Sensitivity of Eigen Value to Damage and Its Identification

The reduction in natural frequencies,however small, of a civil engineering structure, is the first and the easiest method of estimating its impending damage. As a first level screening for health-monitoring, information on the frequency reduction of a few fundamentalmodes can be used to estimate the positions and the magnitude of damage in a smeared fashion. The paper presents the Eigen value sensitivity equations, derived from first-order perturbation technique, for typical infra-structural systems like a simply supported bridge girder, modelled as a beam, an endbearing pile, modelled as an axial rod and a simply supported plate as a continuum dynamic system. A discrete structure, like a building frame is solved for damage using Eigen-sensitivity derived by a computationalmodel. Lastly, neural network based damage identification is also demonstrated for a simply supported bridge beam, where the known-pairs of damage-frequency vector is used to train a neural network. The performance of these methods under the influence of measurement error is outlined. It is hoped that the developed method could be integrated in a typical infra-structural management program, such that magnitudes of damage and their positions can be obtained using acquired natural frequencies, synthesized from the excited/ambient vibration signatures.

Comparative study on damage identification from lso-Eigen-Value-Change contours and smeared damage model

The paper proposes two methodologies for damage identification from measured natural frequencies of a contiguously damaged reinforced concrete beam, idealised with distributed damage model. The first method identifies damage from Iso-Eigen-Value-Change contours, plotted between pairs of different frequencies. The performance of the method is checked for a wide variation of damage positions and extents. The method is also extended to a discrete structure in the form of a five-storied shear building and the simplicity of the method is demonstrated. The second method is through smeared damage model, where the damage is assumed constant for different segments of the beam and the lengths and centres of these segments are the known inputs. First-order perturbation method is used to derive the relevant expressions. Both these methods are based on distributed damage models and have been checked with experimental program on simply supported reinforced concrete beams, subjected to different stages of symmetric and un-symmetric damages. The results of the experiments are encouraging and show that both the methods can be adopted together in a damage identification scenario.

Evaluation of document binarization using eigen value decomposition

A necessary step for the recognition of scanned documents is binarization, which is essentially the segmentation of the document. In order to binarize a scanned document, we can find several algorithms in the literature. What is the best binarization result for a given document image? To answer this question, a user needs to check different binarization algorithms for suitability, since different algorithms may work better for different type of documents. Manually choosing the best from a set of binarized documents is time consuming. To automate the selection of the best segmented document, either we need to use ground-truth of the document or propose an evaluation metric. If ground-truth is available, then precision and recall can be used to choose the best binarized document. What is the case, when ground-truth is not available? Can we come up with a metric which evaluates these binarized documents? Hence, we propose a metric to evaluate binarized document images using eigen value decomposition. We have evaluated this measure on DIBCO and H-DIBCO datasets. The proposed method chooses the best binarized document that is close to the ground-truth of the document.

Eigen-value problems,

"This work was supported in part by the Department of Computer Science, University of Illinois, Urbana, Illinois, and in part by the Advanced Research Projects Agency as administered by the Rome Air Development Center under contract no. US AF 30(602)4144."

A study on determining the theoretical dispersion curve for Rayleigh wave propagation

A method has been presented to establish the theoretical dispersion curve for performing the inverse analysis for the Rayleigh wave propagation. The proposed formulation is similar to the one available in literature, and is based on the finite difference formulation of the governing partial differential equations of motion. The method is framed in such a way that it ultimately leads to an Eigen value problem for which the solution can be obtained quite easily with respect to unknown frequency. The maximum absolute value of the vertical displacement at the ground surface is formed as the basis for deciding the governing mode of propagation. With the proposed technique, the numerical solutions were generated for a variety of problems, comprising of a number of different layers, associated with both ground and pavements. The results are found to be generally satisfactory. (C) 2011 Elsevier Ltd. All rights reserved.

Genetic Algorithm for Damage Assessment

Genetic Algorithms (GAs) are recognized as an alternative class of computational model, which mimic natural evolution to solve problems in a wide domain including machine learning, music generation, genetic synthesis etc. In the present study Genetic Algorithm has been employed to obtain damage assessment of composite structural elements. It is considered that a state of damage can be modeled as reduction in stiffness. The task is to determine the magnitude and location of damage. In a composite plate that is discretized into a set of finite elements, if a jth element is damaged, the GA based technique will predict the reduction in Ex and Ey and the location j. The fact that the natural frequency decreases with decrease in stiffness is made use of in the method. The natural frequency of any two modes of the damaged plates for the assumed damage parameters is facilitated by the use of Eigen sensitivity analysis. The Eigen value sensitivities are the derivatives of the Eigen values with respect to certain design parameters. If ωiu is the natural frequency of the ith mode of the undamaged plate and ωid is that of the damaged plate, with δωi as the difference between the two, while δωk is a similar difference in the kth mode, R is defined as the ratio of the two. For a random selection of Ex,Ey and j, a ratio Ri is obtained. A proper combination of Ex,Ey and j which makes Ri−R=0 is obtained by Genetic Algorithm.

The relationship of SIF between plate and plane fracture problems and the effect of the plate thickness on SIF

In the present paper, it is shown that the zero series eigenfunctions of Reissner plate cracks/notches fracture problems are analogous to the eigenfunctions of anti-plane and in-plane. The singularity in the double series expression of plate problems only arises in zero series parts. In view of the relationship with eigen-values of anti-plane and in-plane problem, the solution of eigen-values for Reissner plates consists of two parts: anti-plane problem and in-plane problem. As a result the corresponding eigen-values or the corresponding eigen-value solving programs with respect to the anti-plane and in-plane problems can be employed and many aggressive SIF computed methods of plane problems can be employed in the plate. Based on those, the approximate relationship of SIFs between the plate and the plane fracture problems is figured out, and the effect relationship of the plate thickness on SIF is given.

Causes of fish depletion: a factor analysis approach

A study was conducted in 54 wetlands of 13 districts of Assam, India to evaluate the causes of fish depletion. Twenty-two variables were considered for the study. Seven factors were extracted through factor analysis (Principal Component Analysis) based on Eigen Value Criteria of more than one. These seven factors together accounted for 69.3% of the total variance. Based on the characteristics of the variables, all the factors were given descriptive names. These variables can be used to measure the extent of management deficiency of the causes of fish depletion in the wetlands. The factors are management deficiency, organic load interference, catchment condition, extrinsic influence, fishermen’s ignorance, external environment and aquaculture program. Management deficiency accounted for a substantial portion of the total variance.

La superdotación : concepto y actitudes de los estudiantes de psicología, ciencias de la educación y magisterio.

Recoger de forma sistemática y precisa las actitudes, conocimientos, intereses y relación en general que los alumnos de psicología, pedagogía y magisterio como futuros profesionales mantienen con respecto a la superdotación. Las hipótesis de trabajo son: H1. El conocimiento que los alumnos de psicología, pedagogía y magisterio tienen sobre el tema de la superdotación es escaso. SH 1.1. Los currícula incluyen poca información sobre superdotación. SH 1.2. Reciben menos información sobre superdotados que sobre deficientes. SH 1.3. Carecen de una definición clara de superdotación. SH 1.4. La información y los conocimientos respecto al tema varían según la especialidad. H2. En la muestra seleccionada existe una escasa relación con el tema de la superdotación. SH 2.1. La relación con el tema varía según la especialidad. SH 2.2. La relación con la deficiencia mental es mayor que con la superdotación. H3. Las actitudes de los alumnos seleccionados hacia el tema de la superdotación son poco favorables. SH 3.1. Las actitudes sobre deficiencia mental son más favorables que aquellas referidas a la superdotación. SH 3.2. Las actitudes varían según la especialidad cursada por los sujetos de la muestra. H4. Los alumnos de psicología, pedagogía y magisterio desconocen cuáles son los objetivos educativos propios del trabajo con superdotados. SH 4.1. La muestra no diferencia los objetivos educativos para el trabajo con niños deficientes, normales o superdotados. SH 4.2. La selección de los objetivos varía en función de la especialidad cursada. 235 estudiantes seleccionados entre los alumnos matriculados en las cuatro especialidades de tercero de magisterio (76), en segundo (16) y quinto (11) de pedagogía, y en tercero (66) y quinto (66) de psicología, durante los cursos 88-89 y 89-90. En la parte teórica se presentan y describen los modelos más relevantes sobre la naturaleza y medición de la inteligencia y, a su vez, las principales investigaciones realizadas sobre el tema de la superdotación. Seguidamente se analizan las distintas definiciones existentes sobre la superdotación, recopilando las características más importantes de la misma. Para concluir se recogen los trabajos más destacados sobre opiniones, creencias y actitudes de distintos profesionales hacia los superdotados. La parte experimental queda claramente reflejada en el resto de apartados. Cuestionario compuesto por cinco partes diferentes: 1. Rejilla: dos, una para la superdotación y otra para deficiencia mental. Con ellas se podrá evaluar la importancia de la superdotación en función de las especialidades y sus currícula correspondientes. 2. Definiciones; para controlar el concepto que se tiene de la superdotación. 3. Cuestionario: dos, uno para superdotación y otro para deficiencia mental; valora las distintas opiniones, relación y conocimientos sobre el tema. 4. Actitudes: escala de Klaus K. Urban sobre actitudes hacia la educación del superdotado. Valora diferentes aspectos relacionados con el tema, como por ejemplo, la educación especial, la integración, etc. 5. Objetivos educativos. Se partió de una escala creada por Klaus K. Urban. Valora qué objetivos son relevantes para el trabajo con superdotados. Análisis descriptivo para rejilla, cuestionario, actitudes y objetivos educativos, lo cual da una primera aproximación a la agrupación de resultados a través de proporciones, separadamente para cada grupo. Contraste entre grupos con el método x2. Análisis factorial para conocer los componentes subyacentes principales con elección de factores eigen value superior a uno y rotación ortogonal VARIMAX. Se utiliza el Stadistical Package for Social Sciencies o SPSS. Análisis de contenido para el apartado de definición: ideas básicas de lo que es un superdotado. 1. Rejilla: la superdotación recibe una escasa atención en los estudios de psicología, pedagogía y magisterio de nuestra universidad. Los pedagogos apenas trabajan el tema. Se constatan diferencias de tiempo, amplitud y profundidad entre deficiencias y superdotación. Se confirma SH 1.1., SH 1.2. y SH 1.4. 2. Definición: suelen centrarse en conceptos psicométricos o características aptitudinales muy difusas confirmándose así la SH 1.3. 3. Cuestionario: Los alumnos no poseen libros sobre la superdotación, la asistencia a cursos, seminarios, conferencias, etc., sobre el tema es casi nula, nadie manifiesta conocer a algún profesional que la trabaje exceptuando el propio ámbito universitario. La cosa cambia bastante al tratar la deficiencia mental: la mayoría posee documentación y conoce a alguien que trabaja el tema. La falta de información sobre superdotados repercute en un menor interés por el tema. Muchos opinan que para trabajar con ellos necesitan mayor preparación. Al poseer mucha información sobre deficientes mentales se valora el tema como muy interesante e importante para su futuro profesional. Se confirma la segunda hipótesis, SH 2.1. y SH 2.2. 4. Actitudes: la superdotación necesita atención especial e integración en centros normales pero hay dispersión acerca de si la identificación temprana es o no perjudicial para su desarrollo y sobre la conveniencia de crear colegios especiales para estos niños. La deficiencia mental debe identificarse tempranamente; educación especial dirigida a sus necesidades, capacidades e intereses, integración aconsejable. La tercera hipótesis debería matizarse. Las actitudes hacia la superdotación son heterogéneas y poco claras aunque mayoritariamente favorables. Se confirma SH 3.1. pero no SH 3.2. 5. Objetivos educativos: se atribuyen los mismos a los grupos normales y superdotados pero no a los deficientes. Se confirma H4 y SH 4.1. pero no SH 4.2. Falta una teoría general que abarque los conocimientos que se tienen sobre el tema de la superdotación. Se detectan amplias perspectivas de futuro, cada vez son más numerosos los libros, revistas especializadas, congresos e instituciones dedicadas al tema. Es necesario preparar a los alumnos porque la demanda social de especialistas en este campo ya ha empezado y porque la buena información es el primer paso para conseguir mayor entendimiento, aceptación e interés hacia el tema.

Well-conditioned configurations of fault-tolerant manipulators

Fault-tolerant motion of redundant manipulators can be obtained by joint velocity reconfiguration. For fault-tolerant manipulators, it is beneficial to determine the configurations that can tolerate the locked-joint failures with a minimum relative joint velocity jump, because the manipulator can rapidly reconfigure itself to tolerate the fault. This paper uses the properties of the condition numbers to introduce those optimal configurations for serial manipulators. The relationship between the manipulator's locked-joint failures and the condition number of the Jacobian matrix is indicated by using a matrix perturbation methodology. Then, it is observed that the condition number provides an upper bound of the required relative joint velocity change for recovering the faults which leads to define the optimal fault-tolerant configuration from the minimization of the condition number. The optimization problem to obtain the minimum condition number is converted to three standard Eigen value optimization problems. A solution is for selected optimization problem is presented. Finally, in order to obtain the optimal fault-tolerant configuration, the proposed method is applied to a 4-DoF planar manipulator.

A novel approach to maximize the sum-rate for MIMO broadcast channels

This paper considers the sum-rate of wireless broadcast systems with multiple antennas at the base station. In a conventional MIMO-BC system with a large number of users, selecting an optimal subset of users to maximizing the overall system capacity is a key design issue. This paper presents a novel approach to investigate the sum-rate using Eigen Value Decomposition (EVD). Particularly, we derive the lower bound on sum-rate of a conventional MIMO-BC using a completely different approach compared to the existing approaches. The paper formulates the rate maximization problem for any number of users and any number of transmitting antennas using EVD approach of the channel matrix. This also shows the impact of channel angle information on the sum-rate of conventional MIMO-BC. Numerical results confirm the benefits of our technique in various MIMO communication scenarios.

Correction procedure applied to a single real transformation matrix -Untransposed three-phase transmission line cases

Clarke's matrix has been used as an eigenvector matrix for transposed three-phase transmission lines and it can be applied as a phase-mode transformation matrix for transposed cases. Considering untransposed three-phase transmission lines, Clarke's matrix is not an exact eigenvector matrix. In this case, the errors related to the diagonal elements of the Z and Y matrices can be considered negligible, if these diagonal elements are compared to the exact elements in domain mode. The mentioned comparisons are performed based on the error and frequency scan analyses. From these analyses and considering untransposed asymmetrical three-phase transmission lines, a correction procedure is determined searching for better results from the Clarke's matrix use as a phase-mode transformation matrix. Using the Clarke's matrix, the relative errors of the eigenvalue matrix elements can be considered negligible and the relative values of the off-diagonal elements are significant. Applying the corrected transformation matrices, the relative values of the off-diagonal elements are decreased. The comparisons among the results of these analyses show that the homopolar mode is more sensitive to the frequency influence than the two other modes related to three-phase lines. © 2006 IEEE.

Eigenvalue analyses for non-transposed three-phase transmission line considering non-implicit ground wires

This paper presents a method for analyzing electromagnetic transients using real transformation matrices in three-phase systems considering the presence of ground wires. So, for the Z and Y matrices that represent the transmission line, the characteristics of ground wires are not implied in the values related to the phases. A first approach uses a real transformation matrix for the entire frequency range considered in this case. This transformation matrix is an approximation to the exact transformation matrix. For those elements related to the phases of the considered system, the transformation matrix is composed of the elements of Clarke's matrix. In part related to the ground wires, the elements of the transformation matrix must establish a relationship with the elements of the phases considering the establishment of a single homopolar reference in the mode domain. In the case of three-phase lines with the presence of two ground wires, it is unable to get the full diagonalization of the matrices Z and Y in the mode domain. This leads to the second proposal for the composition of real transformation matrix: obtain such transformation matrix from the multiplication of two real and constant matrices. In this case, the inclusion of a second matrix had the objective to minimize errors from the first proposal for the composition of the transformation matrix mentioned. © 2012 IEEE.

The Causal Links between FDI and Economic Growth in Developing Countries: A Case Study of the Republic of Rwanda

The study examines the short-run and long-run causality running from real economic growth to real foreign direct investment inflows (RFDI). Other variables such as education (involving combination of primary, secondary and tertiary enrolment as a proxy to education), real development finance, unskilled labour, to real RFDI inflows are included in the study. The time series data covering the period of 1983 -2013 are examined. First, I applied Augmented Dicky-Fuller (ADF) technique to test for unit root in variables. Findings shows all variables integrated of order one [I(1)]. Thereafter, Johansen Co-integration Test (JCT) was conducted to establish the relationship among variables. Both trace and maximum Eigen value at 5% level of significance indicate 3 co-integrated equations. Vector error correction method (VECM) was applied to capture short and long-run causality running from education, economic growth, real development finance, and unskilled labour to real foreign direct investment inflows in the Republic of Rwanda. Findings shows no short-run causality running from education, real development finance, real GDP and unskilled labour to real FDI inflows, however there were existence of long-run causality. This can be interpreted that, in the short-run; education, development finance, finance and economic growth does not influence inflows of foreign direct investment in Rwanda; but it does in long-run. From the policy perspective, the Republic of Rwanda should focus more on long term goal of investing in education to improve human capital, undertake policy reforms that promotes economic growth, in addition to promoting good governance to attract development finance – especially from Nordics countries (particularly Norway and Denmark).

Avoiding Overfitting in Inverse Modeling of Chloride Migration in Concrete

Inverse analysis for reactive transport of chlorides through concrete in the presence of electric field is presented. The model is solved using MATLAB’s built-in solvers “pdepe.m” and “ode15s.m”. The results from the model are compared with experimental measurements from accelerated migration test and a function representing the lack of fit is formed. This function is optimised with respect to varying amount of key parameters defining the model. Levenberg-Marquardt trust-region optimisation approach is employed. The paper presents a method by which the degree of inter-dependency between parameters and sensitivity (significance) of each parameter towards model predictions can be studied on models with or without clearly defined governing equations. Eigen value analysis of the Hessian matrix was employed to investigate and avoid over-parametrisation in inverse analysis. We investigated simultaneous fitting of parameters for diffusivity, chloride binding as defined by Freundlich isotherm (thermodynamic) and binding rate (kinetic parameter). Fitting of more than 2 parameters, simultaneously, demonstrates a high degree of parameter inter-dependency. This finding is significant as mathematical models for representing chloride transport rely on several parameters for each mode of transport (i.e., diffusivity, binding, etc.), which combined may lead to unreliable simultaneous estimation of parameters.