Search results for: eigenvalues eigenvectors

Authors: Humayun R. H. Kabir

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An analytical solution before used for static and free-vibration response has been extended for thermal buckling response on cylindrical panel with anti-symmetric laminations. The partial differential equations that govern kinematic behavior of shells produce five coupled differential equations. The basic displacement and rotational unknowns are similar to first order shear deformation theory---three displacement in spatial space, and two rotations about in-plane axes. No drilling degree of freedom is considered. Boundary conditions are considered as complete hinge in all edges so that the panel respond on thermal inductions. Two sets of double Fourier series are considered in the analytical solution process. The sets are selected that satisfy mixed type of natural boundary conditions. Numerical results are presented for the first 10 eigenvalues, and first 10 mode shapes for Ux, Uy, and Uz components. The numerical results are compared with a finite element based solution.

Keywords: higher order shear deformation, composite, thermal buckling, angle-ply laminations

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Authors: O. P. Popoola, O. A. Alawode, M. O. Olayiwola, A. M. Oladele

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This research work is based on using discriminant analysis to forecast crime rate in Nigeria between 1996 and 2008. The work is interested in how gender (male and female) relates to offences committed against the government, against other properties, disturbance in public places, murder/robbery offences and other offences. The data used was collected from the National Bureau of Statistics (NBS). SPSS, the statistical package was used to analyse the data. Time plot was plotted on all the 29 offences gotten from the raw data. Eigenvalues and Multivariate tests, Wilks’ Lambda, standardized canonical discriminant function coefficients and the predicted classifications were estimated. The research shows that the distribution of the scores from each function is standardized to have a mean O and a standard deviation of 1. The magnitudes of the coefficients indicate how strongly the discriminating variable affects the score. In the predicted group membership, 172 cases that were predicted to commit crime against Government group, 66 were correctly predicted and 106 were incorrectly predicted. After going through the predicted classifications, we found out that most groups numbers that were correctly predicted were less than those that were incorrectly predicted.

Keywords: discriminant analysis, DA, multivariate analysis of variance, MANOVA, canonical correlation, and Wilks’ Lambda

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Authors: Mehrnaz Alibeikloo, Hadi Khabbaz, Behzad Fatahi

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The spectral random field method is one of the widely used methods to obtain more reliable and accurate results in geotechnical problems involving material variability. Karhunen-Loeve (K-L) expansion method was applied to perform random field discretization of cross-correlated creep parameters. Karhunen-Loeve expansion method is based on eigenfunctions and eigenvalues of covariance function adopting Kernel integral solution. In this paper, the accuracy of Karhunen-Loeve expansion was investigated to predict long-term settlement of soft soils adopting elastic visco-plastic creep model. For this purpose, a parametric study was carried to evaluate the effect of K-L expansion terms and spatial correlation length on the reliability of results. The results indicate that small values of spatial correlation length require more K-L expansion terms. Moreover, by increasing spatial correlation length, the coefficient of variation (COV) of creep settlement increases, confirming more conservative and safer prediction.

Keywords: Karhunen-Loeve expansion, long-term settlement, reliability analysis, spatial correlation length

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Authors: Nancy Ibrahim Abdalla, Abdelaziz Karamalla Gaiballa

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Rangelands in semi-arid areas provide a good source for feeding huge numbers of animals and serving environmental, economic and social importance; therefore, these areas are considered economically very important for the pastoral sector in Sudan. This paper investigates the means of differentiating between different rangelands sites according to soil types using principal component analysis to assist in monitoring and assessment purposes. Three rangeland sites were identified in the study area as flat sandy sites, sand dune site, and hard clay site. Principal component analysis (PCA) was used to reduce the number of factors needed to distinguish between rangeland sites and produce a new set of data including the most useful spectral information to run satellite image processing. It was performed using selected types of data (two vegetation indices, topographic data and vegetation surface reflectance within the three bands of MODIS data). Analysis with PCA indicated that there is a relatively high correspondence between vegetation and soil of the total variance in the data set. The results showed that the use of the principal component analysis (PCA) with the selected variables showed a high difference, reflected in the variance and eigenvalues and it can be used for differentiation between different range sites.

Keywords: principal component analysis, PCA, rangeland sites, semi-arid areas, soil types

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Authors: Arka Roy, Chandra Prakash Dubey

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Inverse problem generally used for recovering hidden information from outside available data. Vertical component of gravity field we will be going to use for underneath density structure calculation. Ill-posing nature is main obstacle for any inverse problem. Linear regularization using Tikhonov formulation are used for appropriate choice of SVD and GSVD components. For real time data handle, signal to noise ratios should have to be less for reliable solution. In our study, 2D and 3D synthetic model with rectangular grid are used for gravity field calculation and its corresponding inversion for density reconstruction. Fine grid also we have considered to hold any irregular structure. Keeping in mind of algebraic ambiguity factor number of observation point should be more than that of number of data point. Picard plot is represented here for choosing appropriate or main controlling Eigenvalues for a regularized solution. Another important study is depth resolution plot (DRP). DRP are generally used for studying how the inversion is influenced by regularizing or discretizing. Our further study involves real time gravity data inversion of Vredeforte Dome South Africa. We apply our method to this data. The results include density structure is in good agreement with known formation in that region, which puts an additional support of our method.

Keywords: depth resolution plot, gravity inversion, Picard plot, SVD, Tikhonov formulation

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Authors: Behnaz Moradijamei, Michael Higgins

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Identifying community structure is a critical task in analyzing social media data sets often modeled by networks. Statistical models such as the stochastic block model have proven to explain the structure of communities in real-world network data. In this work, we develop a goodness-of-fit test to examine community structure's existence by using a distinguishing property in networks: cyclic structures are more prevalent within communities than across them. To better understand how communities are shaped by the cyclic structure of the network rather than just the number of edges, we introduce a novel method for deciding on the existence of communities. We utilize these structures by using renewal non-backtracking random walk (RNBRW) to the existing goodness-of-fit test. RNBRW is an important variant of random walk in which the walk is prohibited from returning back to a node in exactly two steps and terminates and restarts once it completes a cycle. We investigate the use of RNBRW to improve the performance of existing goodness-of-fit tests for community detection algorithms based on the spectral properties of the adjacency matrix. Our proposed test on community structure is based on the probability distribution of eigenvalues of the normalized retracing probability matrix derived by RNBRW. We attempt to make the best use of asymptotic results on such a distribution when there is no community structure, i.e., asymptotic distribution under the null hypothesis. Moreover, we provide a theoretical foundation for our statistic by obtaining the true mean and a tight lower bound for RNBRW edge weights variance.

Keywords: hypothesis testing, RNBRW, network inference, community structure

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Authors: Naser B. Almari, Salem S. Alghamdi, Muhammad Afzal, Mohamed Helmy El Shal

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Wheat landraces are a rich genetic resource for boosting agronomic qualities in breeding programs while also providing diversity and unique adaptation to local environmental conditions. These genotypes have grown increasingly important in the face of recent climate change challenges. This research aimed to look at the genetic diversity of Saudi Durum wheat landraces using morpho-phenological and molecular data. The principal components analysis (PCA) analysis recorded 78.47 % variance and 1.064 eigenvalues for the first six PCs of the total, respectively. The significant characters contributed more to the diversity are the length of owns at the tip relative to the length of the ear, culm: glaucosity of the neck, flag leaf: glaucosity of the sheath, flag leaf: anthocyanin coloration of auricles, plant: frequency of plants with recurved flag leaves, ear: length, and ear: shape in profile in the PC1. The significant wheat genotypes contributed more in the PC1 (8, 14, 497, 650, 569, 590, 594, 598, 600, 601, and 604). The cluster analysis recorded an 85.42 cophenetic correlation among the 22 wheat genotypes and grouped the genotypes into two main groups. Group, I contain 8 genotypes, however, the 2nd group contains 12 wheat genotypes, while two genotypes (13 and 497) are standing alone in the dendrogram and unable to make a group with any one of the genotypes. The second group was subdivided into two subgroups. The genotypes (14, 602, and 600) were present in the second sub-group. The genotypes were grouped into two main groups. The first group contains 17 genotypes, while the second group contains 3 (8, 977, and 594) wheat genotypes. The genotype (602) was standing alone and unable to make a group with any wheat genotype. The genotypes 650 and 13 also stand alone in the first group. Using the Mantel test, the data recorded a significant (R2 = 0.0006) correlation (phenotypic and genetic) among 22 wheat durum genotypes.

Keywords: durum wheat, PCA, cluster analysis, SRAP, genetic diversity

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Authors: H. Jung, N. Kim, B. Kang, J. Choe

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History matching is a crucial procedure for predicting reservoir performances and making future decisions. However, it is difficult due to uncertainties of initial reservoir models. Therefore, it is important to have reliable initial models for successful history matching of highly heterogeneous reservoirs such as channel reservoirs. In this paper, we proposed a novel scheme for regenerating geological models using support vector machine (SVM) and principal component analysis (PCA). First, we perform PCA for figuring out main geological characteristics of models. Through the procedure, permeability values of each model are transformed to new parameters by principal components, which have eigenvalues of large magnitude. Secondly, the parameters are projected into two-dimensional plane by multi-dimensional scaling (MDS) based on Euclidean distances. Finally, we train an SVM classifier using 20% models which show the most similar or dissimilar well oil production rates (WOPR) with the true values (10% for each). Then, the other 80% models are classified by trained SVM. We select models on side of low WOPR errors. One hundred channel reservoir models are initially generated by single normal equation simulation. By repeating the classification process, we can select models which have similar geological trend with the true reservoir model. The average field of the selected models is utilized as a probability map for regeneration. Newly generated models can preserve correct channel features and exclude wrong geological properties maintaining suitable uncertainty ranges. History matching with the initial models cannot provide trustworthy results. It fails to find out correct geological features of the true model. However, history matching with the regenerated ensemble offers reliable characterization results by figuring out proper channel trend. Furthermore, it gives dependable prediction of future performances with reduced uncertainties. We propose a novel classification scheme which integrates PCA, MDS, and SVM for regenerating reservoir models. The scheme can easily sort out reliable models which have similar channel trend with the reference in lowered dimension space.

Keywords: history matching, principal component analysis, reservoir modelling, support vector machine

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Authors: Mancho Manev

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The concept of almost paracontact Riemannian manifolds (abbr., apcR manifolds) was introduced by I. Sato in 1976 as an analogue of almost contact Riemannian manifolds. The notion of an apcR manifold of type (p,q) was defined by S. Sasaki in 1980, where p and q are respectively the numbers of the multiplicity of the structure eigenvalues 1 and -1. It also has a simple eigenvalue of 0. In our work, we consider (2n+1)-dimensional apcR manifolds of type (n,n), i.e., the paracontact distribution of the studied manifold can be considered as a 2n-dimensional almost paracomplex Riemannian distribution with almost paracomplex structure and structure group O(n) × O(n). The aim of the present study is to introduce a new class of apcR manifolds. Such a manifold is obtained using the construction of a certain Riemannian cone over it, and the resulting manifold is a paraholomorphic paracomplex Riemannian manifold (abbr., phpcR manifold). We call it a para-Sasaki-like Riemannian manifold (abbr., pSlR manifold) and give some explicit examples. We study the structure of pSlR spaces and find that the paracontact form η is closed and each pSlR manifold locally can be considered as a certain product of the real line with a phpcR manifold, which is locally a Riemannian product of two equidimensional Riemannian spaces. We also obtain that the curvature of the pSlR manifolds is completely determined by the curvature of the underlying local phpcR manifold. Moreover, the ξ-directed Ricci curvature is equal to -2n, while in the Sasaki case, it is 2n. Accordingly, the pSlR manifolds can be interpreted as the counterpart of the Sasaki manifolds; the skew-symmetric part of ∇η vanishes, while in the Sasaki case, the symmetric part vanishes. We define a hyperbolic extension of a (complete) phpcR manifold that resembles a certain warped product, and we indicate that it is a (complete) pSlR manifold. In addition, we consider the hyperbolic extension of a phpcR manifold and prove that if the initial manifold is a complete Einstein manifold with negative scalar curvature, then the resulting manifold is a complete Einstein pSlR manifold with negative scalar curvature. In this way, we produce new examples of a complete Einstein Riemannian manifold with negative scalar curvature. Finally, we define and study para contact conformal/homothetic deformations by deriving a subclass that preserves the para-Sasaki-like condition. We then find that if we apply a paracontact homothetic deformation of a pSlR space, we obtain that the Ricci tensor is invariant.

Keywords: almost paracontact Riemannian manifolds, Einstein manifolds, holomorphic product manifold, warped product manifold

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Authors: M. Maier, I. Dedigama, J. Majasan, Y. Wu, Q. Meyer, L. Castanheira, G. Hinds, P. R. Shearing, D. J. L. Brett

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Increasing the efficiency of electrolyser technology is commonly seen as one of the main challenges on the way to the Hydrogen Economy. There is a significant lack of understanding of the different states of operation of polymer electrolyte membrane water electrolysers (PEMWE) and how these influence the overall efficiency. This in particular means the two-phase flow through the membrane, gas diffusion layers (GDL) and flow channels. In order to increase the efficiency of PEMWE and facilitate their spread as commercial hydrogen production technology, new analytic approaches have to be found. Acoustic emission (AE) offers the possibility to analyse the processes within a PEMWE in a non-destructive, fast and cheap in-situ way. This work describes the generation and analysis of AE data coming from a PEM water electrolyser, for, to the best of our knowledge, the first time in literature. Different experiments are carried out. Each experiment is designed so that only specific physical processes occur and AE solely related to one process can be measured. Therefore, a range of experimental conditions is used to induce different flow regimes within flow channels and GDL. The resulting AE data is first separated into different events, which are defined by exceeding the noise threshold. Each acoustic event consists of a number of consequent peaks and ends when the wave diminishes under the noise threshold. For all these acoustic events the following key attributes are extracted: maximum peak amplitude, duration, number of peaks, peaks before the maximum, average intensity of a peak and time till the maximum is reached. Each event is then expressed as a vector containing the normalized values for all criteria. Principal Component Analysis is performed on the resulting data, which orders the criteria by the eigenvalues of their covariance matrix. This can be used as an easy way of determining which criteria convey the most information on the acoustic data. In the following, the data is ordered in the two- or three-dimensional space formed by the most relevant criteria axes. By finding spaces in the two- or three-dimensional space only occupied by acoustic events originating from one of the three experiments it is possible to relate physical processes to certain acoustic patterns. Due to the complex nature of the AE data modern machine learning techniques are needed to recognize these patterns in-situ. Using the AE data produced before allows to train a self-learning algorithm and develop an analytical tool to diagnose different operational states in a PEMWE. Combining this technique with the measurement of polarization curves and electrochemical impedance spectroscopy allows for in-situ optimization and recognition of suboptimal states of operation.

Keywords: acoustic emission, gas diffusion layers, in-situ diagnosis, PEM water electrolyser

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Authors: Getachew Weldemichael, Sentayehu Alamerew, Leta Tulu, Gezahegn Berecha

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Coffee quality improvement program is becoming the focus of coffee research, as the world coffee consumption pattern shifted to high-quality coffee. However, there is limited information on the genetic variation of C. Arabica for quality improvement in potential specialty coffee growing areas of Ethiopia. Therefore, this experiment was conducted with the objectives of determining the magnitude of variation among 105 coffee accessions collected from east Wollega coffee growing areas and assessing correlations between the different coffee qualities attributes. It was conducted in RCRD with three replications. Data on green bean physical characters (shape and make, bean color and odor) and organoleptic cup quality traits (aromatic intensity, aromatic quality, acidity, astringency, bitterness, body, flavor, and overall standard of the liquor) were recorded. Analysis of variance, clustering, genetic divergence, principal component and correlation analysis was performed using SAS software. The result revealed that there were highly significant differences (P<0.01) among the accessions for all quality attributes except for odor and bitterness. Among the tested accessions, EW104 /09, EW101 /09, EW58/09, EW77/09, EW35/09, EW71/09, EW68/09, EW96 /09, EW83/09 and EW72/09 had the highest total coffee quality values (the sum of bean physical and cup quality attributes). These genotypes could serve as a source of genes for green bean physical characters and cup quality improvement in Arabica coffee. Furthermore, cluster analysis grouped the coffee accessions into five clusters with significant inter-cluster distances implying that there is moderate diversity among the accessions and crossing accessions from these divergent inter-clusters would result in hetrosis and recombinants in segregating generations. The principal component analysis revealed that the first three principal components with eigenvalues greater than unity accounted for 83.1% of the total variability due to the variation of nine quality attributes considered for PC analysis, indicating that all quality attributes equally contribute to a grouping of the accessions in different clusters. Organoleptic cup quality attributes showed positive and significant correlations both at the genotypic and phenotypic levels, demonstrating the possibility of simultaneous improvement of the traits. Path coefficient analysis revealed that acidity, flavor, and body had a high positive direct effect on overall cup quality, implying that these traits can be used as indirect criteria to improve overall coffee quality. Therefore, it was concluded that there is considerable variation among the accessions, which need to be properly conserved for future improvement of the coffee quality. However, the variability observed for quality attributes must be further verified using biochemical and molecular analysis.

Keywords: accessions, Coffea arabica, cluster analysis, correlation, principal component

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Authors: Dragan Ribarić

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We employ the so-called problem-dependent linked interpolation concept to develop two cubic 4-node quadrilateral Mindlin plate finite elements with 12 external degrees of freedom. In the problem-independent linked interpolation, the interpolation functions are independent of any problem material parameters and the rotation fields are not expressed in terms of the nodal displacement parameters. On the contrary, in the problem-dependent linked interpolation, the interpolation functions depend on the material parameters and the rotation fields are expressed in terms of the nodal displacement parameters. Two cubic 4-node quadrilateral plate elements are presented, named Q4-U3 and Q4-U3R5. The first one is modelled with one displacement and two rotation degrees of freedom in every of the four element nodes and the second element has five additional internal degrees of freedom to get polynomial completeness of the cubic form and which can be statically condensed within the element. Both elements are able to pass the constant-bending patch test exactly as well as the non-zero constant-shear patch test on the oriented regular mesh geometry in the case of cylindrical bending. In any mesh shape, the elements have the correct rank and only the three eigenvalues, corresponding to the solid body motions are zero. There are no additional spurious zero modes responsible for instability of the finite element models. In comparison with the problem-independent cubic linked interpolation implemented in Q9-U3, the nine-node plate element, significantly less degrees of freedom are employed in the model while retaining the interpolation conformity between adjacent elements. The presented elements are also compared to the existing problem-independent quadratic linked-interpolation element Q4-U2 and to the other known elements that also use the quadratic or the cubic linked interpolation, by testing them on several benchmark examples. Simple functional upgrading from the quadratic to the cubic linked interpolation, implemented in Q4-U3 element, showed no significant improvement compared to the quadratic linked form of the Q4-U2 element. Only when the additional bubble terms are incorporated in the displacement and rotation function fields, which complete the full cubic linked interpolation form, qualitative improvement is fulfilled in the Q4-U3R5 element. Nevertheless, the locking problem exists even for the both presented elements, like in all pure displacement elements when applied to very thin plates modelled by coarse meshes. But good and even slightly better performance can be noticed for the Q4-U3R5 element when compared with elements from the literature, if the model meshes are moderately dense and the plate thickness not extremely thin. In some cases, it is comparable to or even better than Q9-U3 element which has as many as 12 more external degrees of freedom. A significant improvement can be noticed in particular when modeling very skew plates and models with singularities in the stress fields as well as circular plates with distorted meshes.

Keywords: Mindlin plate theory, problem-independent linked interpolation, problem-dependent interpolation, quadrilateral displacement-based plate finite elements

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Authors: Kaleeswari R. K., Seevagan L .

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Soil quality in an agroecosystem is influenced by the cropping system, water and soil fertility management. A valid soil quality index would help to assess the soil and crop management practices for desired productivity and soil health. The soil quality indices also provide an early indication of soil degradation and needy remedial and rehabilitation measures. Imbalanced fertilization and inadequate organic carbon dynamics deteriorate soil quality in an intensive cropping system. The rice soil ecosystem is different from other arable systems since rice is grown under submergence, which requires a different set of key soil attributes for enhancing soil quality and productivity. Assessment of the soil quality index involves indicator selection, indicator scoring and comprehensive score into one index. The most appropriate indicator to evaluate soil quality can be selected by establishing the minimum data set, which can be screened by linear and multiple regression factor analysis and score function. This investigation was carried out in intensive rice cultivating regions (having >1.0 lakh hectares) of Tamil Nadu viz., Thanjavur, Thiruvarur, Nagapattinam, Villupuram, Thiruvannamalai, Cuddalore and Ramanathapuram districts. In each district, intensive rice growing block was identified. In each block, two sampling grids (10 x 10 sq.km) were used with a sampling depth of 10 – 15 cm. Using GIS coordinates, and soil sampling was carried out at various locations in the study area. The number of soil sampling points were 41, 28, 28, 32, 37, 29 and 29 in Thanjavur, Thiruvarur, Nagapattinam, Cuddalore, Villupuram, Thiruvannamalai and Ramanathapuram districts, respectively. Principal Component Analysis is a data reduction tool to select some of the potential indicators. Principal Component is a linear combination of different variables that represents the maximum variance of the dataset. Principal Component that has eigenvalues equal or higher than 1.0 was taken as the minimum data set. Principal Component Analysis was used to select the representative soil quality indicators in rice soils based on factor loading values and contribution percent values. Variables having significant differences within the production system were used for the preparation of the minimum data set. Each Principal Component explained a certain amount of variation (%) in the total dataset. This percentage provided the weight for variables. The final Principal Component Analysis based soil quality equation is SQI = ∑ i=1 (W ᵢ x S ᵢ); where S- score for the subscripted variable; W-weighing factor derived from PCA. Higher index scores meant better soil quality. Soil respiration, Soil available Nitrogen and Potentially Mineralizable Nitrogen were assessed as soil quality indicators in rice soil of the Cauvery Delta zone covering Thanjavur, Thiruvavur and Nagapattinam districts. Soil available phosphorus could be used as a soil quality indicator of rice soils in the Cuddalore district. In rain-fed rice ecosystems of coastal sandy soil, DTPA – Zn could be used as an effective soil quality indicator. Among the soil parameters selected from Principal Component Analysis, Microbial Biomass Nitrogen could be used quality indicator for rice soils of the Villupuram district. Cauvery Delta zone has better SQI as compared with other intensive rice growing zone of Tamil Nadu.

Keywords: soil quality index, soil attributes, soil mapping, and rice soil

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