SOUZA JUNIOR, A. H. Regional models and minimal learning machines for nonlinear dynamical system identification. 2014. 116 f. Tese (Doutorado em Engenharia de Teleinformática) – Centro de Tecnologia, Universidade Federal do Ceará, Fortaleza, 2014. / Submitted by Marlene Sousa (mmarlene@ufc.br) on 2015-05-26T13:38:05Z No. of bitstreams: 1 2014_dis_ahsouzajunior.pdf: 5675945 bytes, checksum: da4cd07b3287237a51c36e519d0cae14 (MD5) / Approved for entry into archive by Marlene Sousa(mmarlene@ufc.br) on 2015-05-27T19:40:24Z (GMT) No. of bitstreams: 1 2014_dis_ahsouzajunior.pdf: 5675945 bytes, checksum: da4cd07b3287237a51c36e519d0cae14 (MD5) / Made available in DSpace on 2015-05-27T19:40:24Z (GMT). No. of bitstreams: 1 2014_dis_ahsouzajunior.pdf: 5675945 bytes, checksum: da4cd07b3287237a51c36e519d0cae14 (MD5) Previous issue date: 2014-10-31 / This thesis addresses the problem of identifying nonlinear dynamic systems from a machine learning perspective. In this context, very little is assumed to be known about the system under investigation, and the only source of information comes from input/output measurements on the system. It corresponds to the black-box modeling approach. Numerous strategies and models have been proposed over the last decades in the machine learning field and applied to modeling tasks in a straightforward way. Despite of this variety, the methods can be roughly categorized into global and local modeling approaches. Global modeling consists in fitting a single regression model to the available data, using the whole set of input and output observations. On the other side of the spectrum stands the local modeling approach, in which the input space is segmented into several small partitions and a specialized regression model is fit to each partition. The first contribution of the thesis is a novel supervised global learning model, the Minimal Learning Machine (MLM). Learning in MLM consists in building a linear mapping between input and output distance matrices and then estimating the nonlinear response from the geometrical configuration of the output points. Given its general formulation, the Minimal Learning Machine is inherently capable of operating on nonlinear regression problems as well as on multidimensional response spaces. Naturally, its characteristics make the MLM able to tackle the system modeling problem. The second significant contribution of the thesis represents a different modeling paradigm, called Regional Modeling (RM), and it is motivated by the parsimonious principle. Regional models stand between the global and local modeling approaches. The proposal consists of a two-level clustering approach in which we first partition the input space using the Self-Organizing Map (SOM), and then perform clustering over the prototypes of the trained SOM. After that, regression models are built over the clusters of SOM prototypes, or regions in the input space. Even though the proposals of the thesis can be thought as quite general regression or supervised learning models, the performance assessment is carried out in the context of system identification. Comprehensive performance evaluation of the proposed models on synthetic and real-world datasets is carried out and the results compared to those achieved by standard global and local models. The experiments illustrate that the proposed methods achieve accuracies that are comparable to, and even better than, more traditional machine learning methods thus offering a valid alternative to such approaches

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-06-21T20:19:46Z No. of bitstreams: 2 Dissertação - Lázaro Antônio da Fonseca Júnior - 2016.pdf: 4302435 bytes, checksum: d5e83d077c918367e41f439d3bab359e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Cláudia Bueno (claudiamoura18@gmail.com) on 2017-07-07T19:54:39Z (GMT) No. of bitstreams: 2 Dissertação - Lázaro Antônio da Fonseca Júnior - 2016.pdf: 4302435 bytes, checksum: d5e83d077c918367e41f439d3bab359e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-07-07T19:54:39Z (GMT). No. of bitstreams: 2 Dissertação - Lázaro Antônio da Fonseca Júnior - 2016.pdf: 4302435 bytes, checksum: d5e83d077c918367e41f439d3bab359e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Currently, the structures are increasingly diverse and complex. In many cases, these structures are model by numerical approximations methods because, due to its complexity, the analytical model does not exist or is not feasible. The finite element method is a numerical approximation methods most used. Thus, the model generated by the finite element method is in most cases considerably too large, and the time taken to perform computer simulations is high. In this context, models reduction methods, it has been studied to meet the need of accurate results while maintaining the dynamic properties of the structure with less processing time. A comparative study of three reduction methods will be presented, the Improved Reduced System (IRS) and the Iterative Improved Reduced System method (IIRS). The third reduction method, it is an enrichment of the IRS method proposed by the author, which provided great improvement in time savings during simulations. This method was called Improved Reduced System Enriched (IRSE). Such reduction methods were applied in non-linear systems with non-localized linear and geometric nonlinearity due to large displacements. Keywords: Finite element method, nonlinear modeling, not linearity located and geometric, reduced models. / Atualmente, as estruturas estão cada vez mais diversificadas e complexas. Em muitos casos, essas estruturas são modeladas por métodos de aproximações numéricas, pois, devido à sua complexidade, o modelo analítico não existe ou não é viável. O método dos elementos finitos é um dos métodos de aproximação numérica mais utilizado. Assim, o modelo gerado pelo método dos elementos finitos é na maioria dos casos consideravelmente muito grande, e o tempo gasto para realizar simulações computacionais é alto. Neste contexto, os métodos de redução de modelos, tem sido estudados a fim de satisfazer a necessidade entre obter resultados precisos, mantendo as propriedades dinâmicas da estrutura, com menor tempo de processamento. Um estudo comparativo entre três métodos de redução será apresentado, a saber Improved Reduced System (IRS) e o método Iterative Improved Reduced System (IIRS). O terceiro método de redução, trata-se de um enriquecimento do método IRS, proposto pelo autor, que proporcionou grande melhora na economia de tempo durante as simulações. Esse método foi chamado Improved Reduced System Enriched (IRSE). Tais métodos de redução, foram aplicados em sistemas não lineares, com não linearidade localizada e não linearidade geométrica, devido a grandes deslocamentos.