performed better than fused PCs. Model analysis was used to identify PCs that strongly contributed to accurate sample classification, and a PC factor loading matrix was used to assess the correlation between PCs and the original variables. This study serves as a reference for future efforts to accurately evaluate the quality of Chinese medicine decoction pieces, promoting medicinal formulation safety.

A GLM-based zero-inflated generalized Poisson factor model for analyzing microbiome data.

High-throughput sequencing technology facilitates the quantitative analysis of microbial communities, improving the capacity to investigate the associations between the human microbiome and diseases. Our primary motivating application is to explore the association between gut microbes and obesity. The complex characteristics of microbiome data, including high dimensionality, zero inflation, and over-dispersion, pose new statistical challenges for downstream analysis. We propose a GLM-based zero-inflated generalized Poisson factor analysis (GZIGPFA) model to analyze microbiome data with complex characteristics. The GZIGPFA model is based on a zero-inflated generalized Poisson (ZIGP) distribution for modeling microbiome count data. A link function between the generalized Poisson rate and the probability of excess zeros is established within the generalized linear model (GLM) framework. The latent parameters of the GZIGPFA model constitute a low-rank matrix comprising a low-dimensional score matrix and a loading matrix. An alternating maximum likelihood algorithm is employed to estimate the unknown parameters, and cross-validation is utilized to determine the rank of the model in this study. The proposed GZIGPFA model demonstrates superior performance and advantages through comprehensive simulation studies and real data applications.

PREPARATION AND FLAME RETARDANT APPLICATION OF CLAY POLYURETHANE NANOCOMPOSITES

In recent years, clay-based organic thermosetting polyurethane polymer nanocomposites have more attracted attention in academia and industries because they exhibit different properties from conventional materials. In this study, we investigated novel thermoplastic Polyurethane (TPU) by adding nanoparticles of clay as a fire-retardant property. By employing an in-situ polymerization technique with a 2:1 ratio of tolylene 2,4-diisocyanate (TPI) and polyethylene glycol (PEG2000), the NCO terminated TPU prepolymer was created. Cloisite 25A (C25A), an organo-modified montmorillonite clay, was utilized to provide sufficient compatibility with the PEG/TPI matrix. The synthesized nanocomposite was examined using thermogravimetric analysis (TGA), SEM analysis, and X-ray diffraction (XRD). FTIR analysis provides information on functional groups. Compared to pure polyurethane, the nanocomposites showed superior thermal stabilities, as determined by thermogravimetric analysis (TGA). The results from X-ray diffraction and Scanning Electron Microscopy confirm the successful formation of an exfoliated polymer clay nanocomposite under all conditions, evidenced by the absence of the distinct peak (2θ = 4.79º) corresponding to the d-spacing of the organoclay. The relationship between clay loading and TPU matrix type and the mechanical characteristics of nanocomposites was examined. As the amount of clay in the Young's TPU/Cl25A nanocomposites grew, so did their tensile strength and modulus. The fire-retardant experiment was studied by a cone colorimeter. There have been notable advancements in the fire-retardant qualities, including smoke, CO output, and heat release rate. Comparing polyurethane integrated with 5-weight percent organoclay to ordinary polyurethane polymer, a noteworthy 53% reduction was observed.

Factor-augmented Model for Functional Data

We propose modeling raw functional data as a mixture of a smooth function and a high-dimensional factor component. The conventional approach to retrieving the smooth function from the raw data is through various smoothing techniques. However, the smoothing model is inadequate to recover the smooth curve or capture the data variation in some situations. These include cases where there is a large amount of measurement error, the smoothing basis functions are incorrectly identified, or the step jumps in the functional mean levels are neglected. A factor-augmented smoothing model is proposed to address these challenges, and an iterative numerical estimation approach is implemented in practice. Including the factor model component in the proposed method solves the aforementioned problems since a few common factors often drive the variation that cannot be captured by the smoothing model. Asymptotic theorems are also established to demonstrate the effects of including factor structures on the smoothing results. Specifically, we show that the smoothing coefficients projected on the complement space of the factor loading matrix are asymptotically normal. As a byproduct of independent interest, an estimator for the population covariance matrix of the raw data is presented based on the proposed model. Extensive simulation studies illustrate that these factor adjustments are essential in improving estimation accuracy and avoiding the curse of dimensionality. The superiority of our model is also shown in modeling Australian temperature data.

인자의 불확정성을 반영한 인자점수 추출 및 인자점수 회귀모형에의 응용

Factor analysis is a multivariate analysis method widely used to extract latent factors from high dimensional data and interpret multidimensional data through dimension reduction. Additionally, factor scores of individual observations for the extracted factors are calculated and used in a subsequent regression analysis. This factor model has the characteristics of parameter indeterminacy which means parameters such as the factor loading matrix or unique variance are not uniquely determined, and factor indeterminacy which represents that latent factors are not uniquely determined even in situations where the parameters of the factor model are determined. In this paper, we examine the indeterminacy of factor scores and propose a new method of calculating factor scores that maximize the correlation coefficient between a response variable and a factor in a factor score regression model. Simulations and real data analysis were conducted to compare the existing factor scores using the regression method and the proposed factor scores utilizing the indeterminate part of factors in factor score regression setting. As a result of data analysis, it was confirmed that the estimation accuracy of regression model was higher when using the proposed factor scores.

A method to evaluate the rank condition for CCE estimators

We develop a binary classifier to evaluate whether the rank condition (RC) is satisfied or not for the Common Correlated Effects (CCE) estimator. The RC postulates that the number of unobserved factors, m, is not larger than the rank of the unobserved matrix of average factor loadings, ϱ. When this condition fails, the CCE estimator is inconsistent, in general. Despite its importance, to date this rank condition could not be verified. The difficulty lies in the fact that factor loadings are unobserved, such that ϱ cannot be directly determined. The key insight in this article is that ϱ can be consistently estimated with existing techniques through the matrix of cross-sectional averages of the data. Similarly, m can be estimated consistently from the data using existing methods. Thus, a binary classifier, constructed by comparing estimates of m and ϱ, correctly determines whether the RC is satisfied or not as . We illustrate the practical relevance of testing the RC by studying the effect of the Dodd-Frank Act on bank profitability. The RC classifier reveals that the rank condition fails for a subperiod of the sample, in which case the estimated effect of bank size on profitability appears to be biased upwards.

Influence Line Identification Method Based on VMD Combined with Improved Wavelet Threshold Denoising

The influence line of bridge can reflect the performance of the bridge under the moving vehicle load. It has a wide range of applications in structural damage detection, performance evaluation, model correction and bridge weigh-in-motion. Fast moving vehicles will cause the dynamic effect of the bridge, resulting in the change of the bridge response curve and the difficulty of identifying the influence line. In this paper, an influence line identification method based on variational mode decomposition (VMD) combined with improved wavelet threshold denoising is proposed. Firstly, the mathematical model of influence line identification is established based on vehicle load matrix and bridge response. Then, VMD combined with improved wavelet threshold denoising method is used to eliminate dynamic fluctuation effect and noise. Finally, the elastic net penalty term is introduced in the influence line identification problem, and the B-spline basis function is used to reconstruct the influence line. In order to verify the effectiveness of the proposed method, a vehicle-bridge coupling model is established for numerical calculation, and the identification of bridge displacement influence lines under different conditions such as vehicle speed, noise level, road roughness and vehicle weight is investigated. The results show that the proposed method can effectively eliminate the dynamic fluctuation components and noise of the bridge response. In the case of good road roughness, the influence line can still be accurately identified when the vehicle speed reaches 15 m/s.

Performance of Principal Components Estimation Method on the Quality of Factor Analysis without and with Varimax Rotation

The objective of this work was to evaluate the performance of the principal components estimation method on the quality of estimates of some parameters of exploratory factor analysis (EFA), without and with varimax rotation. To this end, 18 parametric correlation matrices (r) were imposed. These matrices were obtained from combinations between six different values of parametric communalities of four normally distributed random variables with three different proportions of distances between the parametric factorial loadings of the first two orthogonal factors. For each matrix r, the following parameters were defined: the first two eigenvalues (l1 and l2), the matrix of factor loadings (G), the four communalities () and the matrix of the specific factors (Y). After the 36 factor analyses, the respective estimates of these parameters were obtained, and their respective absolute deviations between the estimates obtained a posteriori and the parameters known a priori were evaluated. With the results of the Student's t test at 5% significance applied to the response surface analysis, it was concluded that the principal components estimation method for estimating orthogonal factors was not adequate and the varimax rotation improved relatively little the quality of the SFA estimates.

Live load matrix recovery from scattering data in linear elasticity

Live load matrix recovery from scattering data in linear elasticity

Robust oblique Target-rotation for small samples

IntroductionOblique Target-rotation in the context of exploratory factor analysis is a relevant method for the investigation of the oblique simple structure. It was argued that minimizing single cross-loadings by means of target rotation may lead to large effects of sampling error on the target rotated factor solutions.MethodIn order to minimize effects of sampling error on results of Target-rotation we propose to compute the mean cross-loadings for each block of salient loadings of the independent clusters model and to perform Target-rotation for the block-wise mean cross-loadings. The resulting transformation-matrix is than applied to the complete unrotated loading matrix in order to produce mean Target-rotated factors.ResultsA simulation study based on correlated independent clusters model and zero-mean cross-loading models revealed that mean oblique Target-rotation resulted in smaller bias of factor inter-correlations than conventional Target-rotation based on single loadings, especially when sample size was small and when the number of factors was large. An empirical example revealed that the similarity of Target-rotated factors computed for small subsamples with Target-rotated factors of the total sample was more pronounced for mean Target-rotation than for conventional Target-rotation.DiscussionMean Target-rotation can be recommended in the context of oblique factor models based on simple structure, especially for small samples. An R-script and an SPSS-script for this form of Target-rotation are provided in the Supplementary Material.

The Application of Statistical Analysis Method in the Effectiveness Evaluation of Ideological and Political Reform in the Course of Human Resource Management

Abstract Based on the student-oriented teaching practice in the ideological and political reform of the Human Resource Management course, this paper established a teaching evaluation index system with four dimensions: teaching context, teaching input, teaching process and teaching product. Kehlenbach alpha coefficient and split-half reliability were utilized to test the reliability of indicators, and expert validity and content validity were adopted to examine the validity of indicators. Multivariate statistical analysis was used for principal component analysis and factor load matrix estimation to construct a comprehensive evaluation based on principal component analysis and an educational evaluation based on the factor analysis method.

Synergistic effect of combined blast loads on UHMWPE fiber mesh reinforced polyurea composites

UHMWPE fiber mesh reinforced polyurea (UFRP) composites are a proposed improvement method that involves incorporating UHMWPE fiber mesh into polyurea coating. Experiments and theoretical analysis were conducted to examine the failure and blast resistance performance of the UFRP under combined air-blast and fragments. The mechanism of UFRP composite failure, the self-healing effect, and counterintuitive behaviors were identified and investigated. Fiber mesh improved structural strength and stopped fracture development, while polyurea increased ductility and protected against blast fragment dispersion. The addition of UHMWPE fiber mesh improved the polyurea matrix's load transmission, integrity, and fracture resistance, and it can even altered the material's failure mode from shear punching to tensile. The loose and elastic filler was generated as polyurea melted in the impact hole as a result of the thermal effect of the impact process and the dynamic action of the penetration of the fragments. The joint load was classified into three categories based on the space-time connection of the loads, the loading duration, and the structure's reaction mechanism. The synergistic effect of the combined loading on the composite plates was evaluated, and an analytical model was developed to examine the occurrence. Synergy is contingent upon not just the reaching moment and duration of the loads, but also the reaction of the structures.