18 resultados para Nonlinear System of Equations
em Universidad Politécnica de Madrid
Resumo:
We present a novel approach for the detection of severe obstructive sleep apnea (OSA) based on patients' voices introducing nonlinear measures to describe sustained speech dynamics. Nonlinear features were combined with state-of-the-art speech recognition systems using statistical modeling techniques (Gaussian mixture models, GMMs) over cepstral parameterization (MFCC) for both continuous and sustained speech. Tests were performed on a database including speech records from both severe OSA and control speakers. A 10 % relative reduction in classification error was obtained for sustained speech when combining MFCC-GMM and nonlinear features, and 33 % when fusing nonlinear features with both sustained and continuous MFCC-GMM. Accuracy reached 88.5 % allowing the system to be used in OSA early detection. Tests showed that nonlinear features and MFCCs are lightly correlated on sustained speech, but uncorrelated on continuous speech. Results also suggest the existence of nonlinear effects in OSA patients' voices, which should be found in continuous speech.
Resumo:
Esta tesis propone una completa formulación termo-mecánica para la simulación no-lineal de mecanismos flexibles basada en métodos libres de malla. El enfoque se basa en tres pilares principales: la formulación de Lagrangiano total para medios continuos, la discretización de Bubnov-Galerkin, y las funciones de forma libres de malla. Los métodos sin malla se caracterizan por la definición de un conjunto de funciones de forma en dominios solapados, junto con una malla de integración de las ecuaciones discretas de balance. Dos tipos de funciones de forma se han seleccionado como representación de las familias interpolantes (Funciones de Base Radial) y aproximantes (Mínimos Cuadrados Móviles). Su formulación se ha adaptado haciendo sus parámetros compatibles, y su ausencia de conectividad predefinida se ha aprovechado para interconectar múltiples dominios de manera automática, permitiendo el uso de mallas de fondo no conformes. Se propone una formulación generalizada de restricciones, juntas y contactos, válida para sólidos rígidos y flexibles, siendo estos últimos discretizados mediante elementos finitos (MEF) o libres de malla. La mayor ventaja de este enfoque reside en que independiza completamente el dominio con respecto de las uniones y acciones externas a cada sólido, permitiendo su definición incluso fuera del contorno. Al mismo tiempo, también se minimiza el número de ecuaciones de restricción necesarias para la definición de uniones realistas. Las diversas validaciones, ejemplos y comparaciones detalladas muestran como el enfoque propuesto es genérico y extensible a un gran número de sistemas. En concreto, las comparaciones con el MEF indican una importante reducción del error para igual número de nodos, tanto en simulaciones mecánicas, como térmicas y termo-mecánicas acopladas. A igualdad de error, la eficiencia numérica de los métodos libres de malla es mayor que la del MEF cuanto más grosera es la discretización. Finalmente, la formulación se aplica a un problema de diseño real sobre el mantenimiento de estructuras masivas en el interior de un reactor de fusión, demostrando su viabilidad en análisis de problemas reales, y a su vez mostrando su potencial para su uso en simulación en tiempo real de sistemas no-lineales. A new complete formulation is proposed for the simulation of nonlinear dynamic of multibody systems with thermo-mechanical behaviour. The approach is founded in three main pillars: total Lagrangian formulation, Bubnov-Galerkin discretization, and meshfree shape functions. Meshfree methods are characterized by the definition of a set of shape functions in overlapping domains, and a background grid for integration of the Galerkin discrete equations. Two different types of shape functions have been chosen as representatives of interpolation (Radial Basis Functions), and approximation (Moving Least Squares) families. Their formulation has been adapted to use compatible parameters, and their lack of predefined connectivity is used to interconnect different domains seamlessly, allowing the use of non-conforming meshes. A generalized formulation for constraints, joints, and contacts is proposed, which is valid for rigid and flexible solids, being the later discretized using either finite elements (FEM) or meshfree methods. The greatest advantage of this approach is that makes the domain completely independent of the external links and actions, allowing to even define them outside of the boundary. At the same time, the number of constraint equations needed for defining realistic joints is minimized. Validation, examples, and benchmarks are provided for the proposed formulation, demonstrating that the approach is generic and extensible to further problems. Comparisons with FEM show a much lower error for the same number of nodes, both for mechanical and thermal analyses. The numerical efficiency is also better when coarse discretizations are used. A final demonstration to a real problem for handling massive structures inside of a fusion reactor is presented. It demonstrates that the application of meshfree methods is feasible and can provide an advantage towards the definition of nonlinear real-time simulation models.
Resumo:
We analyze a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite’s temperature is analyzed by qualitative, perturbation and numerical methods, which prove that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.
Resumo:
In this work we propose a method to accelerate time dependent numerical solvers of systems of PDEs that require a high cost in computational time and memory. The method is based on the combined use of such numerical solver with a proper orthogonal decomposition, from which we identify modes, a Galerkin projection (that provides a reduced system of equations) and the integration of the reduced system, studying the evolution of the modal amplitudes. We integrate the reduced model until our a priori error estimator indicates that our approximation in not accurate. At this point we use again our original numerical code in a short time interval to adapt the POD manifold and continue then with the integration of the reduced model. Application will be made to two model problems: the Ginzburg-Landau equation in transient chaos conditions and the two-dimensional pulsating cavity problem, which describes the motion of liquid in a box whose upper wall is moving back and forth in a quasi-periodic fashion. Finally, we will discuss a way of improving the performance of the method using experimental data or information from numerical simulations
Resumo:
The nonlinear streamwise growth of a spanwise periodic array of steady streaks in a flat plate boundary layer is numerically computed using the well known Reduced Navier-Stokes formulation. It is found that the flow configuration changes substantially when the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-spanwise plane), which is normally not considered, becomes non-negligible in the nonlinear regime, and it strongly distorts the streamwise velocity profiles, which end up being quite different from those predicted by the linear theory. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks, and compare them with available experimental results.
Resumo:
The nonlinear streamwise growth of a spanwise periodic array of steady streaks in a flat plate boundary layer is numerically computed using the well known Reduced Navier- Stokes formulation. It is found that the flow configuration changes substantially when the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-spanwise plane), which is normally not considered, becomes non-negligible in the nonlinear regime, and it strongly distorts the streamwise velocity profiles, which end up being quite different from those predicted by the linear theory. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks, and compare them with available experimental results.
Resumo:
In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.
Resumo:
Using the Monte Carlo method the behavior of a system of true hard cylinders has been studied. Values of the length-to-breadth ratio L/D and packing fraction η have been chosen similar to those of real nematic liquid crystals. Results include radial distribution function g(r), structure factor S(k), and orientational order parameter M. These results lead to the conclusion that the hard cylinder model may be a useful reference for real mesomorphic phases.
Resumo:
Smart Grids are advanced power networks that introduce intelligent management, control, and operation systems to address the new challenges generated by the growing energy demand and the appearance of renewal energies. In the literature, Smart Grids are presented as an exemplar SoS: systems composed of large heterogeneous and independent systems that leverage emergent behavior from their interaction. Smart Grids are currently scaling up the electricity service to millions of customers. These Smart Grids are known as Large-Scale Smart Grids. From the experience in several projects about Large-Scale Smart Grids, this paper defines Large-Scale Smart Grids as a SoS that integrate a set of SoS and conceptualizes the properties of this SoS. In addition, the paper defines the architectural framework for deploying the software architectures of Large-Scale Smart Grid SoS.
Resumo:
After the extensive research on the capabilities of the Boundary Integral Equation Method produced during the past years the versatility of its applications has been well founded. Maybe the years to come will see the in-depth analysis of several conflictive points, for example, adaptive integration, solution of the system of equations, etc. This line is clear in academic research. In this paper we comment on the incidence of the manner of imposing the boundary conditions in 3-D coupled problems. Here the effects are particularly magnified: in the first place by the simple model used (constant elements) and secondly by the process of solution, i.e. first a potential problem is solved and then the results are used as data for an elasticity problem. The errors add to both processes and small disturbances, unimportant in separated problems, can produce serious errors in the final results. The specific problem we have chosen is especially interesting. Although more general cases (i.e. transient)can be treated, here the domain integrals can be converted into boundary ones and the influence of the manner in which boundary conditions are applied will reflect the whole importance of the problem.
Resumo:
This paper develops an automatic procedure for the optimal numbering of members and nodes in tree structures. With it the stiffness matrix is optimally conditioned either if a direct solution algorithm or a frontal one is used to solve the system of equations. In spite of its effectiveness, the procedure is strikingly simple and so is the computer program shown below.
Resumo:
The efficiency of a Power Plant is affected by the distribution of the pulverized coal within the furnace. The coal, which is pulverized in the mills, is transported and distributed by the primary gas through the mill-ducts to the interior of the furnace. This is done with a double function: dry and enter the coal by different levels for optimizing the combustion in the sense that a complete combustion occurs with homogeneous heat fluxes to the walls. The mill-duct systems of a real Power Plant are very complex and they are not yet well understood. In particular, experimental data concerning the mass flows of coal to the different levels are very difficult to measure. CFD modeling can help to determine them. An Eulerian/Lagrangian approach is used due to the low solid–gas volume ratio.
Resumo:
This document is the result of a process of web development to create a tool that will allow to Cracow University of Technology consult, create and manage timetables. The technologies chosen for this purpose are Apache Tomcat Server, My SQL Community Server, JDBC driver, Java Servlets and JSPs for the server side. The client part counts on Javascript, jQuery, AJAX and CSS technologies to perform the dynamism. The document will justify the choice of these technologies and will explain some development tools that help in the integration and development of all this elements: specifically, NetBeans IDE and MySQL workbench have been used as helpful tools. After explaining all the elements involved in the development of the web application, the architecture and the code developed are explained through UML diagrams. Some implementation details related to security are also deeper explained through sequence diagrams. As the source code of the application is provided, an installation manual has been developed to run the project. In addition, as the platform is intended to be a beta that will be grown, some unimplemented ideas for future development are also exposed. Finally, some annexes with important files and scripts related to the initiation of the platform are attached. This project started through an existing tool that needed to be expanded. The main purpose of the project along its development has focused on setting the roots for a whole new platform that will replace the existing one. For this goal, it has been needed to make a deep inspection on the existing web technologies: a web server and a SQL database had to be chosen. Although the alternatives were a lot, Java technology for the server was finally selected because of the big community backwards, the easiness of modelling the language through UML diagrams and the fact of being free license software. Apache Tomcat is the open source server that can use Java Servlet and JSP technology. Related to the SQL database, MySQL Community Server is the most popular open-source SQL Server, with a big community after and quite a lot of tools to manage the server. JDBC is the driver needed to put in contact Java and MySQL. Once we chose the technologies that would be part of the platform, the development process started. After a detailed explanation of the development environment installation, we used UML use case diagrams to set the main tasks of the platform; UML class diagrams served to establish the existing relations between the classes generated; the architecture of the platform was represented through UML deployment diagrams; and Enhanced entity–relationship (EER) model were used to define the tables of the database and their relationships. Apart from the previous diagrams, some implementation issues were explained to make a better understanding of the developed code - UML sequence diagrams helped to explain this. Once the whole platform was properly defined and developed, the performance of the application has been shown: it has been proved that with the current state of the code, the platform covers the use cases that were set as the main target. Nevertheless, some requisites needed for the proper working of the platform have been specified. As the project is aimed to be grown, some ideas that could not be added to this beta have been explained in order not to be missed for future development. Finally, some annexes containing important configuration issues for the platform have been added after proper explanation, as well as an installation guide that will let a new developer get the project ready. In addition to this document some other files related to the project are provided: - Javadoc. The Javadoc containing the information of every Java class created is necessary for a better understanding of the source code. - database_model.mwb. This file contains the model of the database for MySQL Workbench. This model allows, among other things, generate the MySQL script for the creation of the tables. - ScheduleManager.war. The WAR file that will allow loading the developed application into Tomcat Server without using NetBeans. - ScheduleManager.zip. The source code exported from NetBeans project containing all Java packages, JSPs, Javascript files and CSS files that are part of the platform. - config.properties. The configuration file to properly get the names and credentials to use the database, also explained in Annex II. Example of config.properties file. - db_init_script.sql. The SQL query to initiate the database explained in Annex III. SQL statements for MySQL initialization. RESUMEN. Este proyecto tiene como punto de partida la necesidad de evolución de una herramienta web existente. El propósito principal del proyecto durante su desarrollo se ha centrado en establecer las bases de una completamente nueva plataforma que reemplazará a la existente. Para lograr esto, ha sido necesario realizar una profunda inspección en las tecnologías web existentes: un servidor web y una base de datos SQL debían ser elegidos. Aunque existen muchas alternativas, la tecnología Java ha resultado ser elegida debido a la gran comunidad de desarrolladores que tiene detrás, además de la facilidad que proporciona este lenguaje a la hora de modelarlo usando diagramas UML. Tampoco hay que olvidar que es una tecnología de uso libre de licencia. Apache Tomcat es el servidor de código libre que permite emplear Java Servlets y JSPs para hacer uso de la tecnología de Java. Respecto a la base de datos SQL, el servidor más popular de código libre es MySQL, y cuenta también con una gran comunidad detrás y buenas herramientas de modelado, creación y gestión de la bases de datos. JDBC es el driver que va a permitir comunicar las aplicaciones Java con MySQL. Tras elegir las tecnologías que formarían parte de esta nueva plataforma, el proceso de desarrollo tiene comienzo. Tras una extensa explicación de la instalación del entorno de desarrollo, se han usado diagramas de caso de UML para establecer cuáles son los objetivos principales de la plataforma; los diagramas de clases nos permiten realizar una organización del código java desarrollado de modo que sean fácilmente entendibles las relaciones entre las diferentes clases. La arquitectura de la plataforma queda definida a través de diagramas de despliegue. Por último, diagramas EER van a definir las relaciones entre las tablas creadas en la base de datos. Aparte de estos diagramas, algunos detalles de implementación se van a justificar para tener una mejor comprensión del código desarrollado. Diagramas de secuencia ayudarán en estas explicaciones. Una vez que toda la plataforma haya quedad debidamente definida y desarrollada, se va a realizar una demostración de la misma: se demostrará cómo los objetivos generales han sido alcanzados con el desarrollo actual del proyecto. No obstante, algunos requisitos han sido aclarados para que la plataforma trabaje adecuadamente. Como la intención del proyecto es crecer (no es una versión final), algunas ideas que se han podido llevar acabo han quedado descritas de manera que no se pierdan. Por último, algunos anexos que contienen información importante acerca de la plataforma se han añadido tras la correspondiente explicación de su utilidad, así como una guía de instalación que va a permitir a un nuevo desarrollador tener el proyecto preparado. Junto a este documento, ficheros conteniendo el proyecto desarrollado quedan adjuntos. Estos ficheros son: - Documentación Javadoc. Contiene la información de las clases Java que han sido creadas. - database_model.mwb. Este fichero contiene el modelo de la base de datos para MySQL Workbench. Esto permite, entre otras cosas, generar el script de iniciación de la base de datos para la creación de las tablas. - ScheduleManager.war. El fichero WAR que permite desplegar la plataforma en un servidor Apache Tomcat. - ScheduleManager.zip. El código fuente exportado directamente del proyecto de Netbeans. Contiene todos los paquetes de Java generados, ficheros JSPs, Javascript y CSS que forman parte de la plataforma. - config.properties. Ejemplo del fichero de configuración que permite obtener los nombres de la base de datos - db_init_script.sql. Las consultas SQL necesarias para la creación de la base de datos.
Resumo:
This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given
Resumo:
In this article, a model for the determination of displacements, strains, and stresses of a submarine pipeline during its construction is presented. Typically, polyethylene outfall pipelines are the ones treated by this model. The process is carried out from an initial floating situation to the final laying position on the seabed. The following control variables are considered in the laying process: the axial load in the pipe, the flooded inner length, and the distance of the control barge from the coast. External loads such as self-weight, dead loads, and forces due to currents and small waves are also taken into account.This paper describes both the conceptual framework for the proposed model and its practical application in a real engineering situation. The authors also consider how the model might be used as a tool to study how sensitive the behavior of the pipeline is to small changes in the values of the control variables. A detailed description of the actions is considered, especially the ones related to the marine environment such as buoyancy, current, and sea waves. The structural behavior of the pipeline is simulated in the framework of a geometrically nonlinear dynamic analysis. The pipeline is assumed to be a two-dimensional Navier_Bernoulli beam. In the nonlinear analysis an updated Lagrangian formulation is used, and special care is taken regarding the numerical aspects of sea bed contact, follower forces due to external water pressures, and dynamic actions. The paper concludes by describing the implementation of the proposed techniques, using the ANSYS computer program with a number of subroutines developed by the authors. This implementation permits simulation of the two-dimensional structural pipe behavior of the whole construction process. A sensitivity analysis of the bending moments, axial forces, and stresses for different values of the control variables is carried out. Using the techniques described, the engineer may optimize the construction steps in the pipe laying process