Observability of nonlinear fractional dynamical systems

We study the observability of linear and nonlinear fractional differential systems of order 0 < α < 1 by using the Mittag-Leffler matrix function and the application of Banach’s contraction mapping theorem. Several examples illustrate the concepts.

Geostatistical Mapping of Outfall Plume Dispersion Data gathered with an autonomous underwater vehicle

The main purpose of this study was to examine the applicability of geostatistical modeling to obtain valuable information for assessing the environmental impact of sewage outfall discharges. The data set used was obtained in a monitoring campaign to S. Jacinto outfall, located off the Portuguese west coast near Aveiro region, using an AUV. The Matheron’s classical estimator was used the compute the experimental semivariogram which was fitted to three theoretical models: spherical, exponential and gaussian. The cross-validation procedure suggested the best semivariogram model and ordinary kriging was used to obtain the predictions of salinity at unknown locations. The generated map shows clearly the plume dispersion in the studied area, indicating that the effluent does not reach the near by beaches. Our study suggests that an optimal design for the AUV sampling trajectory from a geostatistical prediction point of view, can help to compute more precise predictions and hence to quantify more accurately dilution. Moreover, since accurate measurements of plume’s dilution are rare, these studies might be very helpful in the future for validation of dispersion models.

Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.

Derivative-free nonlinear optimization filter simplex

The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. In these cases it becomes essential to use optimization methods where the calculation of the derivatives or the verification of their existence is not necessary: direct search methods or derivative-free methods are examples of such techniques. In this work we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of simplex and filter methods. This method neither computes nor approximates derivatives, penalty constants or Lagrange multipliers.

Ontology mapping evolution

Introdução Hoje em dia, o conceito de ontologia (Especificação explícita de uma conceptualização [Gruber, 1993]) é um conceito chave em sistemas baseados em conhecimento em geral e na Web Semântica em particular. Entretanto, os agentes de software nem sempre concordam com a mesma conceptualização, justificando assim a existência de diversas ontologias, mesmo que tratando o mesmo domínio de discurso. Para resolver/minimizar o problema de interoperabilidade entre estes agentes, o mapeamento de ontologias provou ser uma boa solução. O mapeamento de ontologias é o processo onde são especificadas relações semânticas entre entidades da ontologia origem e destino ao nível conceptual, e que por sua vez podem ser utilizados para transformar instâncias baseadas na ontologia origem em instâncias baseadas na ontologia destino. Motivação Num ambiente dinâmico como a Web Semântica, os agentes alteram não só os seus dados mas também a sua estrutura e semântica (ontologias). Este processo, denominado evolução de ontologias, pode ser definido como uma adaptação temporal da ontologia através de alterações que surgem no domínio ou nos objectivos da própria ontologia, e da gestão consistente dessas alterações [Stojanovic, 2004], podendo por vezes deixar o documento de mapeamento inconsistente. Em ambientes heterogéneos onde a interoperabilidade entre sistemas depende do documento de mapeamento, este deve reflectir as alterações efectuadas nas ontologias, existindo neste caso duas soluções: (i) gerar um novo documento de mapeamento (processo exigente em termos de tempo e recursos computacionais) ou (ii) adaptar o documento de mapeamento, corrigindo relações semânticas inválidas e criar novas relações se forem necessárias (processo menos existente em termos de tempo e recursos computacionais, mas muito dependente da informação sobre as alterações efectuadas). O principal objectivo deste trabalho é a análise, especificação e desenvolvimento do processo de evolução do documento de mapeamento de forma a reflectir as alterações efectuadas durante o processo de evolução de ontologias. Contexto Este trabalho foi desenvolvido no contexto do MAFRA Toolkit1. O MAFRA (MApping FRAmework) Toolkit é uma aplicação desenvolvida no GECAD2 que permite a especificação declarativa de relações semânticas entre entidades de uma ontologia origem e outra de destino, utilizando os seguintes componentes principais: Concept Bridge – Representa uma relação semântica entre um conceito de origem e um de destino; Property Bridge – Representa uma relação semântica entre uma ou mais propriedades de origem e uma ou mais propriedades de destino; Service – São aplicados às Semantic Bridges (Property e Concept Bridges) definindo como as instâncias origem devem ser transformadas em instâncias de destino. Estes conceitos estão especificados na ontologia SBO (Semantic Bridge Ontology) [Silva, 2004]. No contexto deste trabalho, um documento de mapeamento é uma instanciação do SBO, contendo relações semânticas entre entidades da ontologia de origem e da ontologia de destino. Processo de evolução do mapeamento O processo de evolução de mapeamento é o processo onde as entidades do documento de mapeamento são adaptadas, reflectindo eventuais alterações nas ontologias mapeadas, tentando o quanto possível preservar a semântica das relações semântica especificadas. Se as ontologias origem e/ou destino sofrerem alterações, algumas relações semânticas podem tornar-se inválidas, ou novas relações serão necessárias, sendo por isso este processo composto por dois sub-processos: (i) correcção de relações semânticas e (ii) processamento de novas entidades das ontologias. O processamento de novas entidades das ontologias requer a descoberta e cálculo de semelhanças entre entidades e a especificação de relações de acordo com a ontologia/linguagem SBO. Estas fases (“similarity measure” e “semantic bridging”) são implementadas no MAFRA Toolkit, sendo o processo (semi-) automático de mapeamento de ontologias descrito em [Silva, 2004].O processo de correcção de entidades SBO inválidas requer um bom conhecimento da ontologia/linguagem SBO, das suas entidades e relações, e de todas as suas restrições, i.e. da sua estrutura e semântica. Este procedimento consiste em (i) identificar as entidades SBO inválidas, (ii) a causa da sua invalidez e (iii) corrigi-las da melhor forma possível. Nesta fase foi utilizada informação vinda do processo de evolução das ontologias com o objectivo de melhorar a qualidade de todo o processo. Conclusões Para além do processo de evolução do mapeamento desenvolvido, um dos pontos mais importantes deste trabalho foi a aquisição de um conhecimento mais profundo sobre ontologias, processo de evolução de ontologias, mapeamento etc., expansão dos horizontes de conhecimento, adquirindo ainda mais a consciência da complexidade do problema em questão, o que permite antever e perspectivar novos desafios para o futuro.

Combined mutation differential evolution to solve systems of nonlinear equations

This paper presents a differential evolution heuristic to compute a solution of a system of nonlinear equations through the global optimization of an appropriate merit function. Three different mutation strategies are combined to generate mutant points. Preliminary numerical results show the effectiveness of the presented heuristic.

Application mapping in NoC-Based many-cores

Many-core platforms based on Network-on-Chip (NoC [Benini and De Micheli 2002]) present an emerging technology in the real-time embedded domain. Although the idea to group the applications previously executed on separated single-core devices, and accommodate them on an individual many-core chip offers various options for power savings, cost reductions and contributes to the overall system flexibility, its implementation is a non-trivial task. In this paper we address the issue of application mapping onto a NoCbased many-core platform when considering fundamentals and trends of current many-core operating systems, specifically, we elaborate on a limited migrative application model encompassing a message-passing paradigm as a communication primitive. As the main contribution, we formulate the problem of real-time application mapping, and propose a three-stage process to efficiently solve it. Through analysis it is assured that derived solutions guarantee the fulfilment of posed time constraints regarding worst-case communication latencies, and at the same time provide an environment to perform load balancing for e.g. thermal, energy, fault tolerance or performance reasons.We also propose several constraints regarding the topological structure of the application mapping, as well as the inter- and intra-application communication patterns, which efficiently solve the issues of pessimism and/or intractability when performing the analysis.

A Java expression evaluator for nonlinear programming

Finding the optimal value for a problem is usual in many areas of knowledge where in many cases it is needed to solve Nonlinear Optimization Problems. For some of those problems it is not possible to determine the expression for its objective function and/or its constraints, they are the result of experimental procedures, might be non-smooth, among other reasons. To solve such problems it was implemented an API contained methods to solve both constrained and unconstrained problems. This API was developed to be used either locally on the computer where the application is being executed or remotely on a server. To obtain the maximum flexibility both from the programmers’ and users’ points of view, problems can be defined as a Java class (because this API was developed in Java) or as a simple text input that is sent to the API. For this last one to be possible it was also implemented on the API an expression evaluator. One of the drawbacks of this expression evaluator is that it is slower than the Java native code. In this paper it is presented a solution that combines both options: the problem can be expressed at run-time as a string of chars that are converted to Java code, compiled and loaded dynamically. To wide the target audience of the API, this new expression evaluator is also compatible with the AMPL format.

Self-adaptive combination of global tabu search and local search for nonlinear equations

Solving systems of nonlinear equations is a very important task since the problems emerge mostly through the mathematical modelling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a self-adaptive combination of a metaheuristic with a classical local search method is able to converge to some difficult problems that are not solved by Newton-type methods.

Web-based application programming interface to solve nonlinear optimization problems

Nonlinear Optimization Problems are usual in many engineering fields. Due to its characteristics the objective function of some problems might not be differentiable or its derivatives have complex expressions. There are even cases where an analytical expression of the objective function might not be possible to determine either due to its complexity or its cost (monetary, computational, time, ...). In these cases Nonlinear Optimization methods must be used. An API, including several methods and algorithms to solve constrained and unconstrained optimization problems was implemented. This API can be accessed not only as traditionally, by installing it on the developer and/or user computer, but it can also be accessed remotely using Web Services. As long as there is a network connection to the server where the API is installed, applications always access to the latest API version. Also an Web-based application, using the proposed API, was developed. This application is to be used by users that do not want to integrate methods in applications, and simply want to have a tool to solve Nonlinear Optimization Problems.

Is multidimensional scaling suitable for mapping the input respiratory impedance in subjects and patients?

This paper presents the application of multidimensional scaling (MDS) analysis to data emerging from noninvasive lung function tests, namely the input respiratory impedance. The aim is to obtain a geometrical mapping of the diseases in a 3D space representation, allowing analysis of (dis)similarities between subjects within the same pathology groups, as well as between the various groups. The adult patient groups investigated were healthy, diagnosed chronic obstructive pulmonary disease (COPD) and diagnosed kyphoscoliosis, respectively. The children patient groups were healthy, asthma and cystic fibrosis. The results suggest that MDS can be successfully employed for mapping purposes of restrictive (kyphoscoliosis) and obstructive (COPD) pathologies. Hence, MDS tools can be further examined to define clear limits between pools of patients for clinical classification, and used as a training aid for medical traineeship.

Intrinsic fractal dynamics in the respiratory system by means of pressure-volume loops

This contribution presents novel concepts for analysis of pressure–volume curves, which offer information about the time domain dynamics of the respiratory system. The aim is to verify whether a mapping of the respiratory diseases can be obtained, allowing analysis of (dis)similarities between the dynamical pattern in the breathing in children. The groups investigated here are children, diagnosed as healthy, asthmatic, and cystic fibrosis. The pressure–volume curves have been measured by means of the noninvasive forced oscillation technique during breathing at rest. The geometrical fractal dimension is extracted from the pressure–volume curves and a power-law behavior is observed in the data. The power-law model coefficients are identified from the three sets and the results show that significant differences are present between the groups. This conclusion supports the idea that the respiratory system changes with disease in terms of airway geometry, tissue parameters, leading in turn to variations in the fractal dimension of the respiratory tree and its dynamics.

Solving nonlinear equations by a tabu search strategy

Solving systems of nonlinear equations is a problem of particular importance since they emerge through the mathematical modeling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a metaheuristic, called Directed Tabu Search (DTS) [16], is able to converge to the solutions of a set of problems for which the fsolve function of MATLAB® failed to converge. We also show the effect of the dimension of the problem in the performance of the DTS.

Fractional describing function of systems with nonlinear friction

This paper studies the describing function (DF) of systems consisting in a mass subjected to nonlinear friction. The friction force is composed in three components namely, the viscous, the Coulomb and the static forces. The system dynamics is analyzed in the DF perspective revealing a fractional-order behaviour. The reliability of the DF method is evaluated through the signal harmonic content and the limit cycle prediction.

Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomena

The development of fractional-order controllers is currently one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. This paper reports on the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order PID controllers in the presence of several nonlinearities is discussed. Some results are provided that indicate the superior robustness of such algorithms.