Machine learning and data decompositions for complex networked dynamical systems

Thesis (Ph.D.)--University of Washington, 2016-08

José Rodrigues Santos de Sousa Ramos (1948-2007): The diversity of dynamical systems

José Rodrigues Santos de Sousa Ramos, mathematician of great merit, passed away on January 1st, 2007, in Lisbon. He was buried in Sobral da Adiça. His death was a huge loss for the development of mathematics in Portugal. The course of time will increase the dimension of this loss. Therefore, we dedicated this theme issue on Dynamical Systems to recall his memory and underline his work. We never forget you.

Sistemas complexos, séries temporais e previsibilidade

Para qualquer sistema observado, físico ou qualquer outro, geralmente se deseja fazer predições para sua evolução futura. Algumas vezes, muito pouco é conhecido sobre o sistema. Se uma série temporal é a única fonte de informação no sistema, predições de valores futuros da série requer uma modelagem da lei da dinâmica do sistema, talvez não linear. Um interesse em particular são as capacidades de previsão do modelo global para análises de séries temporais. Isso pode ser um procedimento muito complexo e computacionalmente muito alto. Nesta dissertação, nos concetraremos em um determinado caso: Em algumas situações, a única informação que se tem sobre o sistema é uma série sequencial de dados (ou série temporal). Supondo que, por detrás de tais dados, exista uma dinâmica de baixa dimensionalidade, existem técnicas para a reconstrução desta dinâmica.O que se busca é desenvolver novas técnicas para poder melhorar o poder de previsão das técnicas já existentes, através da programação computacional em Maple e C/C++.

Chaotic, memory, and cooling rate effects in spin glasses: Evaluation of the Edwards-Anderson model

We investigate chaotic, memory, and cooling rate effects in the three-dimensional Edwards-Anderson model by doing thermoremanent (TRM) and ac susceptibility numerical experiments and making a detailed comparison with laboratory experiments on spin glasses. In contrast to the experiments, the Edwards-Anderson model does not show any trace of reinitialization processes in temperature change experiments (TRM or ac). A detailed comparison with ac relaxation experiments in the presence of dc magnetic field or coupling distribution perturbations reveals that the absence of chaotic effects in the Edwards-Anderson model is a consequence of the presence of strong cooling rate effects. We discuss possible solutions to this discrepancy, in particular the smallness of the time scales reached in numerical experiments, but we also question the validity of the Edwards-Anderson model to reproduce the experimental results.

Robust fault detection using consistency techniques for uncertainty handling

Often practical performance of analytical redundancy for fault detection and diagnosis is decreased by uncertainties prevailing not only in the system model, but also in the measurements. In this paper, the problem of fault detection is stated as a constraint satisfaction problem over continuous domains with a big number of variables and constraints. This problem can be solved using modal interval analysis and consistency techniques. Consistency techniques are then shown to be particularly efficient to check the consistency of the analytical redundancy relations (ARRs), dealing with uncertain measurements and parameters. Through the work presented in this paper, it can be observed that consistency techniques can be used to increase the performance of a robust fault detection tool, which is based on interval arithmetic. The proposed method is illustrated using a nonlinear dynamic model of a hydraulic system

SQualTrack: A Tool for Robust Fault Detection

One of the techniques used to detect faults in dynamic systems is analytical redundancy. An important difficulty in applying this technique to real systems is dealing with the uncertainties associated with the system itself and with the measurements. In this paper, this uncertainty is taken into account by the use of intervals for the parameters of the model and for the measurements. The method that is proposed in this paper checks the consistency between the system's behavior, obtained from the measurements, and the model's behavior; if they are inconsistent, then there is a fault. The problem of detecting faults is stated as a quantified real constraint satisfaction problem, which can be solved using the modal interval analysis (MIA). MIA is used because it provides powerful tools to extend the calculations over real functions to intervals. To improve the results of the detection of the faults, the simultaneous use of several sliding time windows is proposed. The result of implementing this method is semiqualitative tracking (SQualTrack), a fault-detection tool that is robust in the sense that it does not generate false alarms, i.e., if there are false alarms, they indicate either that the interval model does not represent the system adequately or that the interval measurements do not represent the true values of the variables adequately. SQualTrack is currently being used to detect faults in real processes. Some of these applications using real data have been developed within the European project advanced decision support system for chemical/petrochemical manufacturing processes and are also described in this paper

An Interval Intelligent-based Approach for Fault Detection and Modelling

Not considered in the analytical model of the plant, uncertainties always dramatically decrease the performance of the fault detection task in the practice. To cope better with this prevalent problem, in this paper we develop a methodology using Modal Interval Analysis which takes into account those uncertainties in the plant model. A fault detection method is developed based on this model which is quite robust to uncertainty and results in no false alarm. As soon as a fault is detected, an ANFIS model is trained in online to capture the major behavior of the occurred fault which can be used for fault accommodation. The simulation results understandably demonstrate the capability of the proposed method for accomplishing both tasks appropriately

Necessary and sufficient conditions for robust stability using modal intervals

In this paper, robustness of parametric systems is analyzed using a new approach to interval mathematics called Modal Interval Analysis. Modal Intervals are an interval extension that, instead of classic intervals, recovers some of the properties required by a numerical system. Modal Interval Analysis not only simplifies the computation of interval functions but allows semantic interpretation of their results. Necessary, sufficient and, in some cases, necessary and sufficient conditions for robust performance are presented

Suspensões de Poisson, ergodicidade e o teorema central do limite

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Sistemas dinâmicos finitos: Paciência Búlgara (Shift em partições e composições cíclicas)

Pós-graduação em Matemática - IBILCE

Controle de dissociação molecular com ferramentas de dinâmica não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Expoentes de escala para mapeamentos discretos bidimensionais

Pós-graduação em Física - IGCE

Leis de escala para o mapa padrão dissipativo

Pós-graduação em Física - IGCE

Propriedades estatísticas de bilhares abertos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O estudo de caos na propagação do raio de som em um guia de onda no oceano

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)